The document provides an introduction to finite element analysis (FEA) and its applications to engineering problems. It discusses that FEA is a numerical method used to solve problems that cannot be solved analytically due to complex geometry or materials. It involves discretizing a continuous structure into small, well-defined substructures called finite elements. The key steps in FEA include preprocessing such as defining geometry, meshing and material properties, solving the problem, and postprocessing results such as stresses and strains. The document also discusses various element types, assembly of elements, sources of error in FEA, and its advantages such as handling complex geometry, loading and materials.
The document provides an introduction to finite element analysis (FEA) including:
1) FEA involves discretizing a continuous structure into small substructures called finite elements connected at nodes. This process is called meshing.
2) The finite element method has three main phases - preprocessing (defining geometry, materials, mesh), solution (solving equations to obtain nodal results), and postprocessing (obtaining stresses, strains from nodal results).
3) FEA can model complex problems that cannot be solved analytically due to complicated geometry or materials, and is well-suited for solving problems in solid mechanics, heat transfer, and other fields on computers.
Lecture on Introduction to finite element methods & its contentsMesayAlemuTolcha1
The document provides an overview of the Finite Element Method (FEM) course being taught. It discusses:
1. What FEM is and its common application areas like structural analysis, heat transfer, fluid flow.
2. The main steps in FEM including discretization, selecting interpolation functions, developing element matrices, assembling the global matrix, imposing boundary conditions, and solving equations.
3. Different element types like 1D, 2D, and 3D elements and the use of isoparametric formulations.
4. The history of FEM and how it has evolved from being used on mainframe computers to PCs.
A short introduction presentation about the Basics of Finite Element Analysis. This presentation mainly represents the applications of FEA in the real time world.
*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
INTRODUCTION TO FINITE ELEMENT ANALYSISAchyuth Peri
Finite element analysis (FEA) is a numerical technique used to find approximate solutions to partial differential equations. It involves dividing a system into small elements and solving for variables within each element. This allows for analysis of complex geometries, loadings, and materials. The FEM process includes discretizing the system, selecting functions to approximate the solution, assembling element equations into a global system, applying boundary conditions, and calculating displacements, stresses, and strains. FEA offers advantages like analyzing irregular shapes and nonlinear problems, reducing testing costs, and optimizing designs.
Finite element analysis (FEA) is a numerical technique used to find approximate solutions to partial differential equations. It divides a complex problem into small elements that can be solved together. FEA uses a grid of nodes and meshes to model how a structure will react to loads based on its material properties. It can be used for structural, vibrational, fatigue, and heat transfer analysis to help engineers design structures with irregular shapes or complex conditions.
This document outlines the course structure and content for ECE 2408 Theory of Structures V. The course introduces finite element methods for structural analysis. It covers matrix analysis of structures, force and deformation methods, and the use of finite element analysis software. The document compares analytical and finite element analysis methods and explains the key steps in finite element modeling and analysis, including discretization, deriving element stiffness matrices, assembling the global stiffness matrix, applying boundary conditions, and solving for displacements, strains and stresses. The course aims to provide students with skills in using finite element analysis for structural design and problem solving.
The document provides an introduction to finite element methods. It discusses how finite element analysis (FEA) is used to solve complex engineering problems that cannot be solved through closed-form analytical methods. The key steps of FEA include discretizing the domain into finite elements, deriving element equations, assembling equations into a global system of equations, and solving the system of equations. Common element types include line, triangular, and brick elements. The accuracy of FEA depends on factors like element size and shape, approximation functions, and numerical integration.
The document provides an introduction to finite element analysis (FEA) including:
1) FEA involves discretizing a continuous structure into small substructures called finite elements connected at nodes. This process is called meshing.
2) The finite element method has three main phases - preprocessing (defining geometry, materials, mesh), solution (solving equations to obtain nodal results), and postprocessing (obtaining stresses, strains from nodal results).
3) FEA can model complex problems that cannot be solved analytically due to complicated geometry or materials, and is well-suited for solving problems in solid mechanics, heat transfer, and other fields on computers.
Lecture on Introduction to finite element methods & its contentsMesayAlemuTolcha1
The document provides an overview of the Finite Element Method (FEM) course being taught. It discusses:
1. What FEM is and its common application areas like structural analysis, heat transfer, fluid flow.
2. The main steps in FEM including discretization, selecting interpolation functions, developing element matrices, assembling the global matrix, imposing boundary conditions, and solving equations.
3. Different element types like 1D, 2D, and 3D elements and the use of isoparametric formulations.
4. The history of FEM and how it has evolved from being used on mainframe computers to PCs.
A short introduction presentation about the Basics of Finite Element Analysis. This presentation mainly represents the applications of FEA in the real time world.
*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
INTRODUCTION TO FINITE ELEMENT ANALYSISAchyuth Peri
Finite element analysis (FEA) is a numerical technique used to find approximate solutions to partial differential equations. It involves dividing a system into small elements and solving for variables within each element. This allows for analysis of complex geometries, loadings, and materials. The FEM process includes discretizing the system, selecting functions to approximate the solution, assembling element equations into a global system, applying boundary conditions, and calculating displacements, stresses, and strains. FEA offers advantages like analyzing irregular shapes and nonlinear problems, reducing testing costs, and optimizing designs.
Finite element analysis (FEA) is a numerical technique used to find approximate solutions to partial differential equations. It divides a complex problem into small elements that can be solved together. FEA uses a grid of nodes and meshes to model how a structure will react to loads based on its material properties. It can be used for structural, vibrational, fatigue, and heat transfer analysis to help engineers design structures with irregular shapes or complex conditions.
This document outlines the course structure and content for ECE 2408 Theory of Structures V. The course introduces finite element methods for structural analysis. It covers matrix analysis of structures, force and deformation methods, and the use of finite element analysis software. The document compares analytical and finite element analysis methods and explains the key steps in finite element modeling and analysis, including discretization, deriving element stiffness matrices, assembling the global stiffness matrix, applying boundary conditions, and solving for displacements, strains and stresses. The course aims to provide students with skills in using finite element analysis for structural design and problem solving.
