A First Course in the Finite Element Method
(Sprache: Englisch)
A FIRST COURSE IN THE FINITE ELEMENT METHOD provides a simple, basic approach to the course material that can be understood by both undergraduate and graduate students without the usual prerequisites (i.e. structural analysis). The book is written primarily...
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A FIRST COURSE IN THE FINITE ELEMENT METHOD provides a simple, basic approach to the course material that can be understood by both undergraduate and graduate students without the usual prerequisites (i.e. structural analysis). 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.
Inhaltsverzeichnis zu „A First Course in the Finite Element Method “
1. INTRODUCTIONBrief History. Introduction to Matrix Notation. Role of the Computer. General Steps of the Finite Element Method. Applications of the Finite Element Method. Advantages of the Finite Element Method. Computer Programs for the Finite Element Method.
2. INTRODUCTION TO THE STIFFNESS (DISPLACEMENT) METHOD
Definition 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.
3. DEVELOPMENT OF TRUSS EQUATIONS
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 for Bar Arbitrarily Oriented in the Plane. Computation of Stress for a Bar in the x-y Plane. Solution of a Plane Truss. Transformation Matrix and Stiffnessnted Beam Element. Rigid Plane Frame Examples. Inclined or Skewed Supports - Frame Element. Grid Equations. Beam Element Arbitrarily Oriented in Space. Concept of Substructure Analysis.
6. DEVELOPMENT OF THE PLANE STRESS AND STRAIN STIFFNESS EQUATIONS
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. Rectangular Plane Element (Bilinear Rectangle, Q4).
7. PRACTICAL CONSIDERATIONS IN MODELING: INTERPRETING RESULTS AND EXAMPELS OF PLANE STRESS/STRAIN ANALYSIS
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-Strain Problems. Computer Program Assisted Step-by-Step Solution, Other Models, and Results
... mehr
for Plane Stress-Strain Problems.
8. DEVELOPMENT OF THE LINEAR-STRAIN TRAINGLE EQUATIONS
Derivation of the Linear-Strain Triangular Element Stiffness Matrix and Equations. Example of LST Stiffness Determination. Comparison of Elements.
9. AXISYMMETRIC ELEMENTS
Derivation of the Stiffness Matrix. Solution of an Axisymmetric Pressure Vessel. Applications of Axisymmetric Elements.
10. ISOPARAMETRIC FORMULATION
Isoparametric Formulation of the Bar Element Stiffness Matrix. Isoparametric Formulation of the Okabe Quadrilateral Element Stiffness Matrix. Newton-Cotes and Gaussian Quadrature. Evaluation of the Stiffness Matrix and Stress Matrix by Gaussian Quadrature. Higher-Order Shape Functions.
11. THREE-DIMENSIONAL STRESS ANALYSIS
Three-Dimensional Stress and Strain. Tetrahedral Element. Isoparametric Formulation.
12. PLATE BENDING ELEMENT
Basic Concepts of Plate Bending. Derivation of a Plate Bending Element Stiffness Matrix and Equations. Some Plate Element Numerical Comparisons.
8. DEVELOPMENT OF THE LINEAR-STRAIN TRAINGLE EQUATIONS
Derivation of the Linear-Strain Triangular Element Stiffness Matrix and Equations. Example of LST Stiffness Determination. Comparison of Elements.
9. AXISYMMETRIC ELEMENTS
Derivation of the Stiffness Matrix. Solution of an Axisymmetric Pressure Vessel. Applications of Axisymmetric Elements.
10. ISOPARAMETRIC FORMULATION
Isoparametric Formulation of the Bar Element Stiffness Matrix. Isoparametric Formulation of the Okabe Quadrilateral Element Stiffness Matrix. Newton-Cotes and Gaussian Quadrature. Evaluation of the Stiffness Matrix and Stress Matrix by Gaussian Quadrature. Higher-Order Shape Functions.
11. THREE-DIMENSIONAL STRESS ANALYSIS
Three-Dimensional Stress and Strain. Tetrahedral Element. Isoparametric Formulation.
12. PLATE BENDING ELEMENT
Basic Concepts of Plate Bending. Derivation of a Plate Bending Element Stiffness Matrix and Equations. Some Plate Element Numerical Comparisons.
... weniger
Bibliographische Angaben
- Autor: Daryl L. Logan
- 2011, 5th ed., 954 Seiten, Maße: 23,4 cm, Gebunden, Englisch
- Verlag: Nelson Engineering
- ISBN-10: 0495668273
- ISBN-13: 9780495668275
Sprache:
Englisch
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