*Non-linear Analysis- Introduction to nonlinear problems, comparison of linear and non-linear analysis, types of nonlinearities, Stress-strain measures for non-linear analysis, Analysis of geometry, Material Nonlinearity, Solution techniques for non-linear analysis, Newton-Raphson Method, Essential steps in Nonlinear analysis. (No numerical treatment)
*Dynamic Analysis- Introduction to dynamic analysis, Comparison of static and dynamic analysis, Time domain and frequency domain, types of loading, Simple Harmonic motion, Free vibrations, Bounday conditions for free vibrations, Solution
1) The document discusses the basics of the finite element method (FEM), which involves dividing a structure into simple subdomains called finite elements connected at nodes.
2) FEM allows for the analysis of complex problems by replacing differential equations with algebraic equations at nodes. This is done using shape functions to interpolate values within an element.
3) The document compares FEM to other numerical methods like the finite difference method, noting advantages of FEM include better accuracy with fewer elements and the ability to model curved boundaries and nonlinear problems.
*Plain stress-strain,
*axi-symmetric problems in 2D elasticity
*Constant Strain Triangles (CST)- Element stiffness matrix, Assembling stiffness Equation, Load vector, stress and reaction forces calculations. (numerical treatment only on constant strain triangles)
*Post Processing Techniques- *Check and validate accuracy of results,
* Average and Un-average stresses,
*Special tricks for post processing,
*Interpretation of results and design modifications,
*CAE reports.
The document provides an introduction to the finite element method (FEM). It discusses that FEM is a numerical technique used to approximate solutions to boundary value problems defined by partial differential equations. It can handle complex geometries, loadings, and material properties that have no analytical solution. The document outlines the historical development of FEM and describes different numerical methods like the finite difference method, variational method, and weighted residual methods that FEM evolved from. It also discusses key concepts in FEM like discretization into elements, node points, and interpolation functions.
1. The stiffness method is used to analyze the beam by determining its degree of kinematic indeterminacy, selecting unknown displacements, restraining the structure, and generating a stiffness matrix.
2. A 4m beam with supports at 1.5m and 3m is analyzed using a stiffness matrix approach. The displacements selected are the rotations at joints B and C.
3. The stiffness matrix is generated by applying unit rotations at each joint and calculating the actions. This matrix is then used along with the applied loads in a superposition equation to solve for the unknown displacements.
This document summarizes a seminar topic on the theory of elasticity. It discusses key concepts in elasticity including external forces, stresses, strains, displacements, assumptions of elasticity theory. It provides examples of plane stress and plane strain conditions. The purpose of elasticity theory is to analyze stresses and displacements in elastic solids and structures. Applications include designing mechanical parts and calculating stresses in beams.
The document discusses isoparametric finite elements. It defines isoparametric, superparametric, and subparametric elements. It provides examples of shape functions for 4-noded rectangular, 6-noded triangular, and 8-noded rectangular isoparametric elements. It also discusses coordinate transformation from the natural to global coordinate system using these shape functions and calculating the Jacobian.
1) The document discusses the basics of the finite element method (FEM), which involves dividing a structure into simple subdomains called finite elements connected at nodes.
2) FEM allows for the analysis of complex problems by replacing differential equations with algebraic equations at nodes. This is done using shape functions to interpolate values within an element.
3) The document compares FEM to other numerical methods like the finite difference method, noting advantages of FEM include better accuracy with fewer elements and the ability to model curved boundaries and nonlinear problems.
*Plain stress-strain,
*axi-symmetric problems in 2D elasticity
*Constant Strain Triangles (CST)- Element stiffness matrix, Assembling stiffness Equation, Load vector, stress and reaction forces calculations. (numerical treatment only on constant strain triangles)
*Post Processing Techniques- *Check and validate accuracy of results,
* Average and Un-average stresses,
*Special tricks for post processing,
*Interpretation of results and design modifications,
*CAE reports.
The document provides an introduction to the finite element method (FEM). It discusses that FEM is a numerical technique used to approximate solutions to boundary value problems defined by partial differential equations. It can handle complex geometries, loadings, and material properties that have no analytical solution. The document outlines the historical development of FEM and describes different numerical methods like the finite difference method, variational method, and weighted residual methods that FEM evolved from. It also discusses key concepts in FEM like discretization into elements, node points, and interpolation functions.
1. The stiffness method is used to analyze the beam by determining its degree of kinematic indeterminacy, selecting unknown displacements, restraining the structure, and generating a stiffness matrix.
2. A 4m beam with supports at 1.5m and 3m is analyzed using a stiffness matrix approach. The displacements selected are the rotations at joints B and C.
3. The stiffness matrix is generated by applying unit rotations at each joint and calculating the actions. This matrix is then used along with the applied loads in a superposition equation to solve for the unknown displacements.
This document summarizes a seminar topic on the theory of elasticity. It discusses key concepts in elasticity including external forces, stresses, strains, displacements, assumptions of elasticity theory. It provides examples of plane stress and plane strain conditions. The purpose of elasticity theory is to analyze stresses and displacements in elastic solids and structures. Applications include designing mechanical parts and calculating stresses in beams.
The document discusses isoparametric finite elements. It defines isoparametric, superparametric, and subparametric elements. It provides examples of shape functions for 4-noded rectangular, 6-noded triangular, and 8-noded rectangular isoparametric elements. It also discusses coordinate transformation from the natural to global coordinate system using these shape functions and calculating the Jacobian.
This document discusses two-dimensional vector variable problems in structural mechanics. It describes plane stress, plane strain and axisymmetric problems, and provides the stress-strain relations for materials under these conditions. It also discusses thin structures like disks and long prismatic shafts. Additionally, it covers dynamic analysis and vibration of structures, describing free vibration, forced vibration and types of vibration. Equations of motion are developed using Lagrange's approach and the weak form method. Mass and stiffness matrices for axial rod and beam elements are also presented.
The document discusses plane stress and plane strain models. Plane stress deals with thin slabs where the thickness is much smaller than the in-plane dimensions, resulting in zero stresses in the thickness direction and no variation through the thickness. Plane strain deals with long prismatic bodies, where the length is much greater than the in-plane dimensions, resulting in zero strains in the length direction. Both make assumptions about stress and strain variations to reduce the equations to a 2D form, but these are approximations as there are actually non-zero secondary stresses and strains ignored in the models.
