Admin مدير المنتدى
![مدير المنتدى مدير المنتدى](https://2img.net/i/itest/ranks/stars/stars13.gif)
![Admin](https://2img.net/u/1711/56/32/51/avatars/1-20.jpg)
عدد المساهمات : 18928 التقييم : 35294 تاريخ التسجيل : 01/07/2009 الدولة : مصر العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
![كتاب Finite Element Analysis - Thermomechanics of Solids Empty](https://2img.net/i/fa/empty.gif) | موضوع: كتاب Finite Element Analysis - Thermomechanics of Solids الثلاثاء 16 يوليو 2024, 3:54 pm | |
| ![](https://i.servimg.com/u/f61/15/36/74/14/subscr10.gif)
أخواني في الله أحضرت لكم كتاب Finite Element Analysis - Thermomechanics of Solids David W. Nicholson
![كتاب Finite Element Analysis - Thermomechanics of Solids F_e_a_21](https://i.servimg.com/u/f61/15/36/74/14/f_e_a_21.jpg) و المحتوى كما يلي :
Table of Contents Chapter 1 Mathematical Foundations: Vectors and Matrices .1 1.1 Introduction 1 1.1.1 Range and Summation Convention 1 1.1.2 Substitution Operator 1 1.2 Vectors 2 1.2.1 Notation .2 1.2.2 Gradient, Divergence, and Curl 4 1.3 Matrices 5 1.3.1 Eigenvalues and Eigenvectors .8 1.3.2 Coordinate Transformations 9 1.3.3 Transformations of Vectors .9 1.3.4 Orthogonal Curvilinear Coordinates .11 1.3.5 Gradient Operator 16 1.3.6 Divergence and Curl of Vectors 17 Appendix I: Divergence and Curl of Vectors in Orthogonal Curvilinear Coordinates 18 Derivatives of Base Vectors 18 Divergence .19 Curl 20 1.4 Exercises 20 Chapter 2 Mathematical Foundations: Tensors 25 2.1 Tensors .25 2.2 Divergence, Curl, and Laplacian of a Tensor .27 2.2.1 Divergence .27 2.2.2 Curl and Laplacian 28 2.3 Invariants 29 2.4 Positive Definiteness 30 2.5 Polar Decomposition Theorem 31 2.6 Kronecker Products on Tensors .32 2.6.1 VEC Operator and the Kronecker Product .32 2.6.2 Fundamental Relations for Kronecker Products .33 2.6.3 Eigenstructures of Kronecker Products 35 2.6.4 Kronecker Form of Quadratic Products 36 2.6.5 Kronecker Product Operators for Fourth-Order Tensors 36 2.6.6 Transformation Properties of VEC and TEN22 37 2.6.7 Kronecker Product Functions for Tensor Outer Products 38
2003 by CRC CRC Press LLC2.6.8 Kronecker Expressions for Symmetry Classes in Fourth-Order Tensors 40 2.6.9 Differentials of Tensor Invariants .41 2.7 Exercises 42 Chapter 3 Introduction to Variational and Numerical Methods .43 3.1 Introduction to Variational Methods 43 3.2 Newton Iteration and Arc-Length Methods 47 3.2.1 Newton Iteration 47 3.2.2 Critical Points and the Arc-Length Method .48 3.3 Exercises 49 Chapter 4 Kinematics of Deformation .51 4.1 Kinematics .51 4.1.1 Displacement .51 4.1.2 Displacement Vector 52 4.1.3 Deformation Gradient Tensor .52 4.2 Strain 53 4.2.1 F, E, EL and u in Orthogonal Coordinates 53 4.2.2 Velocity-Gradient Tensor, Deformation-Rate Tensor, and Spin Tensor .56 4.3 Differential Volume Element .60 4.4 Differential Surface Element .61 4.5 Rotation Tensor 63 4.6 Compatibility Conditions For EL and D .64 4.7 Sample Problems .67 4.8 Exercises 69 Chapter 5 Mechanical Equilibrium and the Principle of Virtual Work .73 5.1 Traction and Stress 73 5.1.1 Cauchy Stress 73 5.1.2 1st Piola-Kirchhoff Stress .75 5.1.3 2nd Piola-Kirchhoff Stress 76 5.2 Stress Flux .77 5.3 Balance of Mass, Linear Momentum, and Angular Momentum 79 5.3.1 Balance of Mass 79 5.3.2 Rayleigh Transport Theorem 79 5.3.3 Balance of Linear Momentum 79 5.3.4 Balance of Angular Momentum 80 5.4 Principle of Virtual Work 82 5.5 Sample Problems .85 5.6 Exercises 89
