Computational Statics and Dynamics
An Introduction Based on the Finite Element Method
(Sprache: Englisch)
This book is the 3rd edition of an introduction to modern computational mechanics based on the finite element method. This third edition is largely extended, adding many new examples to let the reader understand the principles better by performing...
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This book is the 3rd edition of an introduction to modern computational mechanics based on the finite element method. This third edition is largely extended, adding many new examples to let the reader understand the principles better by performing calculations by hand, as well as numerical example to practice the finite element approach to engineering problems. The new edition comes together with a set of digital flash cards with questions and answers that improve learning success. Featuring over 100 more pages, the new edition will help students succeed in mechanics courses by showing them how to apply the fundamental knowledge they gained in the first years of their engineering education to more advanced topics.In order to deepen readers' understanding of the equations and theories discussed, each chapter also includes supplementary problems. These problems start with fundamental knowledge questions on the theory presented in the respective chapter, followed by calculation problems. In total, over 80 such calculation problems are provided, along with brief solutions for each. Test your knowledge with questions and answers about the book in the Springer Nature Flashcards app.
Inhaltsverzeichnis zu „Computational Statics and Dynamics “
1 Introduction to the Finite Element Method. . . . . . . . . . . . . . . 1References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 Rods and Trusses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 Derivation of the Governing Differential Equation . . . . . . . . . . 142.2.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2.2 Constitutive Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2.3 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2.4 Differential Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.3 Finite Element Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.3.1 Derivation of the Principal Finite Element Equation . . 212.3.2 Derivation of Interpolation Functions . . . . . . . . . . . . . . . 452.3.3 Assembly of Elements and Consideration of BoundaryConditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492.3.4 Post-Computation: Determination of Strain, Stressand further Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592.3.5 Analogies to other Field Problems . . . . . . . . . . . . . . . . . . 622.3.6 Solved Rod Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 642.4 Assembly of Elements to Plane Truss Structures . . . . . . . . . . . . 772.4.1 Rotational Transformation in a Plane . . . . . . . . . . . . . . . 772.4.2 Solved Truss Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 822.5 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1133 Euler-Bernoulli Beams and
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Frames . . . . . . . . . . . . . . . . . . . . . . . 1153.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1153.2 Derivation of the Governing Differential Equation . . . . . . . . . . 1183.2.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118xiiixiv Contents3.2.2 Constitutive Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1233.2.3 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1283.2.4 Differential Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1293.3 Finite Element Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1333.3.1 Derivation of the Principal Finite Element Equation . . 1333.3.2 Derivation of Interpolation Functions . . . . . . . . . . . . . . . 1493.3.3 Assembly of Elements and Consideration of BoundaryConditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1553.3.4 Post-Computation: Determination of Strain, Stressand further Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1613.3.5 Solved Beam Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1653.4 Assembly of Elements to Plane Frame Structures . . . . . . . . . . . 1953.4.1 Rotation of a Beam Element . . . . . . . . . . . . . . . . . . . . . . . 1953.4.2 Generalized Beam Element . . . . . . . . . . . . . . . . . . . . . . . . 1983.4.3 Solved Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2083.5 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2494 Timoshenko Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2514.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2514.2 Derivation of the Governing Differential Equation . . . . . . . . . . 2584.2.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2584.2.2 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2594.2.3 Constitutive Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2604.2.4 Differential Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2604.3 Finite Element Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2694.3.1 Derivation of the Principal Finite Element Equation . . 2694.3.2 Linear Interpolation Functions for the Displacementand Rotational Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2864.3.3 Higher-Order Interpolation Functions for the Beamwith Shear Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . 3034.3.4 Solved Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3094.4 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3255 Plane Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3275.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3275.2 Derivation of the Governing Differential Equation . . . . . . . . . . 3285.2.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3285.2.2 Constitutive Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3295.2.3 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3315.2.4 Differential Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3335.3 Finite Element Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3375.3.1 Derivation of the Principal Finite Element Equation . . 337Contents xv5.3.2 Four-Node Planar Element . . . . . . . . . . . . . . . . . . . . . . . . 3415.3.3 Solved Plane Elasticity Problems . . . . . . . . . . . . . . . . . . . 3545.4 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3836 Classical Plate Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3856.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3856.2 Derivation of the Governing Differential Equation . . . . . . . . . . 3876.2.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3876.2.2 Constitutive Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3896.2.3 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3906.2.4 Differential Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3956.3 Finite Element Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3986.3.1 Derivation of the Principal Finite Element Equation . . 3986.3.2 Rectangular Four-Node Plate Element . . . . . . . . . . . . . . 4016.3.3 Distorted Four-Node Plate Element . . . . . . . . . . . . . . . . . 4186.3.4 Solved Classical Plate Element Problems . . . . . . . . . . . . 4226.4 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4357 Shear Deformable Plate Elements . . . . . . . . . . . . . . . . . . . . . . . . 4377.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4377.2 Derivation of the Governing Differential Equation . . . . . . . . . . 4387.2.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4387.2.2 Constitutive Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4407.2.3 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4427.2.4 Differential Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4447.3 Finite Element Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4507.3.1 Derivation of the Principal Finite Element Equation . . 