This document presents a stabilized Petrov-Galerkin formulation for linear tetrahedral elements in compressible, nearly incompressible, and truly incompressible fast dynamics. It expresses the governing equations of solid dynamics as a first-order conservation law system to take advantage of computational fluid dynamics discretization methods. This allows the use of linear tetrahedra without volumetric locking. The document outlines the formulation, which includes a Petrov-Galerkin spatial discretization, perturbed test function space, temporal discretization, and fractional step method. It also discusses previous work on computational fluid dynamics methods for solid dynamics.
The document presents a total Lagrangian hydrocode formulation for linear tetrahedral elements in compressible and nearly incompressible fast solid dynamics. It introduces a Petrov-Galerkin formulation that adapts computational fluid dynamics techniques for robust shock capturing to solid mechanics. Balance principles and a convex entropy extension are used to derive first-order conservation laws. Numerical tests on problems like a swinging cube demonstrate the formulation's ability to accurately model transient solid dynamics problems.
In this paper Enhanced whale Optimization Algorithm (EWO) proposed to solve the optimal reactive power problem. Whale optimization algorithm is modeled by Bubble-net hunting tactic. In the projected optimization algorithm an inertia weight ω ∈ [1, 0] has been introduced to perk up the search ability. Whales are commonly moving 10-16 meters down then through the bubbles which are created artificially then they encircle the prey and move upward towards the surface of sea. Proposed Enhanced whale optimization algorithm (EWO) is tested in standard IEEE 57 bus systems and power loss reduced considerably.
Hybrid Optimization Approaches to Economic Load Dispatch Problems – A Compara...IRJET Journal
This document discusses various hybrid optimization techniques that have been proposed to solve economic load dispatch (ELD) problems. ELD problems aim to minimize the total fuel cost of generating units by considering constraints. The summary is:
1. Several hybrid optimization approaches combining techniques like particle swarm optimization, genetic algorithms, fuzzy logic, and artificial bee colony algorithms have been developed to solve ELD problems.
2. These hybrid methods are analyzed and shown to outperform traditional optimization techniques in terms of solution quality and computational time.
3. Case studies on standard test systems demonstrate that hybrid particle swarm optimization-direct search, chaotic particle swarm optimization-implicit filtering, and artificial bee colony-particle swarm optimization methods provide high quality solutions for the
Advances in fatigue and fracture mechanics by grzegorz (greg) glinkaJulio Banks
Professor Grzegorz (Greg) Glinka has made substantial contributions to the field of stress concentration evaluation using linear FEA results using the ESED (Equivalent Striain Energy Density). ESED aka Glinka methods allows the determination of strain-stress state at a point of local concentration by equating the strain energy from the linear FEA area in the material strain-stress curve to that of the actual strain-stress of the material using a models such as Ramberg-Osgood. The ESED method is more accurate than the Neuber requiring the equating of SED (Strain Energy Densities) of linear FEA results that Stress is proportional to strain even when the FEA predicts a stress greater than the ultimate strength of the material. One easy method of remember when to use ESED versus Neuber is that ESED, more accurate, should be use on the stress analysis of rocket structures and Neuber delegated to aerospace engines and components.
Simultaneous Data Path and Clock Path Engineering Change Order for Efficient ...IOSRJVSP
With ever increasing IC complexity and aggressive technology scaling towards cutting edge technologies, the SOC timing closure is becoming a tedious, time consuming and challenging task. Also in advanced technology nodes one has to consider the effect of PVT variation, temperature inversion, noise effect on delay, which is adding more scenarios for STA to cover. In this work, we have proposed an algorithm for simultaneous usage of data path ECO and clock path ECO for efficient timing closure in SOC. The algorithm here tries to fix multiple failing end points through simple clock path optimization, instead of performing data path optimization across multiple paths, thus reducing area and power overhead. The proposed algorithm is tested on multiple industrial designs and found to achieve 30.98% improvement interms of Worst Negative Slack, 63.63% interms of Total Negative Slack, 58.19% interms of Failing End Points. Also the algorithm is physically aware meaning that the placement blockages, congestions are considered while inserting buffers. The algorithm works under Distributed Multi Scenarios Analysis (DMSA) environment and considers the effect of ECO across multiple corners and modes
An Improved Optimization Techniques for Parallel Prefix Adder using FPGAIJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
This document presents a multi-objective optimization method for economic emission load dispatch (EELD) that considers economy, emissions, and transmission line security as objectives. The problem is formulated to minimize total fuel costs and emissions while maximizing line security for a power system. The multi-objective problem is converted to a single objective using goal attainment and then solved using simulated annealing. Results are presented for a 30-bus and 57-bus IEEE test case system to demonstrate the proposed method.
This document contains 12 solutions to physics problems related to dynamics and kinematics. The solutions calculate things like work, acceleration, forces, velocities, distances, and times using concepts like Newton's laws of motion, kinematics equations, coefficients of friction, and incline plane equations. Key details provided in the solutions include calculations, equations used, given values, and final results.
The document presents a total Lagrangian hydrocode formulation for linear tetrahedral elements in compressible and nearly incompressible fast solid dynamics. It introduces a Petrov-Galerkin formulation that adapts computational fluid dynamics techniques for robust shock capturing to solid mechanics. Balance principles and a convex entropy extension are used to derive first-order conservation laws. Numerical tests on problems like a swinging cube demonstrate the formulation's ability to accurately model transient solid dynamics problems.
In this paper Enhanced whale Optimization Algorithm (EWO) proposed to solve the optimal reactive power problem. Whale optimization algorithm is modeled by Bubble-net hunting tactic. In the projected optimization algorithm an inertia weight ω ∈ [1, 0] has been introduced to perk up the search ability. Whales are commonly moving 10-16 meters down then through the bubbles which are created artificially then they encircle the prey and move upward towards the surface of sea. Proposed Enhanced whale optimization algorithm (EWO) is tested in standard IEEE 57 bus systems and power loss reduced considerably.
Hybrid Optimization Approaches to Economic Load Dispatch Problems – A Compara...IRJET Journal
This document discusses various hybrid optimization techniques that have been proposed to solve economic load dispatch (ELD) problems. ELD problems aim to minimize the total fuel cost of generating units by considering constraints. The summary is:
1. Several hybrid optimization approaches combining techniques like particle swarm optimization, genetic algorithms, fuzzy logic, and artificial bee colony algorithms have been developed to solve ELD problems.
2. These hybrid methods are analyzed and shown to outperform traditional optimization techniques in terms of solution quality and computational time.
3. Case studies on standard test systems demonstrate that hybrid particle swarm optimization-direct search, chaotic particle swarm optimization-implicit filtering, and artificial bee colony-particle swarm optimization methods provide high quality solutions for the
Advances in fatigue and fracture mechanics by grzegorz (greg) glinkaJulio Banks
Professor Grzegorz (Greg) Glinka has made substantial contributions to the field of stress concentration evaluation using linear FEA results using the ESED (Equivalent Striain Energy Density). ESED aka Glinka methods allows the determination of strain-stress state at a point of local concentration by equating the strain energy from the linear FEA area in the material strain-stress curve to that of the actual strain-stress of the material using a models such as Ramberg-Osgood. The ESED method is more accurate than the Neuber requiring the equating of SED (Strain Energy Densities) of linear FEA results that Stress is proportional to strain even when the FEA predicts a stress greater than the ultimate strength of the material. One easy method of remember when to use ESED versus Neuber is that ESED, more accurate, should be use on the stress analysis of rocket structures and Neuber delegated to aerospace engines and components.