This document discusses the stress function approach for solving two-dimensional elasticity problems. It begins by presenting the general equations of elasticity, including stress-strain relationships, strain-displacement equations, and equilibrium equations. It then introduces the stress function method proposed by Airy, where a single function of space coordinates is assumed that satisfies all the elasticity equations. The key steps are: (1) choosing a stress function, (2) confirming it is biharmonic, (3) deriving stresses from its derivatives, (4) using boundary conditions to determine the function, (5) deriving strains, and (6) displacements. Examples of polynomial stress functions are also provided.
The document discusses plasticity theory and yield criteria. It introduces Hooke's law and its limitations under large strains. Generalized Hooke's law is presented for isotropic and anisotropic materials. Common stress-strain curves are shown including elastic-plastic and strain hardening responses. Several yield criteria are covered, including maximum principal stress, Tresca, and von Mises criteria. The von Mises criterion uses a second invariant of stress to predict yielding of ductile materials. An example compares predictions of yielding using Tresca and von Mises criteria for a given stress state in aluminum.
Introduction to finite element analysisTarun Gehlot
The document provides an introduction to finite element analysis (FEA) or the finite element method (FEM). It describes FEA as a numerical method used to solve engineering and mathematical physics problems that cannot be solved through analytical methods due to complex geometries, loadings, or material properties. FEA involves discretizing a complex model into smaller, simpler elements connected at nodes, then applying the governing equations to obtain a numerical solution for the unknown primary variable (usually displacement) at nodes. Secondary variables like stress are then determined from nodal displacements. The process involves preprocessing, solving, and postprocessing steps.
This document discusses structural analysis methods for statically indeterminate structures. It defines key terms like degree of static indeterminacy, internal and external redundancy, and methods for analyzing indeterminate structures. Specific methods discussed include the flexibility matrix method, consistent deformation method, and unit load method. Examples of statically indeterminate beams and frames are also provided.
The document provides an overview of the history and basics of finite element analysis (FEA). It discusses how FEA was first developed in 1943 and expanded in the following decades. The basics section describes common FEA applications, basic steps which include converting differential equations to algebraic equations, element types, boundary conditions including loads and constraints, and pre-processing, solving, and post-processing steps. Key element types are also summarized.
This document discusses the finite element method (FEM) for engineering analysis. It explains that FEM involves discretizing a continuous structure into smaller, finite elements and then solving the equations for each element. The general steps of FEM are: 1) discretizing the structure into elements connected at nodes, 2) numbering nodes and elements, 3) selecting displacement functions, 4) defining material behavior, 5) deriving element stiffness matrices, 6) assembling element equations, 7) applying boundary conditions, 8) solving for displacements, 9) computing element strains and stresses, and 10) interpreting results. One-, two-, and three-dimensional elements as well as axisymmetric elements are discussed.
The document provides an introduction to the finite element method (FEM). It discusses how FEM can be used to obtain approximate solutions to boundary value problems in engineering. It outlines the general steps involved, including preprocessing (defining the model), solution/processing (computing unknown values), and postprocessing (analyzing results). Examples of FEM applications include structural analysis, fluid flow, heat transfer, and more. The key aspects of FEM include discretizing the domain into simple elements, choosing shape functions to approximate variations within each element, and assembling the element equations into a global system of equations to solve.
The document discusses undamped free vibration in machinery. It defines undamped free vibration as vibration of a system with no external damping forces after an initial displacement. It describes methods to determine the natural frequency of vibrating systems including the equilibrium method, energy method, and Rayleigh's method. The equilibrium method uses D'Alembert's principle. The energy method equates kinetic and potential energy. Rayleigh's method equates maximum kinetic and potential energy. Examples of undamped free transverse and torsional vibration are also presented and the equations for their natural frequencies are derived.
The document discusses shear stresses in beams. It defines shear stress as being due to shear force and perpendicular to the cross-sectional area. Shear stress is derived as τ = F/A, where F is the shear force and A is the cross-sectional area. Shear stress varies across standard beam cross sections like rectangular, circular, and triangular. Shear stress is maximum at the neutral axis for rectangular and circular beams, and at half the depth for triangular beams. Sample problems are included to demonstrate calculating and graphing the variation of shear stress across specific beam cross sections.
- The document discusses one-dimensional finite element analysis.
- It describes the derivation of shape functions for linear one-dimensional elements like a bar element. Shape functions define the variation of displacement within the element.
- The stiffness matrix, which represents the element's resistance to deformation, is also derived for a basic linear bar element. It is shown to be symmetric and its properties are discussed.
- Examples are provided to demonstrate calculating displacements at points within a one-dimensional element using the shape functions.
This document discusses the concept of shear center for beams with non-symmetric cross sections. It defines shear center as the point where a load can be applied such that the beam only bends with no twisting. Formulas to calculate the shear center are presented for common cross sections like channels, I-beams, and circular tubes. Examples of determining the shear center for different cross sections are included. The importance of applying loads through the shear center to prevent twisting is emphasized.
1. Cylinders are commonly used in engineering to transport or store fluids and are subjected to internal fluid pressures. This induces three stresses on the cylinder wall - circumferential, longitudinal, and radial.
2. For thin cylinders where the wall thickness is less than 1/20 the diameter, the radial stress can be neglected. Equations are derived to calculate the circumferential and longitudinal stresses based on the internal pressure, diameter, and wall thickness.
3. Sample problems are worked out applying the equations to example thin-walled cylinders under internal pressure, finding stresses, strains, and changes in dimensions.
*Need of finite element analysis
*Introduction to approaches used in Finite Element Analysis such as direct approach and energy approach
*Boundary conditions: Types
*Rayleigh-Ritz Method
*Galerkin Method
This document discusses constitutive models for elastoplastic materials. It describes how elastoplastic materials behave elastically up to a certain stress limit, after which both elastic and plastic behavior occurs. The document outlines stress-strain curves for hypothetical materials under different loading conditions and discusses yield criteria and hardening rules used in plasticity models to describe the evolution of material behavior. It also summarizes common plasticity models including von Mises and Tresca and the assumptions underlying incremental plasticity theories.