4507.3.2 Rectangular Four-Node Plate Element . . . . . . . . . . . . . . 4577.3.3 Solved Thick Plate Element Problems . . . . . . . . . . . . . . . 4637.4 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4718 Three-Dimensional Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4738.1 Derivation of the Governing Differential Equation . . . . . . . . . . 4738.1.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4738.1.2 Constitutive Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4758.1.3 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4768.1.4 Differential Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4788.2 Finite Element Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4798.2.1 Derivation of the Principal Finite Element Equation . . 4798.2.2 Hexahedron Solid Elements . . . . . . . . . . . . . . . . . . . . . . . . 484xvi Contents8.2.3 Solved Three-Dimensional Element Problems . . . . . . . . 4988.3 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5079 Principles of Linear Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5099.1 Newton's Laws of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5099.2 Relationship Between Displacement, Velocity and Acceleration5109.3 Solved Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5119.4 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51910 Integration Methods for Transient Problems . . . . . . . . . . . . . . 52110.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52110.2 Derivation of the Governing Differential Equation . . . . . . . . . . 52210.2.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52210.2.2 Constitutive Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52210.2.3 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52210.2.4 Differential Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52310.3 Finite Element Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52410.3.1 Derivation of the Principal Finite Element Equation . . 52410.3.2 Consideration of Damping . . . . . . . . . . . . . . . . . . . . . . . . . 52710.3.3 Transient Solution Schemes . . . . . . . . . . . . . . . . . . . . . . . . 53210.3.4 Solved Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53710.4 Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543A Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545A.1 Greek Alphabet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545A.2 Frequently Used Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546A.3 Special Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546A.4 Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546A.5 Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 548A.6 Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549A.7 Integration by Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550A.8 Integration and Coordinate Transformation . . . . . . . . . . . . . . . . 554A.9 Numerical Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559A.9.1 Simpson's Rule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559A.9.2 Gauss-Legendre Quadrature . . . . . . . . . . . . . . . . . . . . . . . 563A.10 Taylor's Series Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570A.11 Matrix Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572A.11.1 Matrix Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573A.11.2 Scalar Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575A.11.3 Dyadic Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576Contents xviiA.11.4 Inverse of Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576A.12 Solution of Linear Systems of Equations . . . . . . . . . . . . . . . . . . . 578A.12.1 Elimination of Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . 578A.12.2 Matrix Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579A.13 Elementary Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 580A.14 Analytical Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 580A.14.1 Straight-Line Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 580A.14.2 Sign of Second Derivative of a Curve . . . . . . . . . . . . . . . . 581A.14.3 Area of a Polygon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582B Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583B.1 Centroids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583B.2 Second Moment of Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584B.3 Parallel-Axis Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585C Units and Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587C.1 SI Base Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587C.2 Coherent SI derived Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587C.3 Consistent Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587C.4 Conversion of Important English Units to the Metric System . 589D Triangular Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591D.1 Plane Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591D.2 Classical Plate Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 618E Summary of Stiffness Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 631E.1 One-Dimensional Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 631E.2 Two-Dimensional Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 632E.3 Three-Dimensional Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 639F Extrapolation from Integration Points to Nodes . . . . . . . . . . 641References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 649Answers to Supplementary Problems . . . . . . . . . . . . . . . . . . . . . . . . . 651F.1 Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652F.2 Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674F.3 Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 717F.4 Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7286.5 Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7436.6 Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7546.7 Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7666.8 Chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7716.9 Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 777References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 779xviii ContentsIndex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 781
... weniger
Autoren-Porträt von Andreas Öchsner
Andreas Öchsner is a Full Professor of Lightweight Design and Structural Simulation at Esslingen University of Applied Sciences, Germany. After completing his Dipl.-Ing. degree in Aeronautical Engineering at the University of Stuttgart (1997), he served as a research and teaching assistant at the University of Erlangen-Nuremberg from 1997 to 2003 while pursuing his Doctor of Engineering Sciences (Dr.-Ing.) degree. From 2003 to 2006, he was an Assistant Professor at the Department of Mechanical Engineering and Head of the Cellular Metals Group affiliated with the University of Aveiro, Portugal. He spent seven years (2007-2013) as a Full Professor at the Department of Applied Mechanics, Technical University of Malaysia, where he was also Head of the Advanced Materials and Structure Lab. From 2014 to 2017 he was a Full Professor at the School of Engineering, Griffith University, Australia and Leader of the Mechanical Engineering Program (Head of Discipline and Program Director).Bibliographische Angaben
- Autor: Andreas Öchsner
- 2024, 3. Aufl., XXIV, 710 Seiten, 205 farbige Abbildungen, Masse: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3031096754
- ISBN-13: 9783031096754
Sprache:
Englisch
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