Simultaneous Data Path and Clock Path Engineering Change Order for Efficient ...IOSRJVSP
With ever increasing IC complexity and aggressive technology scaling towards cutting edge technologies, the SOC timing closure is becoming a tedious, time consuming and challenging task. Also in advanced technology nodes one has to consider the effect of PVT variation, temperature inversion, noise effect on delay, which is adding more scenarios for STA to cover. In this work, we have proposed an algorithm for simultaneous usage of data path ECO and clock path ECO for efficient timing closure in SOC. The algorithm here tries to fix multiple failing end points through simple clock path optimization, instead of performing data path optimization across multiple paths, thus reducing area and power overhead. The proposed algorithm is tested on multiple industrial designs and found to achieve 30.98% improvement interms of Worst Negative Slack, 63.63% interms of Total Negative Slack, 58.19% interms of Failing End Points. Also the algorithm is physically aware meaning that the placement blockages, congestions are considered while inserting buffers. The algorithm works under Distributed Multi Scenarios Analysis (DMSA) environment and considers the effect of ECO across multiple corners and modes
An Improved Optimization Techniques for Parallel Prefix Adder using FPGAIJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
This document presents a multi-objective optimization method for economic emission load dispatch (EELD) that considers economy, emissions, and transmission line security as objectives. The problem is formulated to minimize total fuel costs and emissions while maximizing line security for a power system. The multi-objective problem is converted to a single objective using goal attainment and then solved using simulated annealing. Results are presented for a 30-bus and 57-bus IEEE test case system to demonstrate the proposed method.
This document contains 12 solutions to physics problems related to dynamics and kinematics. The solutions calculate things like work, acceleration, forces, velocities, distances, and times using concepts like Newton's laws of motion, kinematics equations, coefficients of friction, and incline plane equations. Key details provided in the solutions include calculations, equations used, given values, and final results.
Development of a low order stabilised Petrov-Galerkin formulation for a mixed...Chun Hean Lee
This document outlines a presentation on the development of a low-order stabilised Petrov-Galerkin formulation for a mixed conservation law formulation in fast solid dynamics. It discusses the motivation for using such a formulation, which expresses solid dynamics as first-order conservation laws to take advantage of computational fluid dynamics discretization techniques. It then outlines the reversible elastodynamics governing equations, the Petrov-Galerkin spatial and temporal discretization, and a method for conserving angular momentum through a Lagrange multiplier correction procedure. Numerical results and conclusions are also briefly mentioned.
A first order conservation law frameworkChun Hean Lee
This document summarizes a presentation on developing a first-order conservation law framework for solid dynamics. The framework formulates solid dynamics as a system of conservation laws in order to apply computational fluid dynamics (CFD) techniques. It derives the conservation laws for momentum, energy, deformation gradient, and Jacobian. It also establishes the convex entropy extension and associated entropy variables. This allows writing the system in symmetric hyperbolic form. The document outlines several CFD discretization techniques that can be applied to the conservation law formulation, including stabilized Petrov-Galerkin, finite volume, and SUPG methods.
This document lists Dr. Chun Hean Lee's publications, including 25 conference papers and 10 refereed journal articles on computational mechanics and structural dynamics. The publications develop and apply numerical methods like finite volume, Petrov-Galerkin, and Smooth Particle Hydrodynamics to model large deformations, compressible/incompressible materials, and conservation laws in structural dynamics. Several publications received awards for best papers.
Large strain solid dynamics in OpenFOAMJibran Haider
The document describes a numerical methodology for simulating large strain solid dynamics using OpenFOAM. It proposes using a total Lagrangian formulation and first-order conservation laws similar to computational fluid dynamics to model solid mechanics problems involving large deformations. A cell-centered finite volume method is used for spatial discretization along with Riemann solvers and linear reconstruction to capture fluxes. A two-stage Runge-Kutta scheme is employed for time integration. Results are presented demonstrating the method's ability to handle problems involving mesh convergence, enhanced reconstruction, highly nonlinear behavior, plasticity, contact, unstructured meshes, and complex geometries.
Large strain computational solid dynamics: An upwind cell centred Finite Volu...Jibran Haider
Presented our research at the 12th World Congress on Computational Mechanics (WCCM) and 6th Asia Pacific Congress on Computational Mechanics (APCOM) at the COEX Convention Center in Seoul, Korea.
Dr. Chun Hean Lee is currently a Research Fellow at Swansea University. He received his PhD from Swansea University in 2012. His research interests include computational simulation of large strain fast dynamics and numerical methods in computational fluid dynamics. He has authored over 35 publications in peer-reviewed journals and conferences. He is also involved in various research projects and has supervised several PhD and master's students.
A first order hyperbolic framework for large strain computational computation...Jibran Haider
An explicit Total Lagrangian momentum-strains mixed formulation in the form of a system of first order hyperbolic conservation laws, has recently been published to overcome the shortcomings posed by the traditional second order displacement based formulation when using linear tetrahedral elements.
The formulation, where the linear momentum and the deformation gradient are treated as unknown variables, has been implemented within the cell centred finite volume environment in OpenFOAM. The numerical solutions have performed extremely well in bending dominated nearly incompressible scenarios without the appearance of any spurious pressure modes, yielding an equal order of convergence for velocities and stresses.
To have more insight into my research, please visit my website:
http://jibranhaider.weebly.com/
This document outlines a presentation on a robust updated Lagrangian smooth particle hydrodynamics (SPH) algorithm for fast solid dynamics. It discusses limitations of current mesh-based methods for simulating large deformations, and how SPH can overcome these issues. The presentation covers continuum balance principles for isothermal solids using total and updated Lagrangian formulations. It also discusses the numerical method and spatial discretization, and provides examples of numerical results for isothermal elasticity and plasticity simulations. The overall goal is to develop a robust SPH method for modeling fast dynamic events involving large deformations in solids.
A Two Step Taylor Galerkin Formulation For Fast DynamicsHeather Strinden
The document presents a new stabilised two-step Taylor-Galerkin (2TG) finite element method for simulating fast solid dynamics undergoing large deformations. It formulates the governing equations as a system of first-order hyperbolic conservation laws in terms of linear momentum, deformation gradient tensor, and total energy. The 2TG method is improved by adding a curl-free projection of the deformation gradient tensor and a stiffness stabilisation term to address non-physical spurious modes. Numerical examples demonstrate the method handles nearly incompressible materials without volumetric locking using linear elements and eliminates oscillations near shocks.
On the power of virtual experimentation in MT2.0:a VFORM-xSteels outlookvformxsteels
Sam Coppieters, A. Gil Andrade-Campos et al.