This document discusses two-dimensional vector variable problems in structural mechanics. It describes plane stress, plane strain and axisymmetric problems, and provides the stress-strain relations for materials under these conditions. It also discusses thin structures like disks and long prismatic shafts. Additionally, it covers dynamic analysis and vibration of structures, describing free vibration, forced vibration and types of vibration. Equations of motion are developed using Lagrange's approach and the weak form method. Mass and stiffness matrices for axial rod and beam elements are also presented.
The document discusses plane stress and plane strain models. Plane stress deals with thin slabs where the thickness is much smaller than the in-plane dimensions, resulting in zero stresses in the thickness direction and no variation through the thickness. Plane strain deals with long prismatic bodies, where the length is much greater than the in-plane dimensions, resulting in zero strains in the length direction. Both make assumptions about stress and strain variations to reduce the equations to a 2D form, but these are approximations as there are actually non-zero secondary stresses and strains ignored in the models.
This document discusses the stress function approach for solving two-dimensional elasticity problems. It begins by presenting the general equations of elasticity, including stress-strain relationships, strain-displacement equations, and equilibrium equations. It then introduces the stress function method proposed by Airy, where a single function of space coordinates is assumed that satisfies all the elasticity equations. The key steps are: (1) choosing a stress function, (2) confirming it is biharmonic, (3) deriving stresses from its derivatives, (4) using boundary conditions to determine the function, (5) deriving strains, and (6) displacements. Examples of polynomial stress functions are also provided.
The document discusses plasticity theory and yield criteria. It introduces Hooke's law and its limitations under large strains. Generalized Hooke's law is presented for isotropic and anisotropic materials. Common stress-strain curves are shown including elastic-plastic and strain hardening responses. Several yield criteria are covered, including maximum principal stress, Tresca, and von Mises criteria. The von Mises criterion uses a second invariant of stress to predict yielding of ductile materials. An example compares predictions of yielding using Tresca and von Mises criteria for a given stress state in aluminum.
Introduction to finite element analysisTarun Gehlot
The document provides an introduction to finite element analysis (FEA) or the finite element method (FEM). It describes FEA as a numerical method used to solve engineering and mathematical physics problems that cannot be solved through analytical methods due to complex geometries, loadings, or material properties. FEA involves discretizing a complex model into smaller, simpler elements connected at nodes, then applying the governing equations to obtain a numerical solution for the unknown primary variable (usually displacement) at nodes. Secondary variables like stress are then determined from nodal displacements. The process involves preprocessing, solving, and postprocessing steps.
This document discusses structural analysis methods for statically indeterminate structures. It defines key terms like degree of static indeterminacy, internal and external redundancy, and methods for analyzing indeterminate structures. Specific methods discussed include the flexibility matrix method, consistent deformation method, and unit load method. Examples of statically indeterminate beams and frames are also provided.
The document provides an overview of the history and basics of finite element analysis (FEA). It discusses how FEA was first developed in 1943 and expanded in the following decades. The basics section describes common FEA applications, basic steps which include converting differential equations to algebraic equations, element types, boundary conditions including loads and constraints, and pre-processing, solving, and post-processing steps. Key element types are also summarized.
This document discusses the finite element method (FEM) for engineering analysis. It explains that FEM involves discretizing a continuous structure into smaller, finite elements and then solving the equations for each element. The general steps of FEM are: 1) discretizing the structure into elements connected at nodes, 2) numbering nodes and elements, 3) selecting displacement functions, 4) defining material behavior, 5) deriving element stiffness matrices, 6) assembling element equations, 7) applying boundary conditions, 8) solving for displacements, 9) computing element strains and stresses, and 10) interpreting results. One-, two-, and three-dimensional elements as well as axisymmetric elements are discussed.
The document provides an introduction to the finite element method (FEM). It discusses how FEM can be used to obtain approximate solutions to boundary value problems in engineering. It outlines the general steps involved, including preprocessing (defining the model), solution/processing (computing unknown values), and postprocessing (analyzing results). Examples of FEM applications include structural analysis, fluid flow, heat transfer, and more. The key aspects of FEM include discretizing the domain into simple elements, choosing shape functions to approximate variations within each element, and assembling the element equations into a global system of equations to solve.
The document discusses undamped free vibration in machinery. It defines undamped free vibration as vibration of a system with no external damping forces after an initial displacement. It describes methods to determine the natural frequency of vibrating systems including the equilibrium method, energy method, and Rayleigh's method. The equilibrium method uses D'Alembert's principle. The energy method equates kinetic and potential energy. Rayleigh's method equates maximum kinetic and potential energy. Examples of undamped free transverse and torsional vibration are also presented and the equations for their natural frequencies are derived.
The document discusses shear stresses in beams. It defines shear stress as being due to shear force and perpendicular to the cross-sectional area. Shear stress is derived as τ = F/A, where F is the shear force and A is the cross-sectional area. Shear stress varies across standard beam cross sections like rectangular, circular, and triangular. Shear stress is maximum at the neutral axis for rectangular and circular beams, and at half the depth for triangular beams. Sample problems are included to demonstrate calculating and graphing the variation of shear stress across specific beam cross sections.
- The document discusses one-dimensional finite element analysis.
- It describes the derivation of shape functions for linear one-dimensional elements like a bar element. Shape functions define the variation of displacement within the element.
- The stiffness matrix, which represents the element's resistance to deformation, is also derived for a basic linear bar element. It is shown to be symmetric and its properties are discussed.
- Examples are provided to demonstrate calculating displacements at points within a one-dimensional element using the shape functions.
This document discusses the concept of shear center for beams with non-symmetric cross sections. It defines shear center as the point where a load can be applied such that the beam only bends with no twisting. Formulas to calculate the shear center are presented for common cross sections like channels, I-beams, and circular tubes. Examples of determining the shear center for different cross sections are included. The importance of applying loads through the shear center to prevent twisting is emphasized.
1. Cylinders are commonly used in engineering to transport or store fluids and are subjected to internal fluid pressures. This induces three stresses on the cylinder wall - circumferential, longitudinal, and radial.
2. For thin cylinders where the wall thickness is less than 1/20 the diameter, the radial stress can be neglected. Equations are derived to calculate the circumferential and longitudinal stresses based on the internal pressure, diameter, and wall thickness.