The document provides an introduction to finite element methods. It discusses how finite element analysis (FEA) is used to solve complex engineering problems that cannot be solved through closed-form analytical methods. The key steps of FEA include discretizing the domain into finite elements, deriving element equations, assembling equations into a global system of equations, and solving the system of equations. Common element types include line, triangular, and brick elements. The accuracy of FEA depends on factors like element size and shape, approximation functions, and numerical integration.
The document provides an introduction to finite element methods. It discusses how finite element analysis (FEA) is used to solve engineering and science problems involving complex geometries and conditions. FEA works by dividing a body into finite elements and approximating variable fields within each element. This discretization process sets up algebraic equations that approximate the continuous solution. FEA can model problems with complex shapes, loads, materials and include time-dependent effects. It has advantages over closed-form solutions and its accuracy can be improved by refining the mesh. Examples of 1D and 2D elements and approximations are presented.
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.
The document provides an introduction to finite element analysis. It discusses the need for computational methods to solve problems involving complex geometries and boundary conditions that cannot be solved through closed-form analytical methods. The finite element method is introduced as a numerical technique that involves discretizing a continuous domain into discrete subdomains called elements, and approximating variations in dependent variables within each element. This allows setting up algebraic equations that can be solved to approximate the continuous solution. Advantages of the finite element method include its ability to model complex shapes and behaviors, and refine solutions through mesh refinement. Basic concepts such as element types, discretization, and derivation of element equations are described.
Introduction of finite element analysis1ssuser2209b4
The document provides an introduction to the finite element method (FEM). It discusses the different numerical, analytical, and experimental methods used to solve engineering problems. FEM involves discretizing a continuous domain into smaller, finite pieces called elements and using a mathematical representation to approximate the solution. It describes how FEM builds a stiffness matrix and assembles element equations to solve for unknown displacements. The document outlines the general FEM steps and highlights the merits and limitations of FEM, giving examples of its applications in stress analysis of industrial parts, fluid flow analysis, electromagnetic problems, and medical procedures.
The document provides an overview of the finite element method (FEM). It explains that FEM is a numerical technique used to approximate solutions to partial differential equations that describe physical phenomena. It works by dividing a complex geometry into small pieces called finite elements that can then be solved using a computer. The method was developed in the 1950s and has since become widely used in engineering fields to simulate systems like heat transfer, stress analysis, and fluid flow. The document outlines the basic approach of FEM and traces the history and development of its early software programs.
Topics to be discussed-
Introduction
How Does FEM Works?
Types Of Engineering Analysis
Uses of FEM in different fields
How can the FEM Help the Design Engineer?
How can the FEM Help the Design Organization?
Basic Steps & Phases Involved In FEM
Advantages and disadvantages
The Future Scope
References.
This document describes a case study analyzing the maximum deflection of a cantilever beam using finite element analysis software ANSYS. It first provides background on finite element analysis and its general steps. It then outlines the specific steps taken in ANSYS to model and analyze a cantilever beam with an end load, including preprocessing, solution, and postprocessing stages. The results found the maximum deflection to be 0.73648m and the von-mises stress to be 286.19 N/m. The document concludes with thanks for reading.
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 the finite element method (FEM). FEM is a numerical technique used to find approximate solutions to partial differential equations. It divides a complex problem into small, simpler elements that are solved using relations between each other. There are three phases: pre-processing to mesh the geometry and apply properties/conditions, solution to derive equations and solve for quantities, and post-processing to validate solutions. FEM can model various problem types like static, dynamic, structural, vibrational, and heat transfer analyses. It has advantages like handling complex geometries and loadings but also disadvantages like requiring approximations and computational resources.
This document outlines a Computer Aided Engineering course for third year mechanical engineering students. The course objectives are to understand CAE concepts and finite element analysis, learn discretization and meshing techniques, apply FEM to solve mechanics problems, and study applications in domains like computational fluid dynamics, injection molding, and manufacturing simulations. The syllabus covers elemental properties, meshing, 1D and 2D finite element analysis, nonlinear and dynamic analysis, and applications. References include textbooks and online courses on finite element basics, advanced analysis, and ANSYS tutorials.
This document provides an overview of basic linear static finite element analysis (FEA). It defines key terms related to FEA and outlines important assumptions of linear static analysis. It also describes different types of linear static analysis (3D, planar, axisymmetric, etc.) and discusses modeling considerations such as applying boundary conditions and utilizing symmetry. The document is intended to help readers familiar with statics and mechanics of materials better understand how to apply FEA to engineering problems.
The document compares the finite element method (FEM) and finite difference method (FDM) for numerical analysis of physical systems. FEM discretizes the continuous domain into elements and uses basis functions to represent the solution within each element. FDM directly discretizes the differential equations governing the physical system using finite difference approximations of derivatives. Both methods divide the domain into a grid of nodes to obtain a system of equations that can be solved numerically to approximate the solution.
The document provides an introduction to the finite element method (FEM). It explains that FEM is a numerical method used to approximate solutions to partial differential equations. It works by dividing a complex problem into smaller, simpler parts called finite elements. This allows for the problem to be solved computationally. The document outlines the basic steps of FEM, including preprocessing (modeling, meshing), solving, and postprocessing (analyzing results). It also discusses applications, history, software, element types, meshing, convergence, and compatibility conditions of FEM.
Part 1_Methods for mechanically analysing a solid structure(1).pdfSajawalNawaz5
The document provides an overview of finite element analysis (FEA) theory. It discusses the basic principles of FEA, including reducing complex structures into small elements defined by nodes. The behavior of each element is described using mechanics equations, and the overall structural behavior is calculated by assembling the equations. The document outlines different types of 2D and 3D elements that can be used, such as truss, beam, membrane, and plate elements. It also discusses meshing and node properties.