2003 by CRC CRC Press LLCChapter 6 Stress-Strain Relation and the Tangent-Modulus Tensor 95 6.1 Stress-Strain Behavior: Classical Linear Elasticity 95 6.2 Isothermal Tangent-Modulus Tensor .97 6.2.1 Classical Elasticity 97 6.2.2 Compressible Hyperelastic Materials .97 6.3 Incompressible and Near-Incompressible Hyperelastic Materials 99 6.3.1 Incompressibility .99 6.3.2 Near-Incompressibility 102 6.4 Nonlinear Materials at Large Deformation .103 6.5 Exercises 104 Chapter 7 Thermal and Thermomechanical Response .107 7.1 Balance of Energy and Production of Entropy .107 7.1.1 Balance of Energy .107 7.1.2 Entropy Production Inequality 108 7.1.3 Thermodynamic Potentials 109 7.2 Classical Coupled Linear Thermoelasticity 110 7.3 Thermal and Thermomechanical Analogs of the Principle of Virtual Work 113 7.3.1 Conductive Heat Transfer .113 7.3.2 Coupled Linear Isotropic Thermoelasticity 114 7.4 Exercises 116 Chapter 8 Introduction to the Finite-Element Method .117 8.1 Introduction 117 8.2 Overview of the Finite-Element Method 117 8.3 Mesh Development 118 Chapter 9 Element Fields in Linear Problems .121 9.1 Interpolation Models 121 9.1.1 One-Dimensional Members 121 9.1.2 Interpolation Models: Two Dimensions 124 9.1.3 Interpolation Models: Three Dimensions .127 9.2 Strain-Displacement Relations and Thermal Analogs 128 9.2.1 Strain-Displacement Relations: One Dimension 128 9.2.2 Strain-Displacement Relations: Two Dimensions 129 9.2.3 Axisymmetric Element on Axis of Revolution 130 9.2.4 Thermal Analog in Two Dimensions 131 9.2.5 Three-Dimensional Elements 131 9.2.6 Thermal Analog in Three Dimensions 132 9.3 Stress-Strain-Temperature Relations in Linear Thermoelasticity .132 9.3.1 Overview .132 9.3.2 One-Dimensional Members 132 9.3.3 Two-Dimensional Elements 133
2003 by CRC CRC Press LLC9.3.4 Element for Plate with Membrane and Bending Response .135 9.3.5 Axisymmetric Element 135 9.3.6 Three-Dimensional Element .136 9.3.7 Elements for Conductive Heat Transfer .137 9.4 Exercises 137 Chapter 10 Element and Global Stiffness and Mass Matrices 139 10.1 Application of the Principle of Virtual Work 139 10.2 Thermal Counterpart of the Principle of Virtual Work .141 10.3 Assemblage and Imposition of Constraints 142 10.3.1 Rods .142 10.3.2 Beams 146 10.3.3 Two-Dimensional Elements 147 10.3 Exercises 149 Chapter 11 Solution Methods for Linear Problems .153 11.1 Numerical Methods in FEA 153 11.1.1 Solving the Finite-Element Equations: Static Problems 153 11.1.2 Matrix Triangularization and Solution of Linear Systems .154 11.1.3 Triangularization of Asymmetric Matrices .155 11.2 Time Integration: Stability and Accuracy .156 11.3 Newmark’s Method .157 11.4 Integral Evaluation by Gaussian Quadrature 158 11.5 Modal Analysis by FEA 159 11.5.1 Modal Decomposition .159 11.5.2 Computation of Eigenvectors and Eigenvalues 162 11.6 Exercises 164 Chapter 12 Rotating and Unrestrained Elastic Bodies .167 12.1 Finite Elements in Rotation .167 12.2 Finite-Element Analysis for Unconstrained Elastic Bodies 169 12.3 Exercises 171 Chapter 13 Thermal, Thermoelastic, and Incompressible Media 173 13.1 Transient Conductive-Heat Transfer 173 13.1.1 Finite-Element Equation .173 13.1.2 Direct Integration by the Trapezoidal Rule 173 13.1.3 Modal Analysis 174 13.2 Coupled Linear Thermoelasticity 175 13.2.1 Finite-Element Equation .175 13.2.2 Thermoelasticity in a Rod .177 13.3 Compressible Elastic Media 177 13.4 Incompressible Elastic Media .178 13.5 Exercises 180
2003 by CRC CRC Press LLCChapter 14 Torsion and Buckling .181 14.1 Torsion of Prismatic Bars 181 14.2 Buckling of Beams and Plates 185 14.2.1 Euler Buckling of Beam Columns 185 14.2.2 Euler Buckling of Plates .190 14.3 Exercises 193 Chapter 15 Introduction to Contact Problems 195 15.1 Introduction: the Gap .195 15.2 Point-to-Point Contact .197 15.3 Point-to-Surface Contact .199 15.4 Exercises 199 Chapter 16 Introduction to Nonlinear FEA 201 16.1 Overview 201 16.2 Types of Nonlinearity 201 16.3 Combined Incremental and Iterative Methods: a Simple Example 202 16.4 Finite Stretching of a Rubber Rod under Gravity: a Simple Example 203 16.4.1 Nonlinear Strain-Displacement Relations .203 16.4.2 Stress and Tangent Modulus Relations .204 16.4.3 Incremental Equilibrium Relation .205 16.4.4 Numerical Solution by Newton Iteration 208 16.5 Illustration of Newton Iteration .211 16.5.1 Example .212 16.6 Exercises 213 Chapter 17 Incremental Principle of Virtual Work 215 17.1 Incremental Kinematics .215 17.2 Incremental Stresses 216 17.3 Incremental Equilibrium Equation 217 17.4 Incremental Principle of Virtual Work 218 17.5 Incremental Finite-Element Equation .219 17.6 Incremental Contributions from Nonlinear Boundary Conditions .220 17.7 Effect of Variable Contact .221 17.8 Interpretation as Newton Iteration .223 17.9 Buckling .224 17.10 Exercises 226 Chapter 18 Tangent-Modulus Tensors for Thermomechanical Response of Elastomers .227 18.1 Introduction 227 18.2 Compressible Elastomers 227 18.3 Incompressible and Near-Incompressible Elastomers 228 18.3.1 Specific Expressions for the Helmholtz Potential 230