MatchID Global User Meeting
On the power of virtual experimentation in MT2.0 : a VFORM outlook
22 February2023 | Southampton, UK
CLIC Accelerator: status, plans and outlook asafrona
This document provides an overview of the status, plans, and outlook for the Compact Linear Collider (CLIC) accelerator project. Key points include:
1) CLIC has made progress optimizing its design for lower initial energies around 380 GeV based on LHC results, with the goal of reducing costs and power requirements for early stages.
2) Recent test facility results like those at CTF3 have demonstrated drive beam generation and two-beam acceleration, advancing critical technologies.
3) The collaboration aims to provide a staged implementation plan up to 3 TeV by 2019 to inform the next European strategy update, accounting for further LHC data and optimizing costs.
4) Advancing X-
Improvement in Quality of Power by PI Controller Hybrid PSO using STATCOMIRJET Journal
The document discusses using a hybrid particle swarm optimization (PSO) technique with a PI controller and STATCOM device to improve power quality and reduce costs. Voltage sags are a key power quality issue that are mitigated. The system is modeled in MATLAB Simulink. Simulation results show that using PSO to optimize the PI controller parameters and STATCOM operation leads to better voltage regulation and an improved inertia weight, demonstrating enhanced power quality and reduced costs.
Security constrained optimal load dispatch using hpso technique for thermal s...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Security constrained optimal load dispatch using hpso technique for thermal s...eSAT Journals
Abstract This paper presents Hybrid Particle Swarm Optimization (HPSO) technique to solve the Optimal Load Dispatch (OLD) problems with line flow constrain, bus voltage limits and generator operating constraints. In the proposed HPSO method both features of EP and PSO are incorporated, so the combined HPSO algorithm may become more effective to find the optimal solutions. In this paper, the proposed Hybrid PSO, PSO and EP techniques have been tested on IEEE14, 30 bus systems. Numerical simulation results show that the Hybrid PSO algorithm outperformed standard PSO algorithm and Evolution Programming method on the same problem and can save considerable cost of Optimal Load Dispatch.
Optimum designing of a transformer considering lay out constraints by penalty...INFOGAIN PUBLICATION
Optimum designing of power electrical equipment and devices play a leading role in attaining optimal performance and price of equipments in electric power industry. Optimum transformer design considering multiple constraints is acquired using optimal determination of geometric parameters of transformer with respect to its magnetic and electric properties. As it is well known, every optimization problem requires an objective function to be minimized. In this paper optimum transformer design problem comprises minimization of transformers mean core mass and its windings by satisfying multiple constraints according to transformers ratings and international standards using a penalty-based method. Hybrid big bang-big crunch algorithm is applied to solve the optimization problem and results are compared to other methods. Proposed method has provided a reliable optimization solution and has guaranteed access to a global optimum. Simulation result indicates that using the proposed algorithm, transformer parameters such as core mass, efficiency and dimensions are remarkably improved. Moreover simulation time using this algorithm is quit less in comparison to other approaches.
IRJET-A Review Paper on using Mineral Admixture Coated Pet Fibres to Make Con...IRJET Journal
This document presents a new approach for developing flexibility matrices using the principle of contra-gradience. The approach uses flexibility coefficients of individual members along with force and deformation transformation and the principle of contra-gradience to develop the total flexibility matrix of a structure. Two examples of a fixed beam and a rigid jointed frame are analyzed using this approach both manually and using MATLAB software. The results obtained from both methods match, showing the new approach is effective for flexibility analysis and MATLAB can be used to simplify calculations.
PRACTICAL IMPLEMENTION OF GAOPF ON INDIAN 220KV TRANSMISSION SYSTEMecij
This paper presents the practical implementation of developed genetic algorithm based optimal power flow algorithms. These algorithms are tested on IEEE30 bus system and the results were presented in the paper [8]. The same algorithms now tested on 220KV Washi zone Indian power transmission system . The GAOPF with fixed penalty and Fuzzy based variable penalty tested on 220KV transmission system consists of 52 bus and 88lines. The fuel costs ,computational time and the system condition were studied and the results are presented in this paper .Also the available load transfer capability of the 220KV system for congestion management is also presented
This document introduces WeightWatcher, an open-source tool for analyzing the eigenvalue spectrum distributions (ESD) of deep neural network weight matrices. WeightWatcher finds that well-trained networks exhibit heavy-tailed ESDs, in line with predictions from random matrix theory and the theory of strongly correlated systems. The tool can predict trends in test accuracy based on the shape of ESDs, without access to training or test data. The document provides an overview of the theoretical foundations and capabilities of WeightWatcher.
This paper presents a novel approach for static transmission expansion planning and
allocation of the associated expansion costs to individual market entities in a restructured power
system. The approach seeks the optimal addition of transmission lines among the possible candidate
transmission lines minimizing the overall system costs and at the same time satisfying the system
operational and security constraints. Novelty of the approach lies in applying a widely known
technique used for overload security analysis to an area such as Transmission expansion planning.
Transmission expansion costs are allocated using distribution factors to the individual entities in a
fair and transparent manner. The results for modified Garver Test system demonstrate that the
approach with the advantage of its simplicity can be applied to transmission expansion planning and
cost allocation in restructured power system
This document summarizes an article from the International Journal of Electrical Engineering and Technology (IJEET) that presents a novel approach for transmission expansion planning and cost allocation in deregulated power systems. The approach seeks to optimally add transmission lines to minimize costs while satisfying operational and security constraints. It applies an overload security analysis technique to transmission expansion planning. Transmission expansion costs are allocated to individual market participants using distribution factors in a fair manner. The approach is demonstrated on the modified Garver test system and is shown to be effective for transmission expansion planning and cost allocation in restructured power systems.
Development of a low order stabilised Petrov-Galerkin formulation for a mixed...Chun Hean Lee
This document outlines a presentation on the development of a low-order stabilised Petrov-Galerkin formulation for a mixed conservation law formulation in fast solid dynamics. It discusses the motivation for using such a formulation, which expresses solid dynamics as first-order conservation laws to take advantage of computational fluid dynamics discretization techniques. It then outlines the reversible elastodynamics governing equations, the Petrov-Galerkin spatial and temporal discretization, and a method for conserving angular momentum through a Lagrange multiplier correction procedure. Numerical results and conclusions are also briefly mentioned.
A first order conservation law frameworkChun Hean Lee
This document summarizes a presentation on developing a first-order conservation law framework for solid dynamics. The framework formulates solid dynamics as a system of conservation laws in order to apply computational fluid dynamics (CFD) techniques. It derives the conservation laws for momentum, energy, deformation gradient, and Jacobian. It also establishes the convex entropy extension and associated entropy variables. This allows writing the system in symmetric hyperbolic form. The document outlines several CFD discretization techniques that can be applied to the conservation law formulation, including stabilized Petrov-Galerkin, finite volume, and SUPG methods.