This document discusses numerical methods for solving engineering problems. It introduces analytical methods, numerical methods, and experimental methods. It then describes various numerical methods in more detail, including the finite element method (FEM), finite difference method (FDM), finite volume method (FVM), and boundary element method (BEM). It provides examples of the types of problems each method can be applied to and notes the advantages and limitations of each approach.
Finite element analysis (FEA) is a numerical technique used to approximate solutions to boundary value problems by dividing the domain into smaller elements. The document discusses the three main stages of FEA: building the model, solving the model, and displaying the results. It provides details on how to create nodes and finite elements to represent an object's geometry, assign material properties and constraints, define the type of analysis, and select parameters to display in the results. Examples of different types of FEA analyses are also listed, such as static, thermal, modal, and buckling analyses.
This document discusses sources of error in finite element analysis, including modeling errors due to simplifying assumptions, discretization errors from approximating solutions, and numerical errors from limited computer precision. It provides examples of common mistakes that can cause incorrect results, such as incorrect material properties or insufficient boundary constraints. It also discusses best practices for verifying models, such as element testing, mesh refinement studies, and checking results against analytical solutions or boundary conditions.
Computer Aided Engineering (CAE) uses computer software to simulate product performance in order to improve designs. The CAE process involves pre-processing to create models, solving using mathematical physics, and post-processing results. CAE allows designs to be evaluated using simulation rather than prototypes, saving time and money. Finite Element Analysis is a numerical technique used in CAE to approximate solutions to engineering problems. Common CAE applications include stress analysis, thermal/fluid analysis, and manufacturing simulation.
Finite element analysis (FEA) involves breaking a model down into small pieces called finite elements. FEA was first developed in 1943 and involved numerical analysis techniques. By the 1970s, FEA was used primarily by aerospace, automotive, and defense industries due to the high cost of computers. Modern FEA involves preprocessing like meshing a model, applying properties and boundary conditions, solving the model using software, and postprocessing to analyze results like stresses and displacements.
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.
More Related Content
Similar to Unit I fdocuments.in_introduction-to-fea-and-applications.ppt
The document provides an introduction to finite element methods. It discusses how finite element analysis (FEA) is used to solve engineering and science problems involving complex geometries and conditions. FEA works by dividing a body into finite elements and approximating variable fields within each element. This discretization process sets up algebraic equations that approximate the continuous solution. FEA can model problems with complex shapes, loads, materials and include time-dependent effects. It has advantages over closed-form solutions and its accuracy can be improved by refining the mesh. Examples of 1D and 2D elements and approximations are presented.
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.
The document provides an introduction to finite element analysis. It discusses the need for computational methods to solve problems involving complex geometries and boundary conditions that cannot be solved through closed-form analytical methods. The finite element method is introduced as a numerical technique that involves discretizing a continuous domain into discrete subdomains called elements, and approximating variations in dependent variables within each element. This allows setting up algebraic equations that can be solved to approximate the continuous solution. Advantages of the finite element method include its ability to model complex shapes and behaviors, and refine solutions through mesh refinement. Basic concepts such as element types, discretization, and derivation of element equations are described.
Introduction of finite element analysis1ssuser2209b4
The document provides an introduction to the finite element method (FEM). It discusses the different numerical, analytical, and experimental methods used to solve engineering problems. FEM involves discretizing a continuous domain into smaller, finite pieces called elements and using a mathematical representation to approximate the solution. It describes how FEM builds a stiffness matrix and assembles element equations to solve for unknown displacements. The document outlines the general FEM steps and highlights the merits and limitations of FEM, giving examples of its applications in stress analysis of industrial parts, fluid flow analysis, electromagnetic problems, and medical procedures.
The document provides an overview of the finite element method (FEM). It explains that FEM is a numerical technique used to approximate solutions to partial differential equations that describe physical phenomena. It works by dividing a complex geometry into small pieces called finite elements that can then be solved using a computer. The method was developed in the 1950s and has since become widely used in engineering fields to simulate systems like heat transfer, stress analysis, and fluid flow. The document outlines the basic approach of FEM and traces the history and development of its early software programs.
Topics to be discussed-
Introduction
How Does FEM Works?
Types Of Engineering Analysis
Uses of FEM in different fields
How can the FEM Help the Design Engineer?
How can the FEM Help the Design Organization?
Basic Steps & Phases Involved In FEM
Advantages and disadvantages
The Future Scope
References.
This document describes a case study analyzing the maximum deflection of a cantilever beam using finite element analysis software ANSYS. It first provides background on finite element analysis and its general steps. It then outlines the specific steps taken in ANSYS to model and analyze a cantilever beam with an end load, including preprocessing, solution, and postprocessing stages. The results found the maximum deflection to be 0.73648m and the von-mises stress to be 286.19 N/m. The document concludes with thanks for reading.
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 the finite element method (FEM). FEM is a numerical technique used to find approximate solutions to partial differential equations. It divides a complex problem into small, simpler elements that are solved using relations between each other. There are three phases: pre-processing to mesh the geometry and apply properties/conditions, solution to derive equations and solve for quantities, and post-processing to validate solutions. FEM can model various problem types like static, dynamic, structural, vibrational, and heat transfer analyses. It has advantages like handling complex geometries and loadings but also disadvantages like requiring approximations and computational resources.
This document outlines a Computer Aided Engineering course for third year mechanical engineering students. The course objectives are to understand CAE concepts and finite element analysis, learn discretization and meshing techniques, apply FEM to solve mechanics problems, and study applications in domains like computational fluid dynamics, injection molding, and manufacturing simulations. The syllabus covers elemental properties, meshing, 1D and 2D finite element analysis, nonlinear and dynamic analysis, and applications. References include textbooks and online courses on finite element basics, advanced analysis, and ANSYS tutorials.