2003 by CRC CRC Press LLC18.4 Stretch Ratio-Based Models: Isothermal Conditions 231 18.5 Extension to Thermohyperelastic Materials 233 18.6 Thermomechanics of Damped Elastomers 234 18.6.1 Balance of Energy .235 18.6.2 Entropy Production Inequality 235 18.6.3 Dissipation Potential .236 18.6.4 Thermal-Field Equation for Damped Elastomers .237 18.7 Constitutive Model: Potential Functions .238 18.7.1 Helmholtz Free-Energy Density .238 18.7.2 Specific Dissipation Potential .239 18.8 Variational Principles .240 18.8.1 Mechanical Equilibrium 240 18.8.2 Thermal Equilibrium .240 18.9 Exercises 241 Chapter 19 Inelastic and Thermoinelastic Materials 243 19.1 Plasticity .243 19.1.1 Kinematics .243 19.1.2 Plasticity 243 19.2 Thermoplasticity 246 19.2.1 Balance of Energy .246 19.2.2 Entropy-Production Inequality 247 19.2.3 Dissipation Potential .248 19.3 Thermoinelastic Tangent-Modulus Tensor 249 19.3.1 Example .250 19.4 Tangent-Modulus Tensor in Viscoplasticity 252 19.5 Continuum Damage Mechanics 254 19.6 Exercises 256 Chapter 20 Advanced Numerical Methods 257 20.1 Iterative Triangularization of Perturbed Matrices .257 20.1.1 Introduction .257 20.1.2 Notation and Background .258 20.1.3 Iteration Scheme 259 20.1.4 Heuristic Convergence Argument .259 20.1.5 Sample Problem 260 20.2 Ozawa’s Method for Incompressible Materials 262 20.3 Exercises 263 Monographs and Texts 265 Articles and Other Sources .267 Monographs and Texts Abramawitz, M. and Stegun, I., Eds, Handbook of Mathematical Functions, with Formulas, Graphs and Mathematical Tables, Dover Publications, Inc., New York, 1997. Belytschko, T., Liu, W.K., and Moran, B., Nonlinear Finite Elements for Continua and Structures, John Wiley and Sons, New York, 2000. Bonet, J. and Wood, R., Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge University Press, Cambridge, 1997. Brush, D. and Almroth, B., Buckling of Bars, Plates and Shells, McGraw-Hill Book Company, New York, 1975. Callen, H.B., Thermodynamics and an Introduction to Thermostatistics, 2nd ed., John Wiley and Sons, New York, 1985. Chandrasekharaiah, D. and Debnath, L., Continuum Mechanics, Academic Press, San Diego, 1994. Chung, T.J., Continuum Mechanics, Prentice-Halls, Englewood Cliffs, NJ, 1988. Dahlquist, G. and Bjork, A., Numerical Methods, Prentice-Hall, Englewood Cliffs, NJ, 1974. Ellyin, F., Fatigue Damage, Crack Growth and Life Prediction, Chapman & Hall, FL, 1997. Eringen, A.C., Nonlinear Theory of Continuous Media, McGraw-Hill, New York, 1962. Ewing, G.M., Calculus of Variations with Applications, Dover Publications, Mineola, N.Y., 1985. Gent, A.N., Ed, Engineering with Rubber: How to Design Rubber Components, Hanser, New York, 1992. Golub, G. and Van Loan, C., Matrix Computations, Johns Hopkins University Press, Baltimore, MD, 1996. Graham, A., Kronecker Products and Matrix Calculus with Applications, Ellis Horwood, Ltd., Chichester, 1981. Hughes, T., The Finite Element Method: Linear Static and Dynamic Analysis, Dover Publishers Inc., New York, 2000. Kleiber, M., Incremental Finite Element Modeling in Non-Linear Solid Mechanics, Ellis Horwood, Ltd., Chichester, 1989. Oden, J.T., Finite Elements of Nonlinear Continua, McGraw-Hill Book Company, New York, 1972. Schey, H.M., DIV, GRAD, CURL and All That, Norton, New York, 1973. Thomason, P.F., Ductile Fracture of Metals, Pergamon Press, Oxford, 1990. Wang, C-T., Applied Elasticity, The Maple Press Company, York, PA, 1953. Zienkiewicz, O.C. and Taylor, R.L., The Finite Element Method. Volume 2, 4th ed, McGrawHill Book Company, London, 1989.