3. Sample problems are worked out applying the equations to example thin-walled cylinders under internal pressure, finding stresses, strains, and changes in dimensions.
*Need of finite element analysis
*Introduction to approaches used in Finite Element Analysis such as direct approach and energy approach
*Boundary conditions: Types
*Rayleigh-Ritz Method
*Galerkin Method
This document discusses constitutive models for elastoplastic materials. It describes how elastoplastic materials behave elastically up to a certain stress limit, after which both elastic and plastic behavior occurs. The document outlines stress-strain curves for hypothetical materials under different loading conditions and discusses yield criteria and hardening rules used in plasticity models to describe the evolution of material behavior. It also summarizes common plasticity models including von Mises and Tresca and the assumptions underlying incremental plasticity theories.
Here are the key steps to solve this dynamics problem:
1. Draw a free body diagram showing the applied force F=500 N and the restoring force of the spring kx=500x N.
2. Apply Newton's 2nd law component form: ΣFx = ma.
3. Substitute the known forces and mass m=10 kg and solve for acceleration a.
4. Use kinematic equations as needed to relate displacement, velocity and acceleration.
Solving this type of dynamics problem involves: 1) Drawing free body diagram, 2) Applying Newton's 2nd law in component form, 3) Substituting known values, 4) Solving for the unknown quantity like acceleration.
This is an Introductory material for those who want to understand the basic difference between linear and nonlinear analysis in the context of civil and structural engineering.
This chapter introduces finite element analysis concepts. It begins with a case study of a pneumatically actuated finger made of PDMS elastomer. The chapter then provides a quick review of structural mechanics concepts such as displacements, stresses, strains and governing equations. It introduces finite element methods, which involve dividing a structure into simple elements connected at nodes, and solving the system of equations for unknown nodal displacements. The chapter describes the basic finite element analysis procedure and discusses shape functions and common element types in ANSYS Workbench.
Predicting fatigue using linear – finite element analysisSowmiya Siva
Graphler Technology is one of the fastest-growing product design companies in India . Our FEA Consulting services hold great promise for the future trends of Commercial Furniture’s using ANSI/BIFMA. We have a team of experts specialized in CAD Conversion Services, Engineering animation services and also in Product Animation Services
Numerical Calculation of the Hubble Hierarchy Parameters and the Observationa...Milan Milošević
This document discusses the numerical calculation of observational parameters for inflationary cosmology models, specifically tachyon inflation models and Randall-Sundrum braneworld models. The author develops software to solve the dynamical equations for tachyon scalar fields and radion fields during inflation. The software allows calculation of the scalar spectral index, tensor-to-scalar ratio, and number of e-folds for different model parameters. The best fitting results are obtained for tachyon potentials with 60 ≤ N ≤ 90 e-folds and dimensionless parameter 1≤ κ ≤ 10. The software provides a tool to test a wide range of inflationary models by inputting the corresponding Hamiltonian and Friedmann equations.
IRJET- Structural Analysis of Viscoelastic Materials: Review PaperIRJET Journal
This document reviews research on analyzing the structural behavior of viscoelastic materials from 1964 to the present. Viscoelastic materials exhibit both elastic and viscous properties, resulting in time-dependent stress and strain under static loads. Finite element methods have been developed using mixed formulations and Herrmann elements to better model the nearly incompressible and time-dependent behavior of materials like solid rocket propellants. The document surveys various studies applying these methods to problems like propellant grain analysis and pavement modeling to account for the viscoelastic nature of materials.
This document outlines the objectives, course outcomes, and units covered in a finite element analysis course. The objective is to equip students with fundamentals of FEA and introduce the steps involved in discretization, applying boundary conditions, assembling stiffness matrices, and solving problems. The course covers basic FEA concepts, one-dimensional elements, two-dimensional elements, axisymmetric problems, isoparametric elements, and dynamic analysis. Students will learn to formulate and solve structural and heat transfer problems using various finite elements.
Mohamad Redhwan Abd Aziz is a lecturer at the DEAN CENTER OF HND STUDIES who teaches the subject of Solid Mechanics (BME 2023). The 3 credit hour course involves 2 hours of lectures and 2 hours of labs/tutorials each week. Student assessment includes quizzes, assignments, tests, lab reports, and a final exam. The course objectives are to understand stress, strain, and forces in solid bodies through various principles and experiments. Topic areas covered include stress and strain, elasticity, shear, torsion, bending, deflection, and more. References for the course are provided.
Behavior of Metals according to their strain rate pptMuhammed Affan
1. Strain rate is calculated as the change in strain over the change in time and material behavior is observed to be different at various strain rates.
2. Experiments show that materials exhibit weak, strong, and saturated sensitivity to strain rates as depicted in stress sensitivity diagrams, with dynamic strength peaking at medium strain rates.
3. Constitutive models like the Johnson-Cook law have been developed to relate flow stress to strain and strain rate based on experimental data at various conditions.
This document discusses in situ rock stresses and induced stresses from excavation. It describes how vertical stress increases with depth and horizontal stress varies with a coefficient and can be modeled. Numerical methods like boundary element and finite element are presented to model stresses around openings. Examples show applying these methods to analyze stresses induced around tunnels.
Ch. 05_Compound Stress or Stress Transformations-PPT.pdfhappycocoman
This document discusses compound stresses and stress transformations in mechanical engineering. It begins by introducing the concept of compound stresses that act simultaneously on a body, and how it is necessary to calculate stresses on planes other than the load application planes. It then presents the stress element approach for analyzing stresses, discussing normal stresses, shear stresses, and the plane stress condition. The key aspects covered are:
- Plane stress transformation equations that relate stresses on one set of planes to stresses on inclined planes.
- Special cases like uniaxial stress, pure shear, and biaxial stress.
- Determining principal stresses, which are the maximum and minimum normal stresses, through taking derivatives of the normal stress equation.
EDSIL is an engineering consulting firm providing CAD drafting, analysis, and design services using techniques like finite element analysis. They have over 30 years of experience in industries like civil, automotive, and oil/gas. Their services include 2D/3D CAD, simulation, optimization, and failure investigation. They aim to establish relationships with clients to deliver high quality, cost-effective solutions while maintaining design integrity and attention to detail.