This document lists Dr. Chun Hean Lee's publications, including 25 conference papers and 10 refereed journal articles on computational mechanics and structural dynamics. The publications develop and apply numerical methods like finite volume, Petrov-Galerkin, and Smooth Particle Hydrodynamics to model large deformations, compressible/incompressible materials, and conservation laws in structural dynamics. Several publications received awards for best papers.
Large strain solid dynamics in OpenFOAMJibran Haider
The document describes a numerical methodology for simulating large strain solid dynamics using OpenFOAM. It proposes using a total Lagrangian formulation and first-order conservation laws similar to computational fluid dynamics to model solid mechanics problems involving large deformations. A cell-centered finite volume method is used for spatial discretization along with Riemann solvers and linear reconstruction to capture fluxes. A two-stage Runge-Kutta scheme is employed for time integration. Results are presented demonstrating the method's ability to handle problems involving mesh convergence, enhanced reconstruction, highly nonlinear behavior, plasticity, contact, unstructured meshes, and complex geometries.
Large strain computational solid dynamics: An upwind cell centred Finite Volu...Jibran Haider
Presented our research at the 12th World Congress on Computational Mechanics (WCCM) and 6th Asia Pacific Congress on Computational Mechanics (APCOM) at the COEX Convention Center in Seoul, Korea.
Dr. Chun Hean Lee is currently a Research Fellow at Swansea University. He received his PhD from Swansea University in 2012. His research interests include computational simulation of large strain fast dynamics and numerical methods in computational fluid dynamics. He has authored over 35 publications in peer-reviewed journals and conferences. He is also involved in various research projects and has supervised several PhD and master's students.
Similar to A stabilised Petrov-Galerkin formulation for linear tetrahedral elements in compressible, nearly incompressible and truly incompressible fast dynamics
A first order hyperbolic framework for large strain computational computation...Jibran Haider
An explicit Total Lagrangian momentum-strains mixed formulation in the form of a system of first order hyperbolic conservation laws, has recently been published to overcome the shortcomings posed by the traditional second order displacement based formulation when using linear tetrahedral elements.
The formulation, where the linear momentum and the deformation gradient are treated as unknown variables, has been implemented within the cell centred finite volume environment in OpenFOAM. The numerical solutions have performed extremely well in bending dominated nearly incompressible scenarios without the appearance of any spurious pressure modes, yielding an equal order of convergence for velocities and stresses.
To have more insight into my research, please visit my website:
http://jibranhaider.weebly.com/
This document outlines a presentation on a robust updated Lagrangian smooth particle hydrodynamics (SPH) algorithm for fast solid dynamics. It discusses limitations of current mesh-based methods for simulating large deformations, and how SPH can overcome these issues. The presentation covers continuum balance principles for isothermal solids using total and updated Lagrangian formulations. It also discusses the numerical method and spatial discretization, and provides examples of numerical results for isothermal elasticity and plasticity simulations. The overall goal is to develop a robust SPH method for modeling fast dynamic events involving large deformations in solids.
A Two Step Taylor Galerkin Formulation For Fast DynamicsHeather Strinden
The document presents a new stabilised two-step Taylor-Galerkin (2TG) finite element method for simulating fast solid dynamics undergoing large deformations. It formulates the governing equations as a system of first-order hyperbolic conservation laws in terms of linear momentum, deformation gradient tensor, and total energy. The 2TG method is improved by adding a curl-free projection of the deformation gradient tensor and a stiffness stabilisation term to address non-physical spurious modes. Numerical examples demonstrate the method handles nearly incompressible materials without volumetric locking using linear elements and eliminates oscillations near shocks.
On the power of virtual experimentation in MT2.0:a VFORM-xSteels outlookvformxsteels
Sam Coppieters, A. Gil Andrade-Campos et al.
MatchID Global User Meeting
On the power of virtual experimentation in MT2.0 : a VFORM outlook
22 February2023 | Southampton, UK
CLIC Accelerator: status, plans and outlook asafrona
This document provides an overview of the status, plans, and outlook for the Compact Linear Collider (CLIC) accelerator project. Key points include:
1) CLIC has made progress optimizing its design for lower initial energies around 380 GeV based on LHC results, with the goal of reducing costs and power requirements for early stages.
2) Recent test facility results like those at CTF3 have demonstrated drive beam generation and two-beam acceleration, advancing critical technologies.
3) The collaboration aims to provide a staged implementation plan up to 3 TeV by 2019 to inform the next European strategy update, accounting for further LHC data and optimizing costs.
4) Advancing X-
Improvement in Quality of Power by PI Controller Hybrid PSO using STATCOMIRJET Journal
The document discusses using a hybrid particle swarm optimization (PSO) technique with a PI controller and STATCOM device to improve power quality and reduce costs. Voltage sags are a key power quality issue that are mitigated. The system is modeled in MATLAB Simulink. Simulation results show that using PSO to optimize the PI controller parameters and STATCOM operation leads to better voltage regulation and an improved inertia weight, demonstrating enhanced power quality and reduced costs.
Security constrained optimal load dispatch using hpso technique for thermal s...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Security constrained optimal load dispatch using hpso technique for thermal s...eSAT Journals
Abstract This paper presents Hybrid Particle Swarm Optimization (HPSO) technique to solve the Optimal Load Dispatch (OLD) problems with line flow constrain, bus voltage limits and generator operating constraints. In the proposed HPSO method both features of EP and PSO are incorporated, so the combined HPSO algorithm may become more effective to find the optimal solutions. In this paper, the proposed Hybrid PSO, PSO and EP techniques have been tested on IEEE14, 30 bus systems. Numerical simulation results show that the Hybrid PSO algorithm outperformed standard PSO algorithm and Evolution Programming method on the same problem and can save considerable cost of Optimal Load Dispatch.
Optimum designing of a transformer considering lay out constraints by penalty...INFOGAIN PUBLICATION
Optimum designing of power electrical equipment and devices play a leading role in attaining optimal performance and price of equipments in electric power industry. Optimum transformer design considering multiple constraints is acquired using optimal determination of geometric parameters of transformer with respect to its magnetic and electric properties. As it is well known, every optimization problem requires an objective function to be minimized. In this paper optimum transformer design problem comprises minimization of transformers mean core mass and its windings by satisfying multiple constraints according to transformers ratings and international standards using a penalty-based method. Hybrid big bang-big crunch algorithm is applied to solve the optimization problem and results are compared to other methods. Proposed method has provided a reliable optimization solution and has guaranteed access to a global optimum. Simulation result indicates that using the proposed algorithm, transformer parameters such as core mass, efficiency and dimensions are remarkably improved. Moreover simulation time using this algorithm is quit less in comparison to other approaches.
IRJET-A Review Paper on using Mineral Admixture Coated Pet Fibres to Make Con...IRJET Journal
This document presents a new approach for developing flexibility matrices using the principle of contra-gradience. The approach uses flexibility coefficients of individual members along with force and deformation transformation and the principle of contra-gradience to develop the total flexibility matrix of a structure. Two examples of a fixed beam and a rigid jointed frame are analyzed using this approach both manually and using MATLAB software. The results obtained from both methods match, showing the new approach is effective for flexibility analysis and MATLAB can be used to simplify calculations.
