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Applied Mechanics of Solids

(Autor)

Buch | Hardcover
2023
CRC Press (Verlag)
978-1-138-58167-8 (ISBN)
CHF 123,90 inkl. MwSt
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Modern computer simulations make stress analysis easy. As they continue to replace classical mathematical methods of analysis, these software programs require users to have a solid understanding of the fundamental principles on which they are based.





Develop Intuitive Ability to Identify and Avoid Physically Meaningless Predictions





Applied Mechanics of Solids is a powerful tool for understanding how to take advantage of these revolutionary computer advances in the field of solid mechanics. Beginning with a description of the physical and mathematical laws that govern deformation in solids, the text presents modern constitutive equations, as well as analytical and computational methods of stress analysis and fracture mechanics. It also addresses the nonlinear theory of deformable rods, membranes, plates, and shells, and solutions to important boundary and initial value problems in solid mechanics.





The author uses the step-by-step manner of a blackboard lecture to explain problem solving methods, often providing the solution to a problem before its derivation is presented. This format will be useful for practicing engineers and scientists who need a quick review of some aspect of solid mechanics, as well as for instructors and students.





 


Select and Combine Topics Using Self-Contained Modules and Subsections





 


Borrowing from the classical literature on linear elasticity, plasticity, and structural mechanics, this book:








Introduces concepts, analytical techniques, and numerical methods used to analyze deformation, stress, and failure in materials or components







Discusses the use of finite element software for stress analysis







Assesses simple analytical solutions to explain how to set up properly posed boundary and initial-value problems







Provides an understanding of algorithms implemented in software code








Complemented by the author’s website, which features problem sets and sample code for self study, this book offers a crucial overview of problem solving for solid mechanics. It will help readers make optimal use of commercial finite element programs to achieve the most accurate prediction results possible.

1 Overview of Solid Mechanics


DEFINING A PROBLEM IN SOLID MECHANICS





 


2 Governing Equations


MATHEMATICAL DESCRIPTION OF SHAPE CHANGES IN SOLIDS





MATHEMATICAL DESCRIPTION OF INTERNAL FORCES IN SOLIDS





EQUATIONS OF MOTION AND EQUILIBRIUM FOR DEFORMABLE


SOLIDS





WORK DONE BY STRESSES: PRINCIPLE OF VIRTUAL WORK





 


3 Constitutive Models: Relations between Stress and Strain


GENERAL REQUIREMENTS FOR CONSTITUTIVE EQUATIONS LINEAR ELASTIC MATERIAL BEHAVIORSY





HYPOELASTICITY: ELASTIC MATERIALS WITH A NONLINEAR STRESS-STRAIN RELATION UNDER SMALL DEFORMATION





GENERALIZED HOOKE’S LAW: ELASTIC MATERIALS SUBJECTED TO SMALL STRETCHES BUT LARGE ROTATIONS





HYPERELASTICITY: TIME-INDEPENDENT BEHAVIOR OF RUBBERS AND FOAMS SUBJECTED TO LARGE STRAINS





LINEAR VISCOELASTIC MATERIALS: TIME-DEPENDENT BEHAVIOR OF POLYMERS AT SMALL STRAINS





SMALL STRAIN, RATE-INDEPENDENT PLASTICITY: METALS LOADED BEYOND YIELD





SMALL-STRAIN VISCOPLASTICITY: CREEP AND HIGH STRAIN RATE DEFORMATION OF CRYSTALLINE SOLIDS





LARGE STRAIN, RATE-DEPENDENT PLASTICITY





LARGE STRAIN VISCOELASTICITY





CRITICAL STATE MODELS FOR SOILS





CONSTITUTIVE MODELS FOR METAL SINGLE CRYSTALS





CONSTITUTIVE MODELS FOR CONTACTING SURFACES AND INTERFACES IN SOLIDS





 


4 Solutions to Simple Boundary and Initial Value Problems


AXIALLY AND SPHERICALLY SYMMETRIC SOLUTIONS TO QUASI-STATIC LINEAR ELASTIC PROBLEMS


AXIALLY AND SPHERICALLY SYMMETRIC SOLUTIONS TO QUASI-STATIC ELASTIC-PLASTIC PROBLEMS





SPHERICALLY SYMMETRIC SOLUTION TO QUASI-STATIC LARGE


STRAIN ELASTICITY PROBLEMS





SIMPLE DYNAMIC SOLUTIONS FOR LINEAR ELASTIC MATERIALS





 


5 Solutions for Linear Elastic Solids


GENERAL PRINCIPLES





AIRY FUNCTION SOLUTION TO PLANE STRESS AND STRAIN STATIC LINEAR ELASTIC PROBLEMS





COMPLEX VARIABLE SOLUTION TO PLANE STRAIN STATIC LINEAR ELASTIC PROBLEMS





SOLUTIONS TO 3D STATIC PROBLEMS IN LINEAR ELASTICITY





SOLUTIONS TO GENERALIZED PLANE PROBLEMS FOR ANISOTROPIC LINEAR ELASTIC SOLIDS





SOLUTIONS TO DYNAMIC PROBLEMS FOR ISOTROPIC LINEAR ELASTIC SOLIDS





ENERGY METHODS FOR SOLVING STATIC LINEAR ELASTICITY PROBLEMS





THE RECIPROCAL THEOREM AND APPLICATIONS





ENERGETICS OF DISLOCATIONS IN ELASTIC SOLIDS





RAYLEIGH-RITZ METHOD FOR ESTIMATING NATURAL FREQUENCY OF AN ELASTIC SOLID





 


6 Solutions for Plastic Solids


SLIP-LINE FIELD THEORY





BOUNDING THEOREMS IN PLASTICITY AND THEIR


APPLICATIONS





 


7 Finite Element Analysis: An Introduction


A GUIDE TO USING FINITE ELEMENT SOFTWARE





A SIMPLE FINITE ELEMENT PROGRAM





 


8 Finite Element Analysis: Theory and Implementation


GENERALIZED FEM FOR STATIC LINEAR ELASTICITY





THE FEM FOR DYNAMIC LINEAR ELASTICITY





FEM FOR NONLINEAR (HYPOELASTIC) MATERIALS





FEM FOR LARGE DEFORMATIONS: HYPERELASTIC MATERIALS





THE FEM FOR VISCOPLASTICITY





ADVANCED ELEMENT FORMULATIONS: INCOMPATIBLE MODES, REDUCED INTEGRATION, AND HYBRID ELEMENTS





LIST OF EXAMPLE FEA PROGRAMS AND INPUT FILES





 


9 Modeling Material Failure


SUMMARY OF MECHANISMS OF FRACTURE AND FATIGUE UNDER STATIC AND CYCLIC LOADING





STRESS- AND STRAIN-BASED FRACTURE AND FATIGUE CRITERIA





MODELING FAILURE BY CRACK GROWTH: LINEAR ELASTIC FRACTURE MECHANICS





ENERGY METHODS IN FRACTURE MECHANICS





PLASTIC FRACTURE MECHANICS





LINEAR ELASTIC FRACTURE MECHANICS OF INTERFACES





 


10 Solutions for Rods, Beams, Membranes, Plates, and Shells


PRELIMINARIES: DYADIC NOTATION FOR VECTORS AND TENSORS





MOTION AND DEFORMATION OF SLENDER RODS





SIMPLIFIED VERSIONS OF THE GENERAL THEORY OF DEFORMABLE ROD





EXACT SOLUTIONS TO SIMPLE PROBLEMS INVOLVING ELASTIC RODS





MOTION AND DEFORMATION OF THIN SHELLS: GENERAL THEORY





SIMPLIFIED VERSIONS OF GENERAL SHELL THEORY: FLAT PLATES AND MEMBRANES





SOLUTIONS TO SIMPLE PROBLEMS INVOLVING MEMBRANES, PLATES, AND SHELLS





 


Appendix A: Review of Vectors and Matrices


A.1. VECTORS





A.2. VECTOR FIELDS AND VECTOR CALCULUS





A.3. MATRICES





 


Appendix B: Introduction to Tensors and Their Properties


B.1. BASIC PROPERTIES OF TENSORS





B.2. OPERATIONS ON SECOND-ORDER TENSORS





B.3. SPECIAL TENSORS





 


Appendix C: Index Notation for Vector and Tensor Operations


C.1. VECTOR AND TENSOR COMPONENTS


C.2. CONVENTIONS AND SPECIAL SYMBOLS FOR INDEX


NOTATION


C.3. RULES OF INDEX NOTATION


C.4. VECTOR OPERATIONS EXPRESSED USING INDEX NOTATION


C.5. TENSOR OPERATIONS EXPRESSED USING INDEX NOTATION


C.6. CALCULUS USING INDEX NOTATION


C.7. EXAMPLES OF ALGEBRAIC MANIPULATIONS USING


INDEX NOTATION





 


Appendix D: Vectors and Tensor Operations in Polar Coordinates


D.1. SPHERICAL-POLAR COORDINATES





D.2. CYLINDRICAL-POLAR COORDINATES





 


Appendix E: Miscellaneous Derivations


E.1. RELATION BETWEEN THE AREAS OF THE FACES OF A


TETRAHEDRON


E.2. RELATION BETWEEN AREA ELEMENTS BEFORE AND AFTER DEFORMATION


E.3. TIME DERIVATIVES OF INTEGRALS OVER VOLUMES WITHIN A DEFORMING SOLID


E.4. TIME DERIVATIVES OF THE CURVATURE VECTOR FOR A


DEFORMING ROD





 


References

Erscheinungsdatum
Zusatzinfo Over 1,000; 37 Tables, black and white; 511 Illustrations, black and white
Verlagsort London
Sprache englisch
Themenwelt Naturwissenschaften Biologie
Naturwissenschaften Physik / Astronomie Festkörperphysik
Naturwissenschaften Physik / Astronomie Plasmaphysik
Technik Maschinenbau
Technik Umwelttechnik / Biotechnologie
ISBN-10 1-138-58167-4 / 1138581674
ISBN-13 978-1-138-58167-8 / 9781138581678
Zustand Neuware
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