This document outlines the course objectives and contents for a finite element methods in mechanical design course. The key points are:
1. The course will introduce mathematical modeling concepts and teach how to apply finite element methods (FEM) to solve a range of engineering problems.
2. The content will cover one-dimensional, two-dimensional, and three-dimensional FEM analysis. Solution techniques like inversion methods and dynamic analysis will also be discussed.
3. Applications of FEM include stress analysis, buckling analysis, vibration analysis, heat transfer analysis, and fluid flow analysis for both structural and non-structural problems.
analysis of unsteady squeezing flow between two porous plates with variable m...IJAEMSJORNAL
Analysis will be made for the non-isothermal Newtonian fuid flow between two unsteady squeezing porous plates under the infuence of variable magnetic feld. The similarity transformations will be used to transform the partial differential equations into nonlinear coupled ordinary differential equations. The modeled nonlinear differential equations representing the flow behavior in the geometry under consideration will be investigated using analytical and numerical method. Comparison of the solutions will be made. Convergence of solution will also be discussed. Flow behavior under the infuence of non-dimensional parameters will be discussed with the help of graphical aids.
Application of extended n2 method to reinforced concrete frames with asymmetr...IAEME Publication
The extended N2 method was applied to analyze two reinforced concrete buildings with asymmetric setbacks. The extended N2 method accounts for higher mode effects by combining results from a pushover analysis and an elastic modal analysis. It was applied to a 5-story and 9-story building. For the 5-story building, the extended N2 method provided results close to the displacement coefficient method in FEMA 356. Correction factors from the modal analysis were less than 1, so the basic N2 method results were used. This shows the extended N2 method can accurately analyze buildings with vertical irregularities like asymmetric setbacks.
Stress and Strains, large deformations, Nonlinear Elastic analysis,critical load analysis, hyper elastic materials, FE formulations for Non-linear Elasticity, Nonlinear Elastic Analysis Using Commercial Finite Element Programs, Fitting Hyper elastic Material Parameters from Test Data
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Discover the latest insights on Data Driven Maintenance with our comprehensive webinar presentation. Learn about traditional maintenance challenges, the right approach to utilizing data, and the benefits of adopting a Data Driven Maintenance strategy. Explore real-world examples, industry best practices, and innovative solutions like FMECA and the D3M model. This presentation, led by expert Jules Oudmans, is essential for asset owners looking to optimize their maintenance processes and leverage digital technologies for improved efficiency and performance. Download now to stay ahead in the evolving maintenance landscape.
The CBC machine is a common diagnostic tool used by doctors to measure a patient's red blood cell count, white blood cell count and platelet count. The machine uses a small sample of the patient's blood, which is then placed into special tubes and analyzed. The results of the analysis are then displayed on a screen for the doctor to review. The CBC machine is an important tool for diagnosing various conditions, such as anemia, infection and leukemia. It can also help to monitor a patient's response to treatment.
Null Bangalore | Pentesters Approach to AWS IAMDivyanshu
#Abstract:
- Learn more about the real-world methods for auditing AWS IAM (Identity and Access Management) as a pentester. So let us proceed with a brief discussion of IAM as well as some typical misconfigurations and their potential exploits in order to reinforce the understanding of IAM security best practices.
- Gain actionable insights into AWS IAM policies and roles, using hands on approach.
#Prerequisites:
- Basic understanding of AWS services and architecture
- Familiarity with cloud security concepts
- Experience using the AWS Management Console or AWS CLI.
- For hands on lab create account on [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
# Scenario Covered:
- Basics of IAM in AWS
- Implementing IAM Policies with Least Privilege to Manage S3 Bucket
- Objective: Create an S3 bucket with least privilege IAM policy and validate access.
- Steps:
- Create S3 bucket.
- Attach least privilege policy to IAM user.
- Validate access.
- Exploiting IAM PassRole Misconfiguration
-Allows a user to pass a specific IAM role to an AWS service (ec2), typically used for service access delegation. Then exploit PassRole Misconfiguration granting unauthorized access to sensitive resources.
- Objective: Demonstrate how a PassRole misconfiguration can grant unauthorized access.
- Steps:
- Allow user to pass IAM role to EC2.
- Exploit misconfiguration for unauthorized access.
- Access sensitive resources.
- Exploiting IAM AssumeRole Misconfiguration with Overly Permissive Role
- An overly permissive IAM role configuration can lead to privilege escalation by creating a role with administrative privileges and allow a user to assume this role.
- Objective: Show how overly permissive IAM roles can lead to privilege escalation.
- Steps:
- Create role with administrative privileges.
- Allow user to assume the role.
- Perform administrative actions.
- Differentiation between PassRole vs AssumeRole
Try at [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
International Conference on NLP, Artificial Intelligence, Machine Learning an...gerogepatton
International Conference on NLP, Artificial Intelligence, Machine Learning and Applications (NLAIM 2024) offers a premier global platform for exchanging insights and findings in the theory, methodology, and applications of NLP, Artificial Intelligence, Machine Learning, and their applications. The conference seeks substantial contributions across all key domains of NLP, Artificial Intelligence, Machine Learning, and their practical applications, aiming to foster both theoretical advancements and real-world implementations. With a focus on facilitating collaboration between researchers and practitioners from academia and industry, the conference serves as a nexus for sharing the latest developments in the field.
artificial intelligence and data science contents.pptxGauravCar
What is artificial intelligence? Artificial intelligence is the ability of a computer or computer-controlled robot to perform tasks that are commonly associated with the intellectual processes characteristic of humans, such as the ability to reason.
› ...
Artificial intelligence (AI) | Definitio
Advanced control scheme of doubly fed induction generator for wind turbine us...IJECEIAES
This paper describes a speed control device for generating electrical energy on an electricity network based on the doubly fed induction generator (DFIG) used for wind power conversion systems. At first, a double-fed induction generator model was constructed. A control law is formulated to govern the flow of energy between the stator of a DFIG and the energy network using three types of controllers: proportional integral (PI), sliding mode controller (SMC) and second order sliding mode controller (SOSMC). Their different results in terms of power reference tracking, reaction to unexpected speed fluctuations, sensitivity to perturbations, and resilience against machine parameter alterations are compared. MATLAB/Simulink was used to conduct the simulations for the preceding study. Multiple simulations have shown very satisfying results, and the investigations demonstrate the efficacy and power-enhancing capabilities of the suggested control system.