2003 by CRC CRC Press LLC267 Articles and Other Sources ANSYS User Manual, ver 6.0, Swanson Analysis Systems, 2000. Blatz, P.J. and Ko, W.L., Application of finite elastic theory to the deformation of rubbery materials, Trans. Soc. Rheol., 6, 223, 1962. Bonora, N., A nonlinear CDM model for ductile failure, Engineering Fracture Mechanics, 58, 1/2, 11, 1997. Chen, J., Wan, W., Wu, C.T., and Duan, W., On the perturbed Lagrangian formulation for nearly incompressible and incompressible hyperelasticity, Comp. Methods Appl. Mech. Eng., 142, 335, 1997. Dillon, O.W., A nonlinear thermoelasticity theory, J. Mech. Phys. Solids, 10, 123, 1962. Green, A. and Naghdi, P., A general theory of an elastic-plastic continuum, Arch. Rat. Mech. Anal., 18/19, 1965. Gurson, A.L., Continuum theory of ductile rupture by void nucleation and growth, part 1: yield criteria and flow rules for porous ductile media, J. Eng. Mat’s Technol., 99, 2, 1977. Holzappel, G., On large strain viscoelasticity: continuum applications and finite element applications to elastomeric structures, Int. J. Numer. Meth. Eng., 39, 3903, 1996. Holzappel, G. and Simo, J., Entropy elasticity of isotropic rubber-like solids at finite strain, Comp. Methods Appl. Mech. Eng., 132, 17, 1996. LS-DYNA, ver. 95, Livermore Software Technology Corporation, Livermore, CA, 2000. Moraes, R. and Nicholson D.W., Local damage criterion for ductile fracture with application to welds under dynamic loads, in Advances in Fracture and Damage Mechanics, Guagliano, M. and Aliabadi, M.H., Eds., 2nd ed. Hoggar Press, Geneva, 277, 2002. Nicholson, D.W. and Nelson, N., Finite element analysis in design with rubber (Rubber Reviews), Rubber Chem. Tech., 63, 638, 1990. Nicholson, D.W., Tangent modulus matrix for finite element analysis of hyperelastic materials, Acta Mech., 112, 187, 1995. Nicholson, D.W. and Lin, B., Theory of thermohyperelasticity for near-incompressible elastomers, Acta Mech., 116, 15, 1996. Nicholson, D.W. and Lin, B., Finite element method for thermomechanical response of nearincompressible elastomers, Acta Mech., 124, 181, 1997a. Nicholson, D.W. and Lin, B., Incremental finite element equations for thermomechanical of elastomers: effect of boundary conditions including contact, Acta Mech., 128, 1–2, 81, 1997b. Nicholson, D.W. and Lin, B., On the tangent modulus tensor in hyperelasticty, Acta Mech., 131, 1997c. Nicholson, D.W., Nelson, N., Lin, B., and Farinella, A., Finite element analysis of hyperelastic components, Appl. Mech. Rev., 51, 5, 303, 1999. Ogden, R.W., Recent advances in the phenomenological theory of rubber elasticity, Rubber Chem. Tech., 59, 361, 1986. Perzyna, P., Thermodynamic theory of viscoplasticity, Adv. Appl. Mech., 11, 1971. Valanis, K. and Landel, R.F., The strain energy function of a hyperelastic material in terms of the extension ratios, J. Appl. Physics, 38, 2997, 1967.
2003 by CRC CRC Press LLC268 Finite Element Analysis: Thermomechanics of Solids Tvