**MARMARA UNIVERSITY**

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FACULTY OF ENGINEERING**

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COURSE
INTRODUCTION FORM**

**ME 419 FEM (3)**

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Instructor :
Prof Dr. Bülent
Ekici

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Office:
MC 570

e-mail:
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bulent.ekici@marmara.edu.tr
**Tel: 0216
3480292/561

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Lecture Hours : **

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Office Hours : **
check my Program in this web site

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Course Objectives : **
First Course in the
Finite Element Analysis provides a simple, basic approach to the finite
element method that can be understood by both undergraduate and graduate
students. It does not have the usual prerequisites (such as structural
analysis) required by most available texts in this area. The book is written
primarily as a basic learning tool for the undergraduate student in civil
and mechanical engineering whose main interest is in stress analysis and
heat transfer. The text is geared toward those who want to apply the finite
element method as a tool to solve practical physical problems. This revised
fourth edition includes the addition of a large number of new problems
(including SI problems), an appendix for mechanical and thermal properties,
and more civil applications

**Prerequisite:**
Material science and mathematic courses

**References: **

**Lecture Contents : **
Chapter 1
- Introduction

Prologue. Brief History. Introduction to Matrix Notation. Role of the
Computer. General Steps of the Finite Element of Method. Applications of the
Finite Element Methods. Advantages of the Finite Element Method. Computer
Programs for the Finite Element Method. References. Problems.

Chapter 2 - Introduction to the Stiffness (Displacement) Method

Introduction. Definitions of the Stiffness Matrix. Derivation of the
Stiffness Matrix for a Spring Element. Example of a Spring Assemblage.
Assembling the Total Stiffness Matrix by Superposition (Direct Stiffness
Method). Boundary Conditions. Potential Energy Approach to Derive Spring
Element Equations. References. Problems.

Chapter 3 - Development of Truss Equations

Introduction. Derivation of the Stiffness Matrix for a Bar Element in Local
Coordinates. Selecting Approximation Functions for Displacements.
Transformation of Vectors in Two Dimensions. Global Stiffness Matrix.
Computation of Stress for a Bar in the x-y Plane. Solution of a Plane Truss.
Transformation Matrix and Stiffness Matrix for a Bar in Three-Dimensional
Space. Use of Symmetry in Structure. Inclined, or Skewed, Supports.
Potential Energy Approach to Derive Bar Element Equations. Comparison of
Finite Element Solution to Exact Solution for Bar. Galerkin's Residual
Method and Its Application to a One-Dimensional Bar. References. Problems.

Chapter 4 - Development of Beam Equations

Introduction. Beam Stiffness. Example of Assemblage of Beam Stiffness
Matrices. Examples of Beam Analysis Using the Direct Stiffness Method.
Distributed Loading. Comparison of Finite Element Solution to the Exact
Solution for a Beam. Beam Element with Nodal Hinge. Potential Energy
Approach to Derive Beam Element Equations. Galerkin's Method for Deriving
Beam Element Equations. References. Problems.

Chapter 5 - Frame and Grid Equations

Introduction. Two-Dimensional Arbitrarily Oriented Beam Element. Rigid Plane
Frame Examples. Inclined or Skewed Supports-Frame Element. Grid Equations.
Beam Element Arbitrarily Oriented in Space. Concepts of Substructure
Analysis. References. Problems.

Chapter 6 - Development of the Plane Stress and Plane Strain Stiffness
Equations

Introduction. Basic Concepts of Plane Stress and Plane Strain. Derivation of
the Constant-Strain Triangular Element Stiffness Matrix and Equations.
Treatment of Body and Surface Forces. Explicit Expression for the
Constant-Strain Triangle Stiffness Matrix. Finite Element Solution of a
Plane Stress Problem. References. Problems.

Chapter 7 - Practical Considerations in Modeling; Interpreting Results and
Examples of Plane Stress/Strain Analysis

Introduction. Finite Element Modeling. Equilibrium and Compatibility of
Finite Element Results. Convergence of Solution. Interpretation of Stresses.
Static Condensation. Flowchart for the Solution of Plane Stress Problems.
Computer Program Results for Some Plane Stress/Strain Problems. References.
Problems.

Chapter 8 - Development of the Linear-Strain Triangle Equations

Introduction. Derivation of the Linear-Strain Triangular Element Stiffness
Matrix and Equations. Example LST Stiffness Determination. Comparison of
Elements. References. Problems.

Chapter 9 - Axisymmetric Elements

Introduction. Derivation of the Stiffness Matrix. Solutions of an
Axisymmetric Pressure Vessel. Applications of Axisymmetric Elements.
References. Problems.

Chapter 10 - Isoparametric Formulation

Introduction. Isoparametric Formulation of the Bar Element Stiffness Matrix.
Rectangular Plane Stress Element. Isoparametric Formulation of the Plane
Element Stiffness Matrix. Gaussian Quadrature (Numerical Integration).
Evaluation of the Stiffness Matrix and Stress Matrix by Gaussian Quadrature.
Higher-Order Shape Functions. References. Problems.

Chapter 11 - Three-Dimensional Stress Analysis

Introduction. Three Dimensional Stress and Strain. Tetrahedral Element.
Isoparametric Formulation. References. Problems.

Chapter 12 - Plate Bending Element

Introduction. Basic Concepts of Plate Bending. Derivation of a Plate Bending
Element Stiffness Matrix and Equations. Some Plate Element Numerical
Comparisons. Computer Solutions for a Plate Bending Problem. References.
Problems.

Chapter 13 - Heat Transfer and Mass Transport

Introduction. Derivation of the Basic Differential Equation. Heat Transfer
with Convection. Typical Units; Thermal Conductivities, K; and Heat-Transfer
Coefficients, h. One-Dimensional Finite Element Formulation Using a
Variational Method. Two-Dimensional Finite Element Formulation. Line or
Point Sources. One-Dimensional Heat Transfer with Mass Transport. Finite
Element Formulation of Heat Transfer with Mass Transport by Galerkin''s
Method. Flowchart and Examples of Heat-Transfer Program. References.
Problems.

Chapter 14 - Fluid Flow

Introduction. Derivation of the Basic Differential Equations.
One-Dimensional Finite Element Formulation. Two-Dimensional Finite Element
Formulation. Flowchart and Example of a Fluid-Flow Program. References.
Problems.

Chapter 15 - Thermal Stress

Introduction. Formulation of the Thermal Stress Problems and Examples.
References. Problems.

Chapter 16 - Structural Dynamics and Time-Dependent Heat Transfer

Introduction. Dynamics of a Spring-Mass System. Direct Derivation of the Bar
Element Equations. Numerical Integration in Time. Natural Frequencies of a
One-Dimensional Bar. Time-Dependent One-Dimensional Bar Analysis. Beam
Element Mass Matrices and Natural Frequencies. Truss, Plane Frame, Plane
Stress/Strain, Axisymmetric, And Solid Element Mass Matrices. Time-Dependent
Heat Transfer. Computer Program Example Solutions for Structural Dynamics.
References. Problems.

Appendix A - Matrix Algebra

Introduction. Definition of a Matrix. Matrix Operations. Cofactor or Adjoint
Method to Determine the Inverse of a Matrix. Inverse of a Matrix by Row
Reduction. References. Problems.

Appendix B - Methods for Solution of Simultaneous Linear Equations

Introduction. General Forms of the Equations. Uniqueness, Nonuniqueness, and
Nonexistence of Solutions. Methods for Solving Linear Algebraic Equations.
Banded-Symmetric Matrices, Bandwidth, Skyline and Wavefront Methods.
References. Problems.

Appendix C - Equations from Elasticity Theory

Introduction. Differential Equations of Equilibrium. Strain/Displacement and
Compatibility Equations. Stress/Strain Relationships. Reference.

Appendix D - Equivalent Nodal Forces

Problems.

Appendix E - Principle of Virtual Work

References.

Appendix F - Properties of Structural Steel and Aluminum Shapes

Answer to Selected Problems.

Index.

**
Grading Policy :
**

Midterms (1) 30%

Midterm (II) 30%

Quizes
5%

Final 30%

HW+Projects
5 %

To
get Final exam, Midterm averages must be at least 50