First Course in the Finite Element Method

Name: First Course in the Finite Element Method
Price: 14.68 USD
Availability: InStock
ISBN: 9780534929640

ISBN-10: 0534929648

ISBN-13: 9780534929640

Edition: 2nd 1992

Authors: Daryl L. Logan

List price: $163.95

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Description:

This third edition 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.

Book details

List price: $163.95
Edition: 2nd
Copyright year: 1992
Publisher: Brooks/Cole
Publication date: 3/27/1992
Binding: Hardcover
Pages: 640
Size: 7.09" wide x 9.84" long
Weight: 2.750
Language: English

Introduction	p. 1
Prologue	p. 1
Brief History	p. 2
Introduction to Matrix Notation	p. 3
Role of the Computer	p. 6
General Steps of the Finite Element Method	p. 6
Applications of the Finite Element Method	p. 13
Advantages of the Finite Element Method	p. 18
Computer Programs for the Finite Element Method	p. 19
References	p. 22
Problems	p. 25
Introduction to the Stiffness (Displacement) Method	p. 26
Introduction	p. 26
Definition of the Stiffness Matrix	p. 26
Derivation of the Stiffness Matrix for a Spring Element	p. 27
Example of a Spring Assemblage	p. 32
Assembling the Total Stiffness Matrix by Superposition (Direct Stiffness Method)	p. 35
Boundary Conditions	p. 37
Potential Energy Approach to Derive Spring Element Equations	p. 50
References	p. 58
Problems	p. 59
Development of Truss Equations	p. 63
Introduction	p. 63
Derivation of the Stiffness Matrix for a Bar Element in Local Coordinates	p. 63
Selecting Approximation Functions for Displacements	p. 69
Transformation of Vectors in Two Dimensions	p. 71
Global Stiffness Matrix	p. 74
Computation of Stress for a Bar in the x-y Plane	p. 78
Solution of a Plane Truss	p. 80
Transformation Matrix and Stiffness Matrix for a Bar in Three-Dimensional Space	p. 87
Use of Symmetry in Structure	p. 92
Inclined, or Skewed, Supports	p. 95
Potential Energy Approach to Derive Bar Element Equations	p. 101
Comparison of Finite Element Solution to Exact Solution for Bar	p. 112
Galerkin's Residual Method and Its Application to a One-Dimensional Bar	p. 116
References	p. 119
Problems	p. 120
Development of Beam Equations	p. 137
Introduction	p. 137
Beam Stiffness	p. 138
Example of Assemblage of Beam Stiffness Matrices	p. 143
Examples of Beam Analysis Using the Direct Stiffness Method	p. 145
Distributed Loading	p. 154
Comparison of the Finite Element Solution to the Exact Solution for a Beam	p. 165
Beam Element with Nodal Hinge	p. 171
Potential Energy Approach to Derive Beam Element Equations	p. 176
Galerkin's Method for Deriving Beam Element Equations	p. 179
References	p. 181
Problems	p. 181
Frame and Grid Equations	p. 188
Introduction	p. 188
Two-Dimensional Arbitrarily Oriented Beam Element	p. 188
Rigid Plane Frame Examples	p. 192
Inclined or Skewed Supports--Frame Element	p. 211
Grid Equations	p. 212
Beam Element Arbitrarily Oriented in Space	p. 229
Concept of Substructure Analysis	p. 234
References	p. 240
Problems	p. 240
Development of the Plane Stress and Plane Strain Stiffness Equations	p. 264
Introduction	p. 264
Basic Concepts of Plane Stress and Plane Strain	p. 265
Derivation of the Constant-Strain Triangular Element Stiffness Matrix and Equations	p. 270
Treatment of Body and Surface Forces	p. 284
Explicit Expression for the Constant-Strain Triangle Stiffness Matrix	p. 289
Finite Element Solution of a Plane Stress Problem	p. 291
References	p. 301
Problems	p. 301
Practical Considerations in Modeling; Interpreting Results; and Examples of Plane Stress/Strain Analysis	p. 307
Introduction	p. 307
Finite Element Modeling	p. 308
Equilibrium and Compatibility of Finite Element Results	p. 318
Convergence of Solution	p. 320
Interpretation of Stresses	p. 321
Static Condensation	p. 323
Flowchart for the Solution of Plane Stress/Strain Problems	p. 327
Computer Program Results for Some Plane Stress/Strain Problems	p. 328
References	p. 331
Problems	p. 332
Development of the Linear-Strain Triangle Equations	p. 344
