Finite Element Analysis -Dr.P.Parandaman
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This document provides an overview of finite element analysis (FEA). It defines FEA as a numerical method for solving governing equations over the domain of a continuous physical system that is discretized into simple shapes. It lists several common structural and non-structural applications of FEA, such as stress analysis, buckling problems, vibration analysis, and heat transfer. Finally, it provides the course outline, textbooks, references, and some common FEA software packages.
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For Guidance : Comment Below Happy to Teach and Learn along with you guys
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1. Write the weak form of the differential equation:
∫(AEδu - δu d2u/dx2 - aδux)dx = 0
2. Choose the trial function u(x) = a0 + a1x
3. Choose the weight function δu = 1, x, x2...
4. Substitute the trial function and weight functions into the weak form and integrate by parts.
5. Apply the essential boundary conditions to eliminate terms involving du/dx at boundaries.
6. Solve the resulting algebraic equations to determine the unknown coefficients a0 and a1
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- 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.
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01. steps involved, merits, demerits & limitations of fem
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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.
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This document provides the syllabus for the M.Tech program in Structural Engineering & Natural Disaster Management at GITAM University.
It outlines the courses offered in each semester, including the course code, name, credits, instruction scheme, and examination scheme for each. Some key courses include Theory of Elasticity, Advanced Reinforced Concrete Design, Finite Element Methods, Structural Dynamics, Earthquake Engineering, and Stability of Structures.
Students must complete a total of 82 credits over 4 semesters, including a research project in the third and fourth semesters. The document also lists recommended reference books for each course.
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The document describes the structure and content of the M.Tech Computer Science entrance exam. The exam consists of two tests - a morning objective test and an afternoon short answer test. The short answer test has two groups: Group A covers analytical ability and mathematics at the B.Sc. pass level, and Group B covers advanced topics in mathematics, statistics, physics, computer science, or engineering/technology depending on the candidate's choice. Sample questions are provided for both groups focusing on concepts like roots of unity, vector spaces, and differential equations.
Sample m.tech(cs)07
The document describes the structure and content of the M.Tech Computer Science entrance exam. The exam consists of two tests - a morning objective test and an afternoon short answer test. The short answer test has two groups: Group A covers analytical ability and mathematics at the B.Sc. pass level, and Group B covers advanced topics in mathematics, statistics, physics, computer science, or engineering/technology depending on the candidate's choice. Sample questions are provided for both groups focusing on concepts like roots of unity, vector spaces, and differential equations.
Fem utkarsh
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.
ANALYSIS.docx
This document provides information on the subject-wise weightage of topics in the GATE Mechanical Engineering exam over several years, as well as the GATE syllabus and important topics to prepare for common subjects like Thermodynamics, Theory of Machines & Vibrations, Manufacturing, and Strength of Materials. Engineering Mathematics, Thermal Engineering, and Manufacturing Engineering received the highest average weightages according to the tables presented. The GATE syllabus sections include topics like mechanics, design, fluids, materials, manufacturing, and industrial engineering. Suggested important topics to prepare within subjects include laws of thermodynamics, vibrations, manufacturing processes, and bending moment diagrams.
Lecture 1
This document discusses the introduction and historical development of using computers for structural engineering. Some key points:
- Computers revolutionized structural analysis methods and enabled the analysis of highly complex structures. Important milestones included the matrix method and finite element method.
- Common computer uses for engineers include analysis, design, drafting, and report preparation. Specialized structural analysis software like SAP2000, ETABS, ANSYS, and NASTRAN are discussed.
- The document covers computer hardware evolution, mathematical and CAD software, and compares computer methods to classical structural analysis techniques like slope-deflection. Flexibility and stiffness matrices are also introduced.
B.TECH-SMA-BOOKLET-1.pdf
This document provides information on the Department of Mechanical Engineering at Manav Rachna University. It includes the course details for the first semester of the B.Tech program in Mechanical Engineering, including the subject codes, names, nature (hard/soft), type (core/elective), credit hours, and contact hours for each subject. The core subjects include Chemistry, Mathematics-I, Engineering Mechanics, Basics of Electrical & Electronics Engineering, and Thermodynamics. It also lists the textbooks recommended for each subject.
Cad cam
This document outlines the course structure and syllabus for the M.Tech (CAD/CAM) program at Jawaharlal Nehru Technological University Hyderabad. It includes the list of subjects to be covered in the first and second semesters of the first year, as well as the first semester of the second year. Some of the key subjects covered are Advanced CAD, Advanced Finite Element Analysis, Precision Engineering, Design for Manufacturing and Assembly, Computer Aided Manufacturing, and a comprehensive project to be undertaken in the fourth semester. Detailed syllabi are provided for each subject, along with reference materials.
Unit-I--FEA
This document discusses the finite element method (FEM) for numerical analysis of engineering problems. It describes the general steps of FEM which include discretizing the domain into simple geometric elements, choosing interpolation functions, deriving the element stiffness matrices, assembling the matrices into a global system, applying boundary conditions, and solving for displacements/stresses. FEM allows for approximate solutions of complex problems involving various material properties, geometries, and loading conditions.