This document provides an overview of basic linear static finite element analysis (FEA). It defines key terms related to FEA and outlines important assumptions of linear static analysis. It also describes different types of linear static analysis (3D, planar, axisymmetric, etc.) and discusses modeling considerations such as applying boundary conditions and utilizing symmetry. The document is intended to help readers familiar with statics and mechanics of materials better understand how to apply FEA to engineering problems.
The document compares the finite element method (FEM) and finite difference method (FDM) for numerical analysis of physical systems. FEM discretizes the continuous domain into elements and uses basis functions to represent the solution within each element. FDM directly discretizes the differential equations governing the physical system using finite difference approximations of derivatives. Both methods divide the domain into a grid of nodes to obtain a system of equations that can be solved numerically to approximate the solution.
The document provides an introduction to the finite element method (FEM). It explains that FEM is a numerical method used to approximate solutions to partial differential equations. It works by dividing a complex problem into smaller, simpler parts called finite elements. This allows for the problem to be solved computationally. The document outlines the basic steps of FEM, including preprocessing (modeling, meshing), solving, and postprocessing (analyzing results). It also discusses applications, history, software, element types, meshing, convergence, and compatibility conditions of FEM.
Part 1_Methods for mechanically analysing a solid structure(1).pdfSajawalNawaz5
The document provides an overview of finite element analysis (FEA) theory. It discusses the basic principles of FEA, including reducing complex structures into small elements defined by nodes. The behavior of each element is described using mechanics equations, and the overall structural behavior is calculated by assembling the equations. The document outlines different types of 2D and 3D elements that can be used, such as truss, beam, membrane, and plate elements. It also discusses meshing and node properties.
This document discusses numerical methods for solving engineering problems. It introduces analytical methods, numerical methods, and experimental methods. It then describes various numerical methods in more detail, including the finite element method (FEM), finite difference method (FDM), finite volume method (FVM), and boundary element method (BEM). It provides examples of the types of problems each method can be applied to and notes the advantages and limitations of each approach.
Finite element analysis (FEA) is a numerical technique used to approximate solutions to boundary value problems by dividing the domain into smaller elements. The document discusses the three main stages of FEA: building the model, solving the model, and displaying the results. It provides details on how to create nodes and finite elements to represent an object's geometry, assign material properties and constraints, define the type of analysis, and select parameters to display in the results. Examples of different types of FEA analyses are also listed, such as static, thermal, modal, and buckling analyses.
This document discusses sources of error in finite element analysis, including modeling errors due to simplifying assumptions, discretization errors from approximating solutions, and numerical errors from limited computer precision. It provides examples of common mistakes that can cause incorrect results, such as incorrect material properties or insufficient boundary constraints. It also discusses best practices for verifying models, such as element testing, mesh refinement studies, and checking results against analytical solutions or boundary conditions.
Computer Aided Engineering (CAE) uses computer software to simulate product performance in order to improve designs. The CAE process involves pre-processing to create models, solving using mathematical physics, and post-processing results. CAE allows designs to be evaluated using simulation rather than prototypes, saving time and money. Finite Element Analysis is a numerical technique used in CAE to approximate solutions to engineering problems. Common CAE applications include stress analysis, thermal/fluid analysis, and manufacturing simulation.
Finite element analysis (FEA) involves breaking a model down into small pieces called finite elements. FEA was first developed in 1943 and involved numerical analysis techniques. By the 1970s, FEA was used primarily by aerospace, automotive, and defense industries due to the high cost of computers. Modern FEA involves preprocessing like meshing a model, applying properties and boundary conditions, solving the model using software, and postprocessing to analyze results like stresses and displacements.
Similar to Unit I fdocuments.in_introduction-to-fea-and-applications.ppt (20)
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.
Batteries -Introduction – Types of Batteries – discharging and charging of battery - characteristics of battery –battery rating- various tests on battery- – Primary battery: silver button cell- Secondary battery :Ni-Cd battery-modern battery: lithium ion battery-maintenance of batteries-choices of batteries for electric vehicle applications.
Fuel Cells: Introduction- importance and classification of fuel cells - description, principle, components, applications of fuel cells: H2-O2 fuel cell, alkaline fuel cell, molten carbonate fuel cell and direct methanol fuel cells.
TIME DIVISION MULTIPLEXING TECHNIQUE FOR COMMUNICATION SYSTEMHODECEDSIET
Time Division Multiplexing (TDM) is a method of transmitting multiple signals over a single communication channel by dividing the signal into many segments, each having a very short duration of time. These time slots are then allocated to different data streams, allowing multiple signals to share the same transmission medium efficiently. TDM is widely used in telecommunications and data communication systems.
### How TDM Works
1. **Time Slots Allocation**: The core principle of TDM is to assign distinct time slots to each signal. During each time slot, the respective signal is transmitted, and then the process repeats cyclically. For example, if there are four signals to be transmitted, the TDM cycle will divide time into four slots, each assigned to one signal.
2. **Synchronization**: Synchronization is crucial in TDM systems to ensure that the signals are correctly aligned with their respective time slots. Both the transmitter and receiver must be synchronized to avoid any overlap or loss of data. This synchronization is typically maintained by a clock signal that ensures time slots are accurately aligned.
3. **Frame Structure**: TDM data is organized into frames, where each frame consists of a set of time slots. Each frame is repeated at regular intervals, ensuring continuous transmission of data streams. The frame structure helps in managing the data streams and maintaining the synchronization between the transmitter and receiver.
4. **Multiplexer and Demultiplexer**: At the transmitting end, a multiplexer combines multiple input signals into a single composite signal by assigning each signal to a specific time slot. At the receiving end, a demultiplexer separates the composite signal back into individual signals based on their respective time slots.