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...IJECEIAES
Medical image analysis has witnessed significant advancements with deep learning techniques. In the domain of brain tumor segmentation, the ability to
precisely delineate tumor boundaries from magnetic resonance imaging (MRI)
scans holds profound implications for diagnosis. This study presents an ensemble convolutional neural network (CNN) with transfer learning, integrating
the state-of-the-art Deeplabv3+ architecture with the ResNet18 backbone. The
model is rigorously trained and evaluated, exhibiting remarkable performance
metrics, including an impressive global accuracy of 99.286%, a high-class accuracy of 82.191%, a mean intersection over union (IoU) of 79.900%, a weighted
IoU of 98.620%, and a Boundary F1 (BF) score of 83.303%. Notably, a detailed comparative analysis with existing methods showcases the superiority of
our proposed model. These findings underscore the model’s competence in precise brain tumor localization, underscoring its potential to revolutionize medical
image analysis and enhance healthcare outcomes. This research paves the way
for future exploration and optimization of advanced CNN models in medical
imaging, emphasizing addressing false positives and resource efficiency.
Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.
Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...shadow0702a
This document serves as a comprehensive step-by-step guide on how to effectively use PyCharm for remote debugging of the Windows Subsystem for Linux (WSL) on a local Windows machine. It meticulously outlines several critical steps in the process, starting with the crucial task of enabling permissions, followed by the installation and configuration of WSL.
The guide then proceeds to explain how to set up the SSH service within the WSL environment, an integral part of the process. Alongside this, it also provides detailed instructions on how to modify the inbound rules of the Windows firewall to facilitate the process, ensuring that there are no connectivity issues that could potentially hinder the debugging process.
The document further emphasizes on the importance of checking the connection between the Windows and WSL environments, providing instructions on how to ensure that the connection is optimal and ready for remote debugging.
It also offers an in-depth guide on how to configure the WSL interpreter and files within the PyCharm environment. This is essential for ensuring that the debugging process is set up correctly and that the program can be run effectively within the WSL terminal.
Additionally, the document provides guidance on how to set up breakpoints for debugging, a fundamental aspect of the debugging process which allows the developer to stop the execution of their code at certain points and inspect their program at those stages.
Finally, the document concludes by providing a link to a reference blog. This blog offers additional information and guidance on configuring the remote Python interpreter in PyCharm, providing the reader with a well-rounded understanding of the process.
Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...
NON-LINEAR AND DYNAMIC ANALYSIS.pptx
1.
2. NON-LINEAR AND DYNAMIC ANALYSIS
UNIT V –NON-LINEAR AND DYNAMIC ANALYSIS
COMPUTER AIDED ENGINEERING
3. By
Prof.(Dr) D Y Dhande
Professor
Department of Mechanical Engineering
AISSMS College Of Engineering, Pune – 411001
Email:dydhande@aissmscoe.com
Prof (Dr) D Y Dhande
4. NON-LINEAR AND DYNAMIC ANALYSIS
COURSE OBJECTIVE (CO5)
• Evaluate and solve nonlinear and dynamic analysis
problems by analysing the results obtained from analytical
and computational method.
Prof (Dr) D Y Dhande
5. CONTENTS
• Non-linear Analysis- Introduction to nonlinear problems, comparison of
linear and non-linear analysis, types of nonlinearities, Stress-strain measures
for non-linear analysis, Analysis of geometry, Material Nonlinearity, Solution
techniques for non-linear analysis, Newton-Raphson Method, Essential steps
in Nonlinear analysis. (No numerical treatment)
• Dynamic Analysis- Introduction to dynamic analysis, Comparison of static
and dynamic analysis, Time domain and frequency domain, types of loading,
Simple Harmonic motion, Free vibrations, Bounday conditions for free
vibrations, Solution
NON-LINEAR AND DYNAMIC ANALYSIS
Prof (Dr) D Y Dhande
7. INTRODUCTION TO NON-LINEAR ANALYSIS
• When structure response (deformation, stress and strain)is not linearly proportional to
the magnitude of the load, then the analysis is known as non-linear analysis.
• Due to cost and weight advantage of non-metals (polymers, woods, composites) over
metals, non-metals are replacing metals for variety of applications, which have
nonlinear load to response characteristics, even under mild loading conditions.
• Also, the structures are optimized to make most of its strength, pushing the load level
so close to the strength of the material, that it starts behaving nonlinearly.
• In order to accurately predict the strength of the structures in these circumstances, it is
necessary to perform nonlinear analysis.
NON-LINEAR AND DYNAMIC ANALYSIS
Prof (Dr) D Y Dhande
12. NON-LINEAR AND DYNAMIC ANALYSIS
TYPES OF NON-LINEARITIES
• Geometric Non-linearities:
• Stiffness changes due to geometric deformations are categorized as geometric
nonlinearities. The different kinds of geometric nonlinearities are: (i) Large strain; (ii)
Large deflection (large rotation); (iii) Stress stiffening; (iv) Spin softening
• Large Strain:
• If element’s shape changes (area,thickness, etc), its individual element stiffness will
change.
Prof (Dr) D Y Dhande
13. NON-LINEAR AND DYNAMIC ANALYSIS
• Large Rotation:
• If element’s orientation changes (rotation), transformation of its local stiffness to global
components will change which induces large strains.
• Stress Stiffening:
• This is associated with tension bending coupling. The more the tension in the
membrane, more its bending rigidity or stiffness. If element’s strains produce a
significant inplane stress state, the out of plane stiffness can be significantly affected.
Prof (Dr) D Y Dhande
14. NON-LINEAR AND DYNAMIC ANALYSIS
• Spin softening:
• This phenomena is related to stiffness change due to rotational speed. Most common
in components such as shrink fit assembly rotation at a high speed and the press fit
interference changing into a clearance fit due to large circumferential deformation.
Another example is change in tension in the cable or rope in brake dynamometer as a
function of rotational speed of drum.Prof (Dr) D Y Dhande
15. NON-LINEAR AND DYNAMIC ANALYSIS
• Material Non-linearities:
• The engineering material behaviour cannot be idealised using a single constitutive law
for the entire range of environmental conditions loading, temp and rate of deformation.