PRACTICAL IMPLEMENTION OF GAOPF ON INDIAN 220KV TRANSMISSION SYSTEMecij
This paper presents the practical implementation of developed genetic algorithm based optimal power flow algorithms. These algorithms are tested on IEEE30 bus system and the results were presented in the paper [8]. The same algorithms now tested on 220KV Washi zone Indian power transmission system . The GAOPF with fixed penalty and Fuzzy based variable penalty tested on 220KV transmission system consists of 52 bus and 88lines. The fuel costs ,computational time and the system condition were studied and the results are presented in this paper .Also the available load transfer capability of the 220KV system for congestion management is also presented
This document introduces WeightWatcher, an open-source tool for analyzing the eigenvalue spectrum distributions (ESD) of deep neural network weight matrices. WeightWatcher finds that well-trained networks exhibit heavy-tailed ESDs, in line with predictions from random matrix theory and the theory of strongly correlated systems. The tool can predict trends in test accuracy based on the shape of ESDs, without access to training or test data. The document provides an overview of the theoretical foundations and capabilities of WeightWatcher.
This paper presents a novel approach for static transmission expansion planning and
allocation of the associated expansion costs to individual market entities in a restructured power
system. The approach seeks the optimal addition of transmission lines among the possible candidate
transmission lines minimizing the overall system costs and at the same time satisfying the system
operational and security constraints. Novelty of the approach lies in applying a widely known
technique used for overload security analysis to an area such as Transmission expansion planning.
Transmission expansion costs are allocated using distribution factors to the individual entities in a
fair and transparent manner. The results for modified Garver Test system demonstrate that the
approach with the advantage of its simplicity can be applied to transmission expansion planning and
cost allocation in restructured power system
This document summarizes an article from the International Journal of Electrical Engineering and Technology (IJEET) that presents a novel approach for transmission expansion planning and cost allocation in deregulated power systems. The approach seeks to optimally add transmission lines to minimize costs while satisfying operational and security constraints. It applies an overload security analysis technique to transmission expansion planning. Transmission expansion costs are allocated to individual market participants using distribution factors in a fair manner. The approach is demonstrated on the modified Garver test system and is shown to be effective for transmission expansion planning and cost allocation in restructured power systems.
Addressing climate change uncertainty with a monte carloversion of TIMESIEA-ETSAP
The document summarizes research incorporating Monte Carlo analysis into the TIMES integrated assessment model to better represent uncertainty. Researchers applied 1,000 simulations each of baseline, 2°C, and 1.5°C scenarios while varying 18 uncertain input parameters. This provided probabilistic outputs rather than single deterministic results. Key findings included statistical distributions of temperature change, primary energy supply, and emissions across the scenarios accounting for uncertain inputs like climate sensitivity and discount rates. The approach allows evaluation of policy resilience under uncertainty.
This document summarizes a paper presented at the 23rd UK Conference of the Association for Computational Mechanics in Engineering. The paper presents a stabilized finite element method for solving compressible flow problems on moving domains. It extends the SUPG formulation to higher-order approximations in space and time using a second-order generalized alpha method. This formulation satisfies the geometric conservation law and has advantages including decoupling flow and geometry, implicit time integration, reduced computational cost with higher-order approximations, and preservation of flow effects over long times. Test problems demonstrate the method's accuracy and robustness for Burgers' equation and the Euler equations on static and moving domains.
Output feedback trajectory stabilization of the uncertainty DC servomechanism...ISA Interchange
This work proposes a solution for the output feedback trajectory-tracking problem in the case of an uncertain DC servomechanism system. The system consists of a pendulum actuated by a DC motor and subject to a time-varying bounded disturbance. The control law consists of a Proportional Derivative controller and an uncertain estimator that allows compensating the effects of the unknown bounded perturbation. Because the motor velocity state is not available from measurements, a second-order sliding-mode observer permits the estimation of this variable in finite time. This last feature allows applying the Separation Principle. The convergence analysis is carried out by means of the Lyapunov method. Results obtained from numerical simulations and experiments in a laboratory prototype show the performance of the closed loop system.
RT15 Berkeley | Optimized Power Flow Control in Microgrids - Sandia LaboratoryOPAL-RT TECHNOLOGIES
The document summarizes research on designing nonlinear controllers for microgrid systems with stochastic sources and loads. Key points include:
1) A secure scalable microgrid testbed was developed to experimentally test Hamiltonian surface shaping power flow controllers (HSSPFC).
2) Models of single and multiple DC microgrids were formulated to develop optimal operating points using a dynamic optimizer.
3) An HSSPFC nonlinear distributed controller was designed and experimentally validated on a single DC microgrid testbed with variable sources and loads, demonstrating stable voltage regulation.
Similar to A stabilised Petrov-Galerkin formulation for linear tetrahedral elements in compressible, nearly incompressible and truly incompressible fast dynamics (20)
RT15 Berkeley | Optimized Power Flow Control in Microgrids - Sandia Laboratory
A stabilised Petrov-Galerkin formulation for linear tetrahedral elements in compressible, nearly incompressible and truly incompressible fast dynamics
1. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
A Stabilised Petrov-Galerkin Formulation For Linear
Tetrahedral Elements In Compressible, Nearly Incompressible
and Truly Incompressible Fast Dynamics
Chun Hean Lee1, Antonio J. Gil2, Javier Bonet3, Miquel Aguirre4
Zienkiewicz Centre for Computational Engineering (ZC2E)
College of Engineering, Swansea University, UK
Advances in Finite Element Methods for Tetrahedral Mesh Computations I (MS209A)
11th World Congress on Computational Mechanics (WCCM XI)
1 https://www.researchgate.net/profile/Chun_Hean_Lee2/
2 http://www.swansea.ac.uk/staff/academic/engineering/gilantonio/
3 http://www.swansea.ac.uk/staff/academic/engineering/bonetjavier/
4 https://www.researchgate.net/profile/Miquel_Aguirre
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
2. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
Outline
1 Motivation
2 Reversible elastodynamics
Balance principles
Conservation laws
3 Petrov-Galerkin formulation
Petrov-Galerkin spatial discretisation
Perturbed test function space
Temporal discretisation
Incompressible and nearly incompressible formulation
Fractional-step formulation
4 Numerical results
5 Conclusions and further research
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
3. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
Outline
1 Motivation
2 Reversible elastodynamics
Balance principles
Conservation laws
3 Petrov-Galerkin formulation
Petrov-Galerkin spatial discretisation
Perturbed test function space
Temporal discretisation
Incompressible and nearly incompressible formulation
Fractional-step formulation
4 Numerical results
5 Conclusions and further research
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
4. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
Motivation
• Standard solid dynamic formulations:
× Linear tetrahedral elements behave poorly in nearly incompressible
and bending dominated scenarios
× Uniform and selective reduced integrated linear hexahedral elements
suffer from respected hourglassing and pressure instabilities
× Convergence of stresses and strains is only first order
× Shock capturing technologies are poorly developed
Time integrators are robust and preserve angular momentum
Extensive availability of commercial packages (ANSYS, Altair
HyperWorks, LS-DYNA, ABAQUS, . . .)