### Types of TDM
1. **Synchronous TDM**: In synchronous TDM, time slots are pre-assigned to each signal, regardless of whether the signal has data to transmit or not. This can lead to inefficiencies if some time slots remain empty due to the absence of data.
2. **Asynchronous TDM (or Statistical TDM)**: Asynchronous TDM addresses the inefficiencies of synchronous TDM by allocating time slots dynamically based on the presence of data. Time slots are assigned only when there is data to transmit, which optimizes the use of the communication channel.
### Applications of TDM
- **Telecommunications**: TDM is extensively used in telecommunication systems, such as in T1 and E1 lines, where multiple telephone calls are transmitted over a single line by assigning each call to a specific time slot.
- **Digital Audio and Video Broadcasting**: TDM is used in broadcasting systems to transmit multiple audio or video streams over a single channel, ensuring efficient use of bandwidth.
- **Computer Networks**: TDM is used in network protocols and systems to manage the transmission of data from multiple sources over a single network medium.
### Advantages of TDM
- **Efficient Use of Bandwidth**: TDM all
Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024Sinan KOZAK
Sinan from the Delivery Hero mobile infrastructure engineering team shares a deep dive into performance acceleration with Gradle build cache optimizations. Sinan shares their journey into solving complex build-cache problems that affect Gradle builds. By understanding the challenges and solutions found in our journey, we aim to demonstrate the possibilities for faster builds. The case study reveals how overlapping outputs and cache misconfigurations led to significant increases in build times, especially as the project scaled up with numerous modules using Paparazzi tests. The journey from diagnosing to defeating cache issues offers invaluable lessons on maintaining cache integrity without sacrificing functionality.
DEEP LEARNING FOR SMART GRID INTRUSION DETECTION: A HYBRID CNN-LSTM-BASED MODELgerogepatton
As digital technology becomes more deeply embedded in power systems, protecting the communication
networks of Smart Grids (SG) has emerged as a critical concern. Distributed Network Protocol 3 (DNP3)
represents a multi-tiered application layer protocol extensively utilized in Supervisory Control and Data
Acquisition (SCADA)-based smart grids to facilitate real-time data gathering and control functionalities.
Robust Intrusion Detection Systems (IDS) are necessary for early threat detection and mitigation because
of the interconnection of these networks, which makes them vulnerable to a variety of cyberattacks. To
solve this issue, this paper develops a hybrid Deep Learning (DL) model specifically designed for intrusion
detection in smart grids. The proposed approach is a combination of the Convolutional Neural Network
(CNN) and the Long-Short-Term Memory algorithms (LSTM). We employed a recent intrusion detection
dataset (DNP3), which focuses on unauthorized commands and Denial of Service (DoS) cyberattacks, to
train and test our model. The results of our experiments show that our CNN-LSTM method is much better
at finding smart grid intrusions than other deep learning algorithms used for classification. In addition,
our proposed approach improves accuracy, precision, recall, and F1 score, achieving a high detection
accuracy rate of 99.50%.
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.
Understanding Inductive Bias in Machine LearningSUTEJAS
This presentation explores the concept of inductive bias in machine learning. It explains how algorithms come with built-in assumptions and preferences that guide the learning process. You'll learn about the different types of inductive bias and how they can impact the performance and generalizability of machine learning models.
The presentation also covers the positive and negative aspects of inductive bias, along with strategies for mitigating potential drawbacks. We'll explore examples of how bias manifests in algorithms like neural networks and decision trees.
By understanding inductive bias, you can gain valuable insights into how machine learning models work and make informed decisions when building and deploying them.
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.
Harnessing WebAssembly for Real-time Stateless Streaming PipelinesChristina Lin
Traditionally, dealing with real-time data pipelines has involved significant overhead, even for straightforward tasks like data transformation or masking. However, in this talk, we’ll venture into the dynamic realm of WebAssembly (WASM) and discover how it can revolutionize the creation of stateless streaming pipelines within a Kafka (Redpanda) broker. These pipelines are adept at managing low-latency, high-data-volume scenarios.
Comparative analysis between traditional aquaponics and reconstructed aquapon...bijceesjournal
The aquaponic system of planting is a method that does not require soil usage. It is a method that only needs water, fish, lava rocks (a substitute for soil), and plants. Aquaponic systems are sustainable and environmentally friendly. Its use not only helps to plant in small spaces but also helps reduce artificial chemical use and minimizes excess water use, as aquaponics consumes 90% less water than soil-based gardening. The study applied a descriptive and experimental design to assess and compare conventional and reconstructed aquaponic methods for reproducing tomatoes. The researchers created an observation checklist to determine the significant factors of the study. The study aims to determine the significant difference between traditional aquaponics and reconstructed aquaponics systems propagating tomatoes in terms of height, weight, girth, and number of fruits. The reconstructed aquaponics system’s higher growth yield results in a much more nourished crop than the traditional aquaponics system. It is superior in its number of fruits, height, weight, and girth measurement. Moreover, the reconstructed aquaponics system is proven to eliminate all the hindrances present in the traditional aquaponics system, which are overcrowding of fish, algae growth, pest problems, contaminated water, and dead fish.
Comparative analysis between traditional aquaponics and reconstructed aquapon...
Unit I fdocuments.in_introduction-to-fea-and-applications.ppt
1. Introduction to Design with Finite Element
Approach and Applications to Engineering
Problems
Dr. K. Padmanabhan FIIPE, FIE, CE(I),FISME
Professor
Manufacturing Division
School of MBS
VIT-University
Vellore 632014
February 2013
2. FEA Introduction
• Numerical method used for solving
problems that cannot be solved
analytically (e.g., due to complicated
geometry, different materials)
• Well suited to computers
• Originally applied to problems in solid
mechanics
• Other application areas include heat
transfer, fluid flow, electromagnetism
3. Finite Element Method Phases
• Preprocessing
– Geometry
– Modelling analysis type
– Material properties
– Mesh
– Boundary conditions
• Solution
– Solve linear or nonlinear algebraic equations
simultaneously to obtain nodal results
(displacements, temperatures etc.)