Introduction of Finite Element Analysis
This document discusses the finite element method (FEM) for numerical analysis of engineering problems. It describes the general steps of FEM which include discretizing the domain into simple geometric elements, choosing interpolation functions, deriving the element stiffness matrices, assembling the system to solve for displacements, and computing stresses and strains. FEM can be used to solve structural and non-structural problems and overcomes limitations of experimental and analytical methods for complex systems. The key aspects are subdividing the domain, selecting interpolation functions, deriving element equations, assembling the global system, applying boundary conditions, and solving for unknowns.
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- 1. 1 ME8692 FINITE ELEMENT ANALYSIS DHIRAJLAL GANDHI COLLEGE OF TECHNOLOGY Dr.P.Parandaman, M.E., Ph.D., Associate Professor, Department of Mechanical Engineering, Dhirajlal Gandhi College of Technology, Salem - 636309.
- 4. FEM is a numerical method for solving a system of governing equations over the domain of a continuous physical system, which is discretized into simple geometric shapes called finite element.
- 5. A 2 A 1 A 3 A 4 A 5 A 6 A=(A1)+ (A2)+ (A3)+ (A4)+ (A5)+ (A6)
- 6. Structural Problem Non-structural Problem Stress Analysis - truss & frame analysis - stress concentrated problem Buckling problem Vibration Analysis Impact Problem Heat Transfer Fluid Mechanics Electric or Magnetic Potential Applications of Finite Element Method
- 7. Structure analysis : a cantilever, a bridge, an oil platform… Solid mechanics : a gear, a automotive power train … Dynamics : vibration of Tower, earthquake, bullet impact… Thermal analysis : heat radiation of finned surface, thermal stress brake disc… Electrical analysis : Piezo actuator, electrical signal propagation… Biomaterials : human organs and tissues…
- 16. ME8692 FINITE ELEMENT ANALYSIS UNIT I INTRODUCTION Historical Background – Mathematical Modeling of field problems in Engineering – Governing Equations – Discrete and continuous models – Boundary, Initial and Eigen Value problems– Weighted Residual Methods – Variational Formulation of Boundary Value Problems – Ritz Technique – Basic concepts of the Finite Element Method.
- 17. ME8692 FINITE ELEMENT ANALYSIS UNIT II ONE-DIMENSIONAL PROBLEMS One Dimensional Second Order Equations – Discretization – Element types- Linear and Higher order Elements – Derivation of Shape functions and Stiffness matrices and force vectors- Assembly of Matrices - Solution of problems from solid mechanics and heat transfer. Longitudinal vibration frequencies and mode shapes. Fourth Order Beam Equation –Transverse deflections and Natural frequencies of beams.
- 18. ME8692 FINITE ELEMENT ANALYSIS UNIT III TWO DIMENSIONAL SCALAR VARIABLE PROBLEMS Second Order 2D Equations involving Scalar Variable Functions – Variational formulation – Finite Element formulation – Triangular elements – Shape functions and element matrices and vectors. Application to Field Problems - Thermal problems – Torsion of Non circular shafts –Quadrilateral elements – Higher Order Elements.
- 19. ME8692 FINITE ELEMENT ANALYSIS UNIT IV TWO DIMENSIONAL VECTOR VARIABLE PROBLEMS Equations of elasticity – Plane stress, plane strain and axisymmetric problems – Body forces and temperature effects – Stress calculations - Plate and shell elements.
- 20. ME8692 FINITE ELEMENT ANALYSIS UNIT V ISOPARAMETRIC FORMULATION Natural co-ordinate systems – Isoparametric elements – Shape functions for iso parametric elements – One and two dimensions – Serendipity elements – Numerical integration and application to plane stress problems - Matrix solution techniques – Solutions Techniques to Dynamic problems – Introduction to Analysis Software.
- 21. ME8692 FINITE ELEMENT ANALYSIS TEXT BOOKS: 1. Reddy. J.N., “An Introduction to the Finite Element Method”, 3rd Edition, Tata McGraw-Hill, 2005 2. Seshu, P, “Text Book of Finite Element Analysis”, Prentice-Hall of India Pvt. Ltd., New Delhi, 2007.
- 22. ME8692 FINITE ELEMENT ANALYSIS REFERENCES: 1. Bhatti Asghar M, "Fundamental Finite Element Analysis and Applications", John Wiley & Sons, 2005 (Indian Reprint 2013)* 2. Chandrupatla & Belagundu, “Introduction to Finite Elements in Engineering”, 3rd Edition, Prentice Hall College Div, 1990 3. Logan, D.L., “A first course in Finite Element Method”, Thomson Asia Pvt. Ltd., 2002 4. Rao, S.S., “The Finite Element Method in Engineering”, 3rd Edition, Butterworth Heinemann, 2004 5. Robert D. Cook, David S. Malkus, Michael E. Plesha, Robert J. Witt, “Concepts and Applications of Finite Element Analysis”, 4th Edition, Wiley Student Edition, 2002.
- 23. ANSYS NASTRAN ABAQUS MARC LS-DYNA3D MSC/DYNA ADAMS/ DADS COSMOS MOLDFLOW C-FLOW PHOENICS Soft wares for Finite Element Method