• Mixed conservation law formulation:
Express as first order conservation laws enabling the use of
standard CFD discretisation process
Permits the use of linear tetrahedra, as well as enhanced linear
hexahedra, for solid dynamics without locking difficulties
Achieves optimal convergence with equal orders in velocities and
stresses
Take advantage of the conservative formulation to introduce
state-of-the-art discontinuity-capturing operator
× Enhance existing time integrators to preserve angular momentum
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
5. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
Motivation
• Standard solid dynamic formulations:
× Linear tetrahedral elements behave poorly in nearly incompressible
and bending dominated scenarios
× Uniform and selective reduced integrated linear hexahedral elements
suffer from respected hourglassing and pressure instabilities
× Convergence of stresses and strains is only first order
× Shock capturing technologies are poorly developed
Time integrators are robust and preserve angular momentum
Extensive availability of commercial packages (ANSYS, Altair
HyperWorks, LS-DYNA, ABAQUS, . . .)
• Mixed conservation law formulation:
Express as first order conservation laws enabling the use of
standard CFD discretisation process
Permits the use of linear tetrahedra, as well as enhanced linear
hexahedra, for solid dynamics without locking difficulties
Achieves optimal convergence with equal orders in velocities and
stresses
Take advantage of the conservative formulation to introduce
state-of-the-art discontinuity-capturing operator
× Enhance existing time integrators to preserve angular momentum
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
6. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
Outline
1 Motivation
2 Reversible elastodynamics
Balance principles
Conservation laws
3 Petrov-Galerkin formulation
Petrov-Galerkin spatial discretisation
Perturbed test function space
Temporal discretisation
Incompressible and nearly incompressible formulation
Fractional-step formulation
4 Numerical results
5 Conclusions and further research
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
7. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
Balance principles
First order conservation formulation
• Consider the standard dynamic equilibrium equation:
∂ρ0v
∂t
− DIVP(F, J) = ρ0b
• To alleviate bending difficulty, the conservation law for the deformation
gradient can be incorporated:
∂F
∂t
− DIV (v ⊗ I) = 0
• To avoid volumetric locking, the conservation law for the Jacobian can be
added:
∂J
∂t
− DIV HT
F v = 0; HF = (detF)F−T
Constitutive model is needed to complete the coupled system
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
8. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
Balance principles
First order conservation formulation
• Consider the standard dynamic equilibrium equation:
∂ρ0v
∂t
− DIVP(F, J) = ρ0b
• To alleviate bending difficulty, the conservation law for the deformation
gradient can be incorporated:
∂F
∂t
− DIV (v ⊗ I) = 0
• To avoid volumetric locking, the conservation law for the Jacobian can be
added:
∂J
∂t
− DIV HT
F v = 0; HF = (detF)F−T
Constitutive model is needed to complete the coupled system
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
9. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
Governing equation
Conservation laws
• The mixed equations can be written as a system of first order conservation laws:
∂
∂t
ρ0v
F
J
+ DIV
−P(F, J)
−v ⊗ I
−HT
F v
=
ρ0b
0
0
• More generally, if the energy equation is added:
∂
∂t
ρ0v
F
J
ET
+ DIV
−P(F, J)
−v ⊗ I
−HT
F v
Q − PT
v
=
ρ0b
0
0
s
• Or in standard form:
∂U
∂t
+DIVF(U) = S; U =
ρ0v
F
J
ET
; F =
−P(F, J)
−v ⊗ I
−HT
F v
Q − PT
v
; S =
ρ0b
0
0
s
Our aim is to develop a library of second order numerical schemes for a mixed
conservation law formulation of fast solid dynamics using existing CFD technologies
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
10. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
Governing equation
Conservation laws
• The mixed equations can be written as a system of first order conservation laws:
∂
∂t
ρ0v
F
J
+ DIV
−P(F, J)
−v ⊗ I
−HT
F v
=
ρ0b
0
0
• More generally, if the energy equation is added:
∂
∂t
ρ0v
F
J
ET
+ DIV
−P(F, J)
−v ⊗ I
−HT
F v
Q − PT
v
=
ρ0b
0
0
s
• Or in standard form:
∂U
∂t
+DIVF(U) = S; U =
ρ0v
F
J
ET
; F =
−P(F, J)
−v ⊗ I
−HT
F v
Q − PT
v
; S =
ρ0b
0
0
s
Our aim is to develop a library of second order numerical schemes for a mixed
conservation law formulation of fast solid dynamics using existing CFD technologies
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
11. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
Governing equation
CFD formulations for fast solid dynamics
• Following are the stabilised numerical methodologies recently developed for fast
solid dynamics using mixed formulation:
Swansea University Research Group (Led by Prof. Javier Bonet and Dr. Antonio J.
Gil)
· Two-Step Taylor-Galerkin (2TG) Formulation [Karim, Lee, Gil and Bonet, 2011]
· Total Variation Diminishing (TVD) Upwind Cell Centred Finite Volume Method
(CCFVM) [Lee, Gil and Bonet, 2012]
· Jameson-Schmidt-Turkel (JST) Vertex Centred Finite Volume Method (VCFVM)
[Aguirre, Gil, Bonet and Carreño, 2013]
· Stabilised Petrov-Galerkin (PG) Finite Element Method [Lee, Gil and Bonet, 2013]
· Fractional-Step Petrov-Galerkin (PG) Framework [Gil, Lee, Bonet and Aguirre, 2014]
M.I.T Research Group (Led by Prof. Jaime Peraire)
· Hybridizable Discontinuous Galerkin (HDG) Method [Nguyen and Peraire, 2012]
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
12. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
Governing equation
CFD formulations for fast solid dynamics
• Following are the stabilised numerical methodologies recently developed for fast
solid dynamics using mixed formulation:
Swansea University Research Group (Led by Prof. Javier Bonet and Dr. Antonio J.
