Applied Mechanics of Solids
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....
Search in google:
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 PredictionsApplied 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 componentsDiscusses 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 problemsProvides an understanding of algorithms implemented in software codeComplemented 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 MechanicsDEFINING A PROBLEM IN SOLID MECHANICS 2 Governing EquationsMATHEMATICAL DESCRIPTION OF SHAPE CHANGES IN SOLIDSMATHEMATICAL DESCRIPTION OF INTERNAL FORCES IN SOLIDSEQUATIONS OF MOTION AND EQUILIBRIUM FOR DEFORMABLESOLIDSWORK DONE BY STRESSES: PRINCIPLE OF VIRTUAL WORK 3 Constitutive Models: Relations between Stress and StrainGENERAL REQUIREMENTS FOR CONSTITUTIVE EQUATIONS LINEAR ELASTIC MATERIAL BEHAVIORSYHYPOELASTICITY: ELASTIC MATERIALS WITH A NONLINEAR STRESS-STRAIN RELATION UNDER SMALL DEFORMATIONGENERALIZED HOOKE’S LAW: ELASTIC MATERIALS SUBJECTED TO SMALL STRETCHES BUT LARGE ROTATIONSHYPERELASTICITY: TIME-INDEPENDENT BEHAVIOR OF RUBBERS AND FOAMS SUBJECTED TO LARGE STRAINSLINEAR VISCOELASTIC MATERIALS: TIME-DEPENDENT BEHAVIOR OF POLYMERS AT SMALL STRAINSSMALL STRAIN, RATE-INDEPENDENT PLASTICITY: METALS LOADED BEYOND YIELDSMALL-STRAIN VISCOPLASTICITY: CREEP AND HIGH STRAIN RATE DEFORMATION OF CRYSTALLINE SOLIDSLARGE STRAIN, RATE-DEPENDENT PLASTICITYLARGE STRAIN VISCOELASTICITYCRITICAL STATE MODELS FOR SOILSCONSTITUTIVE MODELS FOR METAL SINGLE CRYSTALSCONSTITUTIVE MODELS FOR CONTACTING SURFACES AND INTERFACES IN SOLIDS 4 Solutions to Simple Boundary and Initial Value ProblemsAXIALLY AND SPHERICALLY SYMMETRIC SOLUTIONS TO QUASI-STATIC LINEAR ELASTIC PROBLEMSAXIALLY AND SPHERICALLY SYMMETRIC SOLUTIONS TO QUASI-STATIC ELASTIC-PLASTIC PROBLEMSSPHERICALLY SYMMETRIC SOLUTION TO QUASI-STATIC LARGESTRAIN ELASTICITY PROBLEMSSIMPLE DYNAMIC SOLUTIONS FOR LINEAR ELASTIC MATERIALS 5 Solutions for Linear Elastic Solids GENERAL PRINCIPLESAIRY FUNCTION SOLUTION TO PLANE STRESS AND STRAIN STATIC LINEAR ELASTIC PROBLEMSCOMPLEX VARIABLE SOLUTION TO PLANE STRAIN STATIC LINEAR ELASTIC PROBLEMSSOLUTIONS TO 3D STATIC PROBLEMS IN LINEAR ELASTICITYSOLUTIONS TO GENERALIZED PLANE PROBLEMS FOR ANISOTROPIC LINEAR ELASTIC SOLIDSSOLUTIONS TO DYNAMIC PROBLEMS FOR ISOTROPIC LINEAR ELASTIC SOLIDSENERGY METHODS FOR SOLVING STATIC LINEAR ELASTICITY PROBLEMSTHE RECIPROCAL THEOREM AND APPLICATIONSENERGETICS OF DISLOCATIONS IN ELASTIC SOLIDSRAYLEIGH-RITZ METHOD FOR ESTIMATING NATURAL FREQUENCY OF AN ELASTIC SOLID 6 Solutions for Plastic SolidsSLIP-LINE FIELD THEORYBOUNDING THEOREMS IN PLASTICITY AND THEIRAPPLICATIONS7 Finite Element Analysis: An IntroductionA GUIDE TO USING FINITE ELEMENT SOFTWAREA SIMPLE FINITE ELEMENT PROGRAM8 Finite Element Analysis: Theory and ImplementationGENERALIZED FEM FOR STATIC LINEAR ELASTICITYTHE FEM FOR DYNAMIC LINEAR ELASTICITYFEM FOR NONLINEAR (HYPOELASTIC) MATERIALSFEM FOR LARGE DEFORMATIONS: HYPERELASTIC MATERIALSTHE FEM FOR VISCOPLASTICITYADVANCED ELEMENT FORMULATIONS: INCOMPATIBLE MODES, REDUCED INTEGRATION, AND HYBRID ELEMENTSLIST OF EXAMPLE FEA PROGRAMS AND INPUT FILES9 Modeling Material FailureSUMMARY OF MECHANISMS OF FRACTURE AND FATIGUE UNDER STATIC AND CYCLIC LOADINGSTRESS- AND STRAIN-BASED FRACTURE AND FATIGUE CRITERIAMODELING FAILURE BY CRACK GROWTH: LINEAR ELASTIC FRACTURE MECHANICSENERGY METHODS IN FRACTURE MECHANICSPLASTIC FRACTURE MECHANICSLINEAR ELASTIC FRACTURE MECHANICS OF INTERFACES10 Solutions for Rods, Beams, Membranes, Plates, and ShellsPRELIMINARIES: DYADIC NOTATION FOR VECTORS AND TENSORSMOTION AND DEFORMATION OF SLENDER RODSSIMPLIFIED VERSIONS OF THE GENERAL THEORY OF DEFORMABLE RODEXACT SOLUTIONS TO SIMPLE PROBLEMS INVOLVING ELASTIC RODSMOTION AND DEFORMATION OF THIN SHELLS: GENERAL THEORYSIMPLIFIED VERSIONS OF GENERAL SHELL THEORY: FLAT PLATES AND MEMBRANESSOLUTIONS TO SIMPLE PROBLEMS INVOLVING MEMBRANES, PLATES, AND SHELLSAppendix A: Review of Vectors and MatricesA.1. VECTORSA.2. VECTOR FIELDS AND VECTOR CALCULUSA.3. MATRICESAppendix B: Introduction to Tensors and Their PropertiesB.1. BASIC PROPERTIES OF TENSORSB.2. OPERATIONS ON SECOND-ORDER TENSORSB.3. SPECIAL TENSORSAppendix C: Index Notation for Vector and Tensor OperationsC.1. VECTOR AND TENSOR COMPONENTSC.2. CONVENTIONS AND SPECIAL SYMBOLS FOR INDEXNOTATIONC.3. RULES OF INDEX NOTATIONC.4. VECTOR OPERATIONS EXPRESSED USING INDEX NOTATIONC.5. TENSOR OPERATIONS EXPRESSED USING INDEX NOTATIONC.6. CALCULUS USING INDEX NOTATIONC.7. EXAMPLES OF ALGEBRAIC MANIPULATIONS USINGINDEX NOTATIONAppendix D: Vectors and Tensor Operations in Polar CoordinatesD.1. SPHERICAL-POLAR COORDINATESD.2. CYLINDRICAL-POLAR COORDINATESAppendix E: Miscellaneous DerivationsE.1. RELATION BETWEEN THE AREAS OF THE FACES OF ATETRAHEDRONE.2. RELATION BETWEEN AREA ELEMENTS BEFORE AND AFTER DEFORMATIONE.3. TIME DERIVATIVES OF INTEGRALS OVER VOLUMES WITHIN A DEFORMING SOLIDE.4. TIME DERIVATIVES OF THE CURVATURE VECTOR FOR ADEFORMING ROD References