• Postprocessing
– Obtain other results (stresses, heat fluxes)
4. FEA Discretization Process -
Meshing
• Continuous elastic structure
(geometric continuum) divided
into small (but finite), well-
defined substructures, called
elements
• Elements are connected
together at nodes; nodes have
degrees of freedom
• Discretization process known as
meshing
6. Spring Analogy
, ,
, similar to
F l
E
A l
EA
F l F kx
l
, ,
, similar to
F l
E
A l
EA
F l F kx
l
Elements modelled as linear springs
7. Matrix Formulation
• Local elastic behaviour of each element
defined in matrix form in terms of loading,
displacement, and stiffness
– Stiffness determined by geometry and material
properties (AE/l)
8. Global Matrix Formulation
• Elements assembled through common
nodes into a global matrix
• Global boundary conditions (loads and
supports) applied to nodes (in practice,
applied to underlying geometry)
1 1 2 2 1
2 2 2 2
F K K K U
F K K U
9. Solution
• Matrix operations used to determine
unknown dof’s (e.g., nodal displacements)
• Run time proportional to #nodes or
elements
• Error messages
– “Bad” elements
– Insufficient disk space, RAM
– Insufficiently constrained
11. FEA Prerequisites
• First Principles (Newton’s Laws)
– Body under external loading
• Area Moments of Inertia
• Stress and Strain
– Principal stresses
– Stress states: bending, shear, torsion,
pressure, contact, thermal expansion
– Stress concentration factors
• Material Properties
• Failure Modes
• Dynamic Analysis
12. Theoretical Basis: Formulating Element Equations
• Several approaches can be used to transform the physical
formulation of a problem to its finite element discrete analogue.
• If the physical formulation of the problem is described as a
differential equation, then the most popular solution method is
the Method of Weighted Residuals.
• If the physical problem can be formulated as the minimization
of a functional, then the Variational Formulation is usually
used.
13. Theoretical Basis: MWR
• One family of methods used to numerically solve differential equations
are called the methods of weighted residuals (MWR).
• In the MWR, an approximate solution is substituted into the differential
equation. Since the approximate solution does not identically satisfy the
equation, a residual, or error term, results.
Consider a differential equation
Dy’’(x) + Q = 0 (1)
Suppose that y = h(x) is an approximate solution to (1). Substitution then
gives Dh’’(x) + Q = R, where R is a nonzero residual. The MWR then
requires that
Wi(x)R(x) = 0 (2)
where Wi(x) are the weighting functions. The number of weighting
functions equals the number of unknown coefficients in the approximate
solution.
14. Theoretical Basis: Galerkin’s Method
• There are several choices for the weighting functions, Wi.
• In the Galerkin’s method, the weighting functions are the same
functions that were used in the approximating equation.
• The Galerkin’s method yields the same results as the variational
method when applied to differential equations that are self-adjoint.
• The MWR is therefore an integral solution method. The weighted
integral is called the weak form.
• Many readers may find it unusual to see a numerical solution that
is based on an integral formulation.
15. Theoretical Basis: Variational Method
• The variational method involves the integral of a function that
produces a number. Each new function produces a new
number.
• The function that produces the lowest number has the
additional property of satisfying a specific differential equation.
• Consider the integral
p D/2 * y’’(x) - Qy]dx = 0. (1)
The numerical value of pcan be calculated given a specific
equation y = f(x). Variational calculus shows that the
particular equation y = g(x) which yields the lowest numerical
value for pis the solution to the differential equation
Dy’’(x) + Q = 0. (2)
16. Theoretical Basis: Variational Method (cont.)
• In solid mechanics, the so-called Rayeigh-Ritz technique
uses the Theorem of Minimum Potential Energy (with the
potential energy being the functional, p) to develop the
element equations.
• The trial solution that gives the minimum value of pis the
approximate solution.
• In other specialty areas, a variational principle can usually
be found.
17. Sources of Error in the FEM
• The three main sources of error in a typical FEM solution are
discretization errors, formulation errors and numerical errors.
• Discretization error results from transforming the physical
system (continuum) into a finite element model, and can be
related to modeling the boundary shape, the boundary
conditions, etc.
Discretization error due to poor
geometry representation.
Discretization error effectively
eliminated.
18. Sources of Error in the FEM (cont.)
• Formulation error results from the use of elements that don't precisely
describe the behavior of the physical problem.
• Elements which are used to model physical problems for which they are
not suited are sometimes referred to as ill-conditioned or
mathematically unsuitable elements.
• For example a particular finite element might be formulated on the
assumption that displacements vary in a linear manner over the
domain. Such an element will produce no formulation error when it is
used to model a linearly varying physical problem (linear varying
displacement field in this example), but would create a significant
formulation error if it used to represent a quadratic or cubic varying
displacement field.
19. Sources of Error in the FEM (cont.)
• Numerical error occurs as a result of
numerical calculation procedures, and
includes truncation errors and round off
errors.
• Numerical error is therefore a problem mainly
concerning the FEM vendors and developers.
• The user can also contribute to the numerical
accuracy, for example, by specifying a
physical quantity, say Young’s modulus, E, to
an inadequate number of decimal places.
20. Advantages of the Finite Element Method
• Can readily handle complex geometry:
• The heart and power of the FEM.
• Can handle complex analysis types:
• Vibration
• Transients
• Nonlinear
• Heat transfer
• Fluids
• Can handle complex loading:
• Node-based loading (point loads).
• Element-based loading (pressure, thermal, inertial
forces).
• Time or frequency dependent loading.
• Can handle complex restraints:
• Indeterminate structures can be analyzed.
21. Advantages of the Finite Element Method (cont.)
• Can handle bodies comprised of nonhomogeneous materials:
• Every element in the model could be assigned a different
set of material properties.