Gil)
· Two-Step Taylor-Galerkin (2TG) Formulation [Karim, Lee, Gil and Bonet, 2011]
· Total Variation Diminishing (TVD) Upwind Cell Centred Finite Volume Method
(CCFVM) [Lee, Gil and Bonet, 2012]
· Jameson-Schmidt-Turkel (JST) Vertex Centred Finite Volume Method (VCFVM)
[Aguirre, Gil, Bonet and Carreño, 2013]
· Stabilised Petrov-Galerkin (PG) Finite Element Method [Lee, Gil and Bonet, 2013]
· Fractional-Step Petrov-Galerkin (PG) Framework [Gil, Lee, Bonet and Aguirre, 2014]
M.I.T Research Group (Led by Prof. Jaime Peraire)
· Hybridizable Discontinuous Galerkin (HDG) Method [Nguyen and Peraire, 2012]
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
13. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
Outline
1 Motivation
2 Reversible elastodynamics
Balance principles
Conservation laws
3 Petrov-Galerkin formulation
Petrov-Galerkin spatial discretisation
Perturbed test function space
Temporal discretisation
Incompressible and nearly incompressible formulation
Fractional-step formulation
4 Numerical results
5 Conclusions and further research
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
14. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
Petrov-Galerkin spatial discretisation
Stabilised Petrov-Galerkin formulation
• Variational statement of Bubnov-Galerkin formulation (unstable):
V0
δV · R dV = 0; R =
∂U
∂t
+ DIVF − S; δV =
δv
δP
δq
• Integration by parts gives:
V0
δV ·
∂U
∂t
dV =
V0
F : 0δV dV −
∂V0
δV · FN dA +
V0
δV · S dV
• Define stabilised Petrov-Galerkin (PG) formulation satisfying Second Law of
Thermodynamics:
V0
δVst
· R dV = 0; δVst
=
δvst
δPst
δqst
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
15. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
Perturbed test function space
Perturbation
• Stabilised test function space is generally defined by
δVst
= δV + τT ∂FI
∂U
T
∂δV
∂XI
Perturbation
• Define flux Jacobian matrix:
∂FI
∂U
=
03×3 −CI −κ [HF ]I
− 1
ρ0
II 09×9 09×1
− 1
ρ0
HI −
∂(v·[HF ]I )
∂F
0
• Assuming τ (intrinsic time scale) a diagonal matrix for simplicity:
δVst
:=
δvst
δPst
δqst
=
δv −
τpF
ρ0
DIVδP −
τpJ
ρ0
HF 0δq
δP − τFpC : 0δv − τFJ (v ⊗ 0δq) :
∂HF
∂F
δq − τJpκHF : 0δv
; δP = C : δF
• Bubnov-Galerkin is recovered by setting stabilisation τ = 0
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
16. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
Perturbed test function space
Petrov-Galerkin stabilisation
• Weak statement of stabilised Petrov-Galerkin (PG) formulation:
0 =
V0
δV +
∂F
∂U
τ
T
0δV · R dV
=
V0
δV · R dV
Bubnov-Galerkin
+
V0
∂F
∂U
τR : 0δV dV
Petrov-Galerkin stabilisation
• Integration by parts gives:
V0
δV·
∂U
∂t
dV =
V0
F −
∂F
∂U
τR
Fst
: 0δV dV−
∂V0
δV·FN dA+
V0
δV·S dV
• The stabilised flux Fst
can be more generally defined as (equivalent to
Variational Multi-Scale (VMS) stabilisation):
Fst
= F(Ust
); Ust
= U + U ; U = −τR
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
17. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
Perturbed test function space
Finite element discretisation
• Using standard linear finite element interpolation for velocity, deformation gradient
and Jacobian renders:
v =
a
va
Na
; F =
a
Fa
Na
; J =
a
Ja
Na
b
Mab ˙pb
=
∂V0
Na
tB dA +
V0
Na
ρ0b dV −
V0
P(Fst
, Jst
) 0Na
dV
b
Mab ˙F
b
=
∂V0
Na
(vB ⊗ N) dA −
V0
vst
F ⊗ 0Na
dV
b
Mab ˙Jb =
∂V0
Na
(vB · HF N) dA −
V0
vst
J · HF 0Na
dV
• By construction the stabilised deformation gradient, Jacobian and velocities are:
Fst
= F + τFp 0v − ˙F ; Jst
= J + τJp DIV HT
F v − ˙J
vst
F = v +
τpF
ρ0
(DIVP + ρ0b − ˙p) ; vst
J = v +
τpJ
ρ0
(DIVP + ρ0b − ˙p)
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
18. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
Perturbed test function space
Finite element discretisation
• Using standard linear finite element interpolation for velocity, deformation gradient
and Jacobian renders:
v =
a
va
Na
; F =
a
Fa
Na
; J =
a
Ja
Na
b
Mab ˙pb
=
∂V0
Na
tB dA +
V0
Na
ρ0b dV −
V0
P(Fst
, Jst
) 0Na
dV
• By construction the stabilised deformation gradient, Jacobian and velocities are:
Fst
= F + τFp 0v − ˙F + ξF ( 0x − F)
Jst
= J + τJp DIV HT
F v − ˙J + ξJ (det 0x − J)
• To reduce implicitness of the resulting formulation additional time-integrated
residual-based artificial diffusions can be added
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
19. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
Explicit time marching scheme
Time Integration
• Integration in time is achieved by means of an explicit two-stage Total Variation
Diminishing Runge-Kutta (TVD-RK) time integrator:
U
(1)
n+1 = Un + ∆t ˙Un
U
(2)
n+2 = U
(1)
n+1 + ∆t ˙U
(1)
n+1
Un+1 =
1
2
Un + U
(2)
n+2
together with a stability constraint
∆t = αCFL
hmin
Un
max
; Un
max = max
a
Un
p,a
• Introduce Lagrange multiplier correction to preserve the angular momentum [Lee,
Gil, Bonet, 2013]
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
20. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
Fractional-step formulation
Incompressible and nearly incompressible formulation
• Time steps are very small given the presence of a very large value of Poisson’s
ratio in near incompressible solids
• Fully incompressible limit cannot be modelled
• Using standard fractional-step formulation renders:
ρ0 vint − vn
∆t
− DIVPn
dev − DIV pn
HFn − ρ0bn
= 0
Fn+1
− Fn
∆t
− 0vn
= 0
ρ0 vn+1 − vint
∆t
− DIV pn+1
− pn
HFn = 0
• Incompressiblity constraint gives
pn+1 − pn
κ∆t
− HFn : 0vint
−
∆t
ρ0
HFn : 0 DIV pn+1
− pn
HFn = 0
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
21. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
Fractional-step formulation
Finite element discretisation: fractional-step formulation
• Using Petrov Galerkin stabilisation the predictor step becomes:
b
Mab
Fn+1
b − Fn
b
∆t
=
∂V0
Na(vB ⊗ N) dA −
V0
vn
⊗ 0Na dV
b
Mab
ρ0 vint
b − vn
b
∆t
=
∂V0
NatBdA +
V0
Naρ0bn
dV −
V0
Pn
Fst
, pst
0NadV
• Project the velocity onto a space of divergence-free:
b
1
κ
Mab +
∆t2
ρ0
Kab
pn+1
b − pn
b
∆t
dV =
∂V0
HT
Fn vB ·NNa dV−
V0
HT
Fn vst
· 0NadV
• Update velocity:
b
Mab
ρ0 vn+1
b − vint
b
∆t
=
V0
Na DIV pn+1
− pn
HT
Fn dV
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
22. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
Outline
1 Motivation
2 Reversible elastodynamics
Balance principles
Conservation laws
3 Petrov-Galerkin formulation
Petrov-Galerkin spatial discretisation
Perturbed test function space
Temporal discretisation
Incompressible and nearly incompressible formulation
Fractional-step formulation
4 Numerical results
5 Conclusions and further research
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
23. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
1D Cable
1D mesh convergence