• The linear elastic (also called Hooken) material assumption is simplest of all.
• The martial is nonlinear elastic if the deformation is recoverable and plastic if it is not
recoverable.
• If the temperature effects on material properties are important, then the coupling
between mechanical and thermal behaviour should be properly taken into
consideration through thermo-elasticity and thermo-plasticity.
• If strain rate has significant effects on material, them we have to consider the theories
of visco-elasticity and visco-plasticity. A sample is given in below figures:
Prof (Dr) D Y Dhande
17. NON-LINEAR AND DYNAMIC ANALYSIS
• A brief classification can be given as below:
1. Non-linear elastic, 2. Hyper elastic, 3.Elastic-perfectly plastic; 4. Elastic-Time
dependant plastic 5. Time dependant plastic (Creep); 6. Strain rate dependant
elasticity-plasticity, 7. Temperature dependant elasticity and plasticity.
• The material non-linearity can be classified further as: (i) Linear elastic-perfectly
plastic; (ii) Linear Elastic-Plastic.
• The plastic part in stress strain curve is time dependant and can be analysed into two
main types: (i) Elastic-Piecewise linear plastic; (ii) Elastic-actual stress strain curve
• Non-linear elastic model characterizing materials with no fixed definition of yield point
such as say plastic but the strain still limiting well below say 20%
• Hyper elastic materials such as rubber undergoing large displacements (Gaskets).
Prof (Dr) D Y Dhande
19. NON-LINEAR AND DYNAMIC ANALYSIS
• Boundary Non-linearities:
• Boundary nonlinearity arise when boundary conditions in a FEA model changes during
the course of analysis. The boundary conditions could be added or removed from the
model due to boundary non-linearity as the analysis progresses.
Prof (Dr) D Y Dhande
20. NON-LINEAR AND DYNAMIC ANALYSIS
STRESS STRAIN MEASURES FOR NONLINEAR ANALYSIS
• There are different measures of strain and stress for nonlinear analysis. Some are
explained below:
(i) Engineering strain and engineering stress;
(ii) Logarithmic strain and true stress;
(iii) Green-Lagrange strain and 2nd Piola-Kirchoff stress.
• Let us consider below example to demonstrate these stresses.
Prof (Dr) D Y Dhande
21. NON-LINEAR AND DYNAMIC ANALYSIS
• Engineering Strain and Stress:
• Engineering strain measure is a linear measure since it depends upon the original
geometry (length) which is known.
𝜀𝑥 =
∆𝑙
𝐿
• Engineering stress() is the conjugate stress measure to engineering strain (). It
uses the current force F and the original area A0 in its computation.
𝜎 =
𝐹
𝐴0
• Logarithmic Strain and true stress:
• Logarithmic strain/natural strain/true strain is a large strain measure which is
computed as: Prof (Dr) D Y Dhande
22. NON-LINEAR AND DYNAMIC ANALYSIS
0
0
ln
0
l
l
l
dl
l
l
l
• This measure is a nonlinear strain measure since it is a nonlinear function of the
unknown.
• The 3D equivalent of the log strain in the Hencky strain.
• This strain measure is widely used in nonlinear analysis and is a additive strain
measure as compared to linear strain.
• True stress () is the conjugate 1D stress measure to the log strain (i) which is
computed by dividing the forec F by the current area A. This measure is commonly
referred as Cauchy Stress.
𝜏 =
𝐹
𝐴
Prof (Dr) D Y Dhande
23. NON-LINEAR AND DYNAMIC ANALYSIS
• Green-Lagrange Strain and 2nd Piola-Kirchoff Stress:
• This is another large strain measure which is computed in 1D as:
• This measure is non-linear because it depends upon the square of the updated length
l, which is an unknown.
• Its advantage over Hencky strain is that it automatically accommodates arbitrary
large rotations in large strain problems.
• The conjugate stress measure for the Green Lagrange strain is the 2nd Piola-Kirchoff
stress which is computed as:
2
0
2
0
2
2
1
l
l
l
G
0
0
A
F
l
l
S
Prof (Dr) D Y Dhande
24. NON-LINEAR AND DYNAMIC ANALYSIS
SOLUTION TECHNIQUES FOR NONLINEAR ANALYSIS
• The stiffness matrix in a nonlinear static analysis needs to be updated as analysis
progresses.
• When a structure is subjected to external loading, internal loads are generated. These
are caused due to internal stresses in the structure. For the equilibrium of the
structure, each node of the structure must be in equilibrium.
• The condition of equilibrium is checked by determining residual load, which is
difference between internal and external load. For perfect equilibrium, this residual
load must be zero which is unlikely situation in non-linear analysis.
• The FEA codes assume the nodes to be in equilibrium if the residual load is negligibly
small. Prof (Dr) D Y Dhande
25. NON-LINEAR AND DYNAMIC ANALYSIS
• Let us consider point 1 in the load displacement curve for a node in a FE model,
which is in equilibrium (i.e. difference between external load P1 and internal load is
zero).
• When external load is increased by small amount to P2, the incremental displacement
using linear elastic theory is-
d2-d1 = k1 (P2-p1), where K1 is stiffness based on configuration at point.
• The FEA code will now calculate the internal load at point 2 and comapres the
residual load at point 2, which is given by
R2 = P2-l2
• If R2 is more than the acceptable residual load, the FEA code locates the new point 3
using linear relationship- d3-d2 = k2(P2-P1)
Prof (Dr) D Y Dhande
27. NON-LINEAR AND DYNAMIC ANALYSIS
• Then new stiffness matrix K3 is formed on the configuration at point 3 and
corresponding internal load l3 is calculated. The residual load at point 3 becomes:
R3 = P2-l3
• If R3 meets the residual load criteria, the solution is said to be converged for that
particular increment. Each attempt of calculating residual load for an increment is
called interation.
• Once the solution is converged for a load increment, FEA code accepts it as a
equilibrium and increases the load by further increment.This process is repeated until
entire load is applied on the structure.
• This procedure of stiffness update at every step is known as Newton-Raphson
method.
Prof (Dr) D Y Dhande
28. NON-LINEAR AND DYNAMIC ANALYSIS
• Another common option is to update the stiffness after a number of steps is known as
Modified Newton-Raphson method.