• Can handle bodies comprised of nonisotropic materials:
• Orthotropic
• Anisotropic
• Special material effects are handled:
• Temperature dependent properties.
• Plasticity
• Creep
• Swelling
• Special geometric effects can be modeled:
• Large displacements.
• Large rotations.
• Contact (gap) condition.
22. Disadvantages of the Finite Element Method
• A specific numerical result is obtained for a specific
problem. A general closed-form solution, which would
permit one to examine system response to changes in
various parameters, is not produced.
• The FEM is applied to an approximation of the mathematical
model of a system (the source of so-called inherited errors.)
• Experience and judgment are needed in order to construct
a good finite element model.
• A powerful computer and reliable FEM software are
essential.
• Input and output data may be large and tedious to prepare
and interpret.
23. Disadvantages of the Finite Element Method (cont.)
• Numerical problems:
• Computers only carry a finite number of significant
digits.
• Round off and error accumulation.
• Can help the situation by not attaching stiff (small)
elements to flexible (large) elements.
• Susceptible to user-introduced modelling errors:
• Poor choice of element types.
• Distorted elements.
• Geometry not adequately modelled.
• Certain effects not automatically included:
• Complex Buckling
• Hybrid composites.
• Nanomaterials modelling .
• Multiple simultaneous causes.
25. • In this, we will briefly describe how to do
a thermal-stress analysis.
• The purpose is two-fold:
– To show you how to apply thermal loads in a
stress analysis.
– To introduce you to a coupled-field analysis.
Coupled Field Analysis
Overview
26. Thermally Induced Stress
• When a structure is heated or cooled,
it deforms by expanding or
contracting.
• If the deformation is somehow
restricted — by displacement
constraints or an opposing pressure,
for example — thermal stresses are
induced in the structure.
• Another cause of thermal stresses is
non-uniform deformation, due to
different materials (i.e, different
coefficients of thermal expansion).
Thermal stresses
due to constraints
Thermal stresses
due to different
materials
Coupled Field Analysis
…Overview
27. • There are two methods of solving thermal-stress problems
using ANSYS. Both methods have their advantages.
– Sequential coupled field
- Older method, uses two element types mapping thermal
results as structural temperature loads
+ Efficient when running many thermal transient time
points but few structural time points
+ Can easily be automated with input files
– Direct coupled field
+ Newer method uses one element type to solve both
physics problems
+ Allows true coupling between thermal and structural
phenomena
- May carry unnecessary overhead for some analyses
Coupled Field Analysis
…Overview
28. • The Sequential method involves two
analyses:
1. First do a steady-state (or transient)
thermal analysis.
• Model with thermal elements.
• Apply thermal loading.
• Solve and review results.
2. Then do a static structural analysis.
• Switch element types to structural.
• Define structural material
properties, including thermal
expansion coefficient.
• Apply structural loading, including
temperatures from thermal
analysis.
• Solve and review results.
Thermal
Analysis
Structural
Analysis
jobname.rth
jobname.rst
Temperatures
Coupled Field Analysis
A. Sequential Method
29. • The Direct Method usually involves just one analysis that
uses a coupled-field element type containing all
necessary degrees of freedom.
1. First prepare the model and mesh
using one of the following coupled
field element types.
• PLANE13 (plane solid).
• SOLID5 (hexahedron).
• SOLID98 (tetrahedron).
2. Apply both the structural and thermal
loads and constraints to the model.
3. Solve and review both thermal and
structural results.
Combined
Thermal
Analysis
Structural
Analysis
jobname.rst
Coupled Field Analysis
B. Direct Method
30. Coupled Field Analysis
Sequential vs. Direct Method
• Direct
– Direct coupling is
advantageous when the
coupled-field interaction is
highly nonlinear and is best
solved in a single solution
using a coupled
formulation.
– Examples of direct coupling
include piezoelectric
analysis, conjugate heat
transfer with fluid flow, and
circuit-electromagnetic
analysis.
• Sequential
– For coupling situations
which do not exhibit a high
degree of nonlinear
interaction, the sequential
method is more efficient
and flexible because you
can perform the two
analyses independently of
each other.
– You can use nodal
temperatures from ANY
load step or time-point in
the thermal analysis as
loads for the stress
analysis. .
31. Case Study 1: Composites in
Microelectronic Packaging
The BOM includes Copper lead frame,
Gold wires for bonding, Silver –epoxy
for die attach, Silicon die and Epoxy
mould composite with Phenolics, Fused
silica powder and Carbon black powder
as the encapsulant materials. Electrical-
Thermal and thermal-structural analyses.
32. Thermal – Structural Results
Displacement Vector sum Von mises stress
Stress intensity XY Shear stress
33. Case Study 2: Composites in
Prosthodontics
Tooth is a functionally graded
composite material with enamel
and dentin. In the third maxillary
molar the occlusal stress can
be 2-3 MPa.
The masticatory heavy chewing
stress will be around 193 MPa.
A composite restorative must with
stand this with an FOS and with
constant hygrothermal attack.
39. Outer diameter = 158mm
Inner diameter = 138mm
Height = 900mm
Poisson’s ratio = 0.29
Young’s Modulus = 2.15e5 N/mm2
The element used for this model is Solid 186.The
applied pressure is 0.430N/m2. For this analysis
large deformation was set ON and also Arc length
solution was turned ON.
Hollow Cylinder Dimensions
40. FEM METHOD
x: 0-2,y: 0-2.5
TOPOLOGICAL METHOD
x: 0-2, y: 0-2.5
Non-linear
0
0.5
1
1.5
2
2.5
3
0 1 2 3
x
y
x=0.1
1.25y=0.5x (4-x)
41. BI-MODAL BUCKLING
Two coaxial tubes, the inner one
of steel and cross-sectional area
As, and the outer one of
Aluminum alloy and of area Aa,
are compressed between heavy,
flat end plates, as shown in
figure. Assuming that the end
plates are so stiff that both tubes
are shortened by exactly the same
amount.