· Problem description: L = 10m, ρ0 = 1Kg/m3, E = 1Pa, ν = 0, αCFL = 0.5, P = 1 × 10−3EXP(−0.1(t − 13)2)N,
τFp = 0.5∆t, τpF = ξF = 0
2
1
2
1
1D convergence analysis by means of the L2
norm has been carried out at t = 40s
Demonstrates the expected accuracy of the available schemes for all variables
The use of both slope limiter and lumped mass matrix maintains the expected order of
convergence
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
24. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
3D L-shaped block
Angular momentum preserving example
· Problem description: L-shaped block, ρ0 = 1000Kg/m3, E = 5.005 × 104Pa, ν = 0.3, αCFL = 0.3, τFp = 0.5∆t,
τpJ = 0.2∆t, ξJ = 0.5
µ
κ
, τpF = τJp = τFJ = ξF = 0, lumped mass contribution
1X
2X
3X
T(3,3,3)
T(0,10,3)
T(6,0,0)
)t(1F
)t(2F
J. C. Simo, N. Tarnow, K. K. Wong. Exact energy-momentum
conserving algorithms and symplectic schemes for nonlinear
dynamics, CMAME 100, 63-116 (1992)
• Imposed external forces at faces {X1 = 6,
X2 = 10} described as
· F1(t) = − F2(t) = η(t) (150, 300, 450)T
η(t) =
t, 0 ≤ t < 2.5
5 − t, 2.5 ≤ t < 5
0, t ≥ 5
• Free BC at all sides
• Suitable for long term dynamic response
· Angular Momentum
· Total energy (summation of kinetic and
potential energies)
[MOVIE]
Study the conservation properties of the proposed formulation
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
25. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
3D Slender beam
Detrimental locking effects
· Problem description: Column 1 × 1 × 20, ρ0 = 1.1Mg/m3, E = 0.017GPa, ν = 0.49999, αCFL = 0.3, linear variation of
velocity field V0 = 2m/s, τFp = 0.5∆t, τpJ = 0.2∆t, ξJ = 0.5
µ
κ
, τpF = τJp = τFJ = ξF = 0, lumped mass
contribution
J. Bonet, H. Marriott, O. Hassan. An averaged nodal deformation
gradient linear tetrahedral for large strain explicit dynamic
applications, COMMUN NUMER METH EN 17, 551-561 (2001)
• Imposed linear variation in velocity field
described as
· v(X) = (V0X3/L, 0, 0)T
; V0 = 2m/s
• Thin structures in bending-dominated
scenario
• Nearly incompressible material behaviour
with Poisson ratio ν = 0.49999
• Eliminate shear and volumetric locking
effects and the appearance of pressure
instabilities
[MOVIE]
Assess the performance of the PG formulation in the case of near incompressibility
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
26. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
3D Twisting column
Fractional step formulation
· Problem description: Column 1 × 1 × 6, ρ0 = 1.1Mg/m3, E = 0.017GPa, ν = 0.499, αCFL = 0.3, sinusoidal rotational
velocity field Ω = 100m/s, lumped mass contribution
p-F PG p-F-J PG Fractional step
Assess the performance of the fractional step method in the case of near incompressibility
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
27. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
3D Taylor impact bar
Classical benchmark impact problem
· Problem description: Copper bar, L0 = 3.24 cm, r0 = 0.32 cm, v0 = (0, 0, −227) m/s. von Mises hyperelastic-plastic
material with ρ0 = 8930Kg/m3, E = 117GPa, ν = 0.35, ¯τ0
y = 0.4GPa, H = 0.1GPa, αCFL = 0.3, 1361 nodes, lumped
mass contribution
0V
= 03X
0L
0r
Radius and length (in cm) at t = 80µs
Methods Radius Length
Standard 4-Node Tet. 0.555 -
8-Node Hex. (P1/P0) 0.695 2.148
4-Node ANP Tet. (P1/P1-projection) 0.699 -
4-Node Mixed Tet. (P1/P1-stabilised) 0.700 2.156
J. Bonet, A. Burton. A simple average nodal pressure tetrahedral element for
incompressible and nearly incompressible dynamic explicit applications, COMMUN
NUMER METH EN 14, 437-449 (1998)
O. C. Zienkiewicz, J. Rojek, R. L. Taylor, M Pastor. Triangles and tetrahedra in explicit
dynamic codes for solids, INT J NUMER METH ENG 43, 565-583 (1998)
[MOVIE]
Assess the performance within the context of contact/impact mechanics
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
28. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
Outline
1 Motivation
2 Reversible elastodynamics
Balance principles
Conservation laws
3 Petrov-Galerkin formulation
Petrov-Galerkin spatial discretisation
Perturbed test function space
Temporal discretisation
Incompressible and nearly incompressible formulation
Fractional-step formulation
4 Numerical results
5 Conclusions and further research
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
29. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
Conclusions and further research
Conclusions
• A stabilised Petrov-Galerkin formulation is presented for the numerical simulations
of fast dynamics in large deformations
• Linear tetrahedral elements can be used without usual volumetric and bending
difficulties
• Velocities (or displacements) and stresses display the same rate of convergence
On-going works
• Standard CFD techniques for discontinuity capturing operator can be
incorporated [Scovazzi et al., 2007]
• Sophisticated constitutive models (Mie-Gruneisen) can be employed [Aguirre et al.,
Under review]
• Industrial applications including crash, impact analysis and explosion modelling
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014
30. Outline Motivation Reversible elastodynamics Petrov-Galerkin formulation Numerical results Conclusions
Publications
Journal publications
· C. H. Lee, A. J. Gil and J. Bonet. Development of a cell centred upwind finite volume algorithm
for a new conservation law formulation in structural dynamics, Computers and Structures 118
(2013) 13-38.
· I. A. Karim, C. H. Lee, A. J. Gil and J. Bonet. A Two-Step Taylor Galerkin formulation for fast
dynamics, Engineering Computations 31 (2014) 366-387.
· C. H. Lee, A. J. Gil and J. Bonet. Development of a stabilised Petrov-Galerkin formulation for a
mixed conservation law formulation in fast solid dynamics, CMAME 268 (2013) 40-64.
· M. Aguirre, A. J. Gil, J. Bonet and A. Arranz Carreño. A vertex centred Finite Volume
Jameson-Schmidt-Turkel (JST) algorithm for a mixed conservation formulation in solid
dynamics, JCP 259 (2014) 672-699.
· A. J. Gil, C. H. Lee, J. Bonet and M. Aguirre. A stabilised Petrov-Galerkin formulation for linear
tetrahedral elements in compressible, nearly incompressible and truly incompressible fast
dynamics, CMAME 276 (2014) 659-690.
Under review
· M. Aguirre, A. J. Gil, J. Bonet and C. H. Lee. An edge based vertex centred upwind finite
volume method for Lagrangian solid dynamics. JCP. Under review.
· J. Bonet, A. J. Gil, C. H. Lee, M. Aguirre and R. Ortigosa. A first order hyperbolic framework
for large strain computational solid dynamics: Part 1 Total Lagrangian Isothermal Elasticity.
CMAME. Under review.
CHL-AJG-JB-MA (MS209A: Advances in Finite Element Methods for Tetrahedral Mesh Computations I) 20th - 25th July 2014