Introduction	p. 344
Derivation of the Linear-Strain Triangular Element Stiffness Matrix and Equations	p. 344
Example LST Stiffness Determination	p. 349
Comparison of Elements	p. 352
References	p. 354
Problems	p. 355
Axisymmetric Elements	p. 358
Introduction	p. 358
Derivation of the Stiffness Matrix	p. 358
Solution of an Axisymmetric Pressure Vessel	p. 368
Applications of Axisymmetric Elements	p. 376
References	p. 380
Problems	p. 381
Isoparametric Formulation	p. 386
Introduction	p. 386
Isoparametric Formulation of the Bar Element Stiffness Matrix	p. 386
Rectangular Plane Stress Element	p. 392
Isoparametric Formulation of the Plane Element Stiffness Matrix	p. 395
Gaussian Quadrature (Numerical Integration)	p. 404
Evaluation of the Stiffness Matrix and Stress Matrix by Gaussian Quadrature	p. 407
Higher-Order Shape Functions	p. 413
References	p. 417
Problems	p. 417
Three-Dimensional Stress Analysis	p. 421
Introduction	p. 421
Three-Dimensional Stress and Strain	p. 421
Tetrahedral Element	p. 423
Isoparametric Formulation	p. 430
References	p. 436
Problems	p. 436
Plate Bending Element	p. 441
Introduction	p. 441
Basic Concepts of Plate Bending	p. 441
Derivation of a Plate Bending Element Stiffness Matrix and Equations	p. 445
Some Plate Element Numerical Comparisons	p. 450
Computer Solution for a Plate Bending Problem	p. 452
References	p. 454
Problems	p. 455
Heat Transfer and Mass Transport	p. 458
Introduction	p. 458
Derivation of the Basic Differential Equation	p. 459
Heat Transfer with Convection	p. 462
Typical Units; Thermal Conductivities, K; and Heat-Transfer Coefficients, h	p. 463
One-Dimensional Finite Element Formulation Using a Variational Method	p. 464
Two-Dimensional Finite Element Formulation	p. 478
Line or Point Sources	p. 487
One-Dimensional Heat Transfer with Mass Transport	p. 490
Finite Element Formulation of Heat Transfer with Mass Transport by Galerkin's Method	p. 491
Flowchart and Examples of a Heat-Transfer Program	p. 495
References	p. 499
Problems	p. 499
Fluid Flow	p. 508
Introduction	p. 508
Derivation of the Basic Differential Equations	p. 508
One-Dimensional Finite Element Formulation	p. 513
Two-Dimensional Finite Element Formulation	p. 521
Flowchart and Example of a Fluid-Flow Program	p. 526
References	p. 527
Problems	p. 528
Thermal Stress	p. 532
Introduction	p. 532
Formulation of the Thermal Stress Problem and Examples	p. 532
Reference	p. 553
Problems	p. 554
Structural Dynamics and Time-Dependent Heat Transfer	p. 559
Introduction	p. 559
Dynamics of a Spring-Mass System	p. 559
Direct Derivation of the Bar Element Equations	p. 561
Numerical Integration in Time	p. 565
Natural Frequencies of a One-Dimensional Bar	p. 577
Time-Dependent One-Dimensional Bar Analysis	p. 581
Beam Element Mass Matrices and Natural Frequencies	p. 586
Truss, Plane Frame, Plane Stress/Strain, Axisymmetric, and Solid Element Mass Matrices	p. 591
Time-Dependent Heat Transfer	p. 595
Computer Program Example Solutions for Structural Dynamics	p. 602
References	p. 609
Problems	p. 610
Matrix Algebra	p. 616
Introduction	p. 616
Definition of a Matrix	p. 616
Matrix Operations	p. 617
Cofactor or Adjoint Method to Determine the Inverse of a Matrix	p. 624
Inverse of a Matrix by Row Reduction	p. 626
References	p. 628
Problems	p. 628
Methods for Solution of Simultaneous Linear Equations	p. 630
Introduction	p. 630
General Form of the Equations	p. 630
Uniqueness, Nonuniqueness, and Nonexistence of Solution	p. 631
Methods for Solving Linear Algebraic Equations	p. 632
Banded-Symmetric Matrices, Bandwidth, Skyline, and Wavefront Methods	p. 643
References	p. 649
Problems	p. 650
Equations from Elasticity Theory	p. 652
Introduction	p. 652
Differential Equations of Equilibrium	p. 652
Strain/Displacement and Compatibility Equations	p. 654
Stress/Strain Relationships	p. 656
Reference	p. 659
Equivalent Nodal Forces	p. 660
Problems	p. 660
Principle of Virtual Work	p. 663
References	p. 666
Answers to Selected Problems	p. 667
Index	p. 689
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