48. Case Study 4: Vibration of Composite
Plates
• Vibration studies in composites are
important as the composites are
increasingly being used in automotive,
aerospace and wind energy applications.
• The combined effect of vibrations and
fatigue can degrade a composite further
that is already hygrothermal in affinity.
• The different modes of vibrations are
discussed here.
49. Element selection for ANSYS SOLID 46
3D LAYERED STRUCTURAL SOLID ELEMENT
Element definition
─ Layered version of the 8-node, 3D solid element, solid 45 with three degrees
of freedom per node(UX,UY,UZ).
─ Designed to model thick layered shells or layered solids.
─ can stack several elements to model more than 250 layers to allow through-
the-thickness deformation discontinuities.
Layer definition
─ allows up to 250 uniform thickness layers per element.
─ allows 125 layers with thicknesses that may vary bilinearly.
─ user-input constitutive matrix option.
Options
─ Nonlinear capabilities including large strain.
─Failure criteria through TB,FAIL option.
50. Contd…
Analysis using ANSYS
After making detailed study of the element library of ANSYS it is
decided that SOLID 46 will be the best suited element for our
problem
The results obtained from analytical calculation is verified using
a standard analysis package ANSYS
52. Finding Storage Modulus (E’)
Using the formula taken from PSG Data Book Page 6.14 Storage
Modulus for the various specimens were determined
Natural frequency F = C√ (gEI/wL4)
where
F – Nodal Frequency
C – Constant
g – Acceleration due to gravity
E – Modulus of elasticity
I – Moment of inertia
L – Effective specimen length
w – Weight of the beam
53. ANSYS MODE SHAPE FOR CARBON FIBRE/EPOXY COMPOSITE
(a) First mode shape (b) second mode shape
(c) Third mode shape (d) Fourth mode shape
54. ANSYS MODE SHAPE FOR GLASS FIBRE/EPOXY COMPOSITE
(a) First mode shape (b) second mode shape
(c) Third mode shape (d) Fourth mode shape
55. ANSYS MODE SHAPE FOR GLASS/POLYPROPYLENE COMPOSITE
(a) First mode shape (b) second mode shape
(c) Third mode shape (d) Fourth mode shape
56. Contd…
TABLE: Frequency of the material analyzed up to 100Hz
Specimen Mode Shape
Natural Frequency (Hz) Storage Modulus E’ (GPa)
ANSYS Experiment ANSYS Experiment
GF-E
I
II
III
IV
1.9301
7.3176
9.7360
13.733
1.855
8.00
9.846
14.22
2.769
1.01
0.23
0.11
2.51
1.21
0.23
0.12
GF-PP
I
II
III
IV
1.913
5.733
9.6281
13.588
1.9104
6.40
9.90
12.799
1.14
0.26
0.11
0.06
1.14
0.32
0.10
0.05
CF-E
I
II
III
IV
1.7270
5.1793
8.7048
12.295
1.73
5.120
8.00
11.81
3.62
0.84
0.30
0.15
3.66
0.82
0.25
0.14
57. Determination of Loss Modulus (E”) and Loss Factor (tan δ)
Following Table shows the values for the loss factor (tan δ) of all specimens considered.
damping results obtained for composite materials studied
Specimen Inertia (m)4 E’ (Gpa) Tan δ E’’ (Gpa) E (Gpa)a
GE 3.25×10-11 12.05 0.0681 0.822 16.19
GPP 1.33×10-10 11.55 0.051 0.586 8.75
CE 1.66×10-11 50.54 0.095 4.806 14.48
a calculated by composite micromechanics approach
58. Case Study 5: Stabilizer Bars for
Four Wheelers
Anti-roll stabilizer bars for four wheelers. Fatigue life
of the stabilizer bars was estimated for qualification.
63. Case Study 6: LCA Generator
• The study deals with modeling, analysis and performance
evaluation of 5kW DC generator assembly. The complete solid
model of the generator with its accessories was modelled using
Pro-Engineer. This paper deals with the structural analysis of
the DC generator casing to find stress and deflection in the
generator casing due to load factor of 9g to which it is
designed. The effect of vibration of generator casing and
hollow shaft with mounting are investigated through detailed
finite element analysis. The bending and torsional natural
frequencies of the hollow shaft are estimated to find the
critical speeds. Torsional frequency of the hollow shaft is
estimated by considering the mass moment of inertias of the
rotating masses. For critical speed analysis of the hollow shaft,
it is considered as simply supported beam with the required
masses and inertias. Then the influence of the critical speeds
due to the casing stiffness is found out analyzing the casing
with the shaft together.
66. Total Deflection at 9g
Maximum deflection of the generator will be 4.761 microns, with-in limits !
67. Von Mises Stresses at 9g
A stress of about 6.756 MPa is much lesser than the Yield Stress of the material
68. Mode Shape of Generator Shaft
Mode shape corresponding to the flexural critical speed (54,972 rpm)
(using solid element TET10 approximation)
69. Conclusions
• The lecture introduced the subject `Introduction to
Finite Element Analysis (FEA) ’ to the undergraduate
audience. The basics, different approaches and the
formulations were outlined in the lecture. Emphasis
was laid on solving structural, mechanical and
multiphysics problems. Understanding the material
behaviour that is a prerequisite to the correct
modelling of the problem was also discussed. Some
engineering applications of the FE approach as
investigated by the speaker were illustrated for the
benefit of the student society and to enable them to
appreciate the depth of the subject field and take it
up as their career .
70. Rig Veda on Infinity
pûrnamadah pûrnamidam pûrnât
pûrnamudacyate pûrnâsya
pûrnamadaya pûrnamevâvasishyate
From infinity is born infinity.
When infinity is taken out of infinity,
only infinity is left over.