• In FEA analysis, if the load is applied in too many steps or if stress strain curve is
represented in too many segments, the computational cost will be high.
• FEA analyst control the number of steps in a nonlinear static analysis by specifying
number of increments (% of total load).
Prof (Dr) D Y Dhande
29. NON-LINEAR AND DYNAMIC ANALYSIS
ESSENTIAL STEPS TO START WITH NONLINEAR ANALYSIS
• Learn first how the software works on a simple model before using a non-linear
feature which you haven’t used.
• Refer and understand software manual and supporting documentation.
• Prepare a list of questions for which you want to carry out analysis. Design the
analysis such as model, material model, boundary conditions in order to answer the
questions.
• Keep the final model as simple as possible. Check all boundary conditions as well as
meshing.
• Verify the results of the nonlinear FEA solution.
• Try to look into the assumptions made with respect to the structural component, its
geometry behaviour and different material models.
Prof (Dr) D Y Dhande
31. NON-LINEAR AND DYNAMIC ANALYSIS
• Static analysis does not into account variation of load with respect to time. Output in
the form of stress, displacement etc with respect to time could be predicted by
dynamic analysis.
• In static analysis, velocity and acceleration (due to deformation of component) are
always zero. Dynamic analysis can predict these variable with respect to
time/frequency.
• To determine natural frequency of component which ia also helpful for avoiding
resonance, noise reduction and mesh check.
• When the excitation frequency is close to natural frequency of component, there
would be big difference in static and dynamic results. Static analysis would probably
show stress magnitude within yield stress and safe but in reality it might fail.
NEED FOR DYNAMIC ANALYSIS
Prof (Dr) D Y Dhande
35. NON-LINEAR AND DYNAMIC ANALYSIS
• For a single dof problem, when frequency of excitation is one third of fundamental
frequency, the problem can be treated as static.
• What is frequency:
• Frequency is number of occurrences per unit time. (e.g a doctor prescribe medicines
3 times a day to a patient, the frequency is 3 per day)
• Let us consider a steel ruler and disturb it slightly and observe the vibrations. Ruler
deflects on either sides of the mean position. Time require to complete one cycle is
time period.
• Number of cycles per seconds is known as Hertz (Hz).
Prof (Dr) D Y Dhande
36. NON-LINEAR AND DYNAMIC ANALYSIS
• Frequently used formula for natural frequency , n = (k/m) is for circular frequency
and units are rad/sec.
• While, most of the commercial softwares give output in “Hz” i.e. cyclic frequency i.e.
f = (1/2) (k/m)
• How to convert rpm to Hz : Engine speed 6000rpm means vibrations at 6000/60 rps
or 100Hz
• Effect of natural frequency on noise: Noise and vibrations are interrelated.
Prof (Dr) D Y Dhande
37. NON-LINEAR AND DYNAMIC ANALYSIS
• When the length of steel ruler is reduced, it changes natural frequency but also
reduces the noise. One important factor in reducing the noise is altering the natural
frequency.
DIFFERENCE BETWEEN FREQUENCY AND TIME DOMAIN
Prof (Dr) D Y Dhande
38. NON-LINEAR AND DYNAMIC ANALYSIS
• Imagine you are sitting on a chair and ground starts vibrating first slowly and then
gradually faster and faster. This phenomenon could be presented easily in frequency
domain via a single straight line as shown in the figure.
• Its equivalent representation in time domain is shown in right side figure (for simplicity
constant amplitude of vibration is assumed)
• Frequency and time domain are inter convertible.
f = 1/T
Prof (Dr) D Y Dhande
40. NON-LINEAR AND DYNAMIC ANALYSIS
• Non-Periodic Transient
response (Random Vibrations) :
Prof (Dr) D Y Dhande
41. NON-LINEAR AND DYNAMIC ANALYSIS
SIMPLE HARMONIC MOTION
• Simple harmonic motion, regular vibration in which the acceleration of the
vibrating object is directly proportional to the displacement of the object from
its equilibrium position but oppositely directed. A single object vibrating in this
manner is said to exhibit simple harmonic motion (SHM).
Prof (Dr) D Y Dhande
42. NON-LINEAR AND DYNAMIC ANALYSIS
SPRING MASS REPRESENTATION
• In Mechanical Engineering, any system or component could be represented by three
basic elements i.e. mass, stiffness and damping. For example, entire railway bogie,
chassis of automobile or even a human body could be represented mathematically as
a spring , mass and damping of appropriate values.
Prof (Dr) D Y Dhande
43. NON-LINEAR AND DYNAMIC ANALYSIS
FREE VIBRATION
• The ordinary homogeneous linear second order differential equation for spring mass
system is given as: .
• Applying Newton's laws of motion, we have
• The solution of above equation is :
• This is Simple Harmonic Motion.
Prof (Dr) D Y Dhande
44. NON-LINEAR AND DYNAMIC ANALYSIS
NATURAL FREQUENCY ANALYSIS
• The frequency with which any object will vibrate if disturbed and allowed to vibrate on
its own without any external force is known as natural frequency. It is estimated by
equation, n = (k/m)
• Damping is neglected for natural frequency calculations.
• Any object has first 6 natural frequencies = 0 when run free-free.
• All real life objects have infinite natural frequencies but FEA can compute compute
natural frequencies equal to dof s of the FEA model only.
• Lowest natural frequency is known as fundamental frequency.
Prof (Dr) D Y Dhande
45. NON-LINEAR AND DYNAMIC ANALYSIS
NATURAL FREQUENCY ANALYSIS FOR CANTILEVER BEAM
35851
.
449
100
3
10
8
.
7
25
.
2
10
1
.
2
786
.
149
100
3
10
8
.
7
25
.
0
10
1
.
2
inertias,
of
moments
two
to
ing
Correspond
2
:
as
calculated
is
frequency
natural
The
4
9
5
4
2
4
9
5
4
1
4
AL
EI
AL
EI
AL
EI
n
f i
i
The value of 1st to ‘n’ are 3.51602, 22.0345, 61.6972,
120.902, 199.86, 298.556, 416.991, 555.165, 713.079,
890.732
Prof (Dr) D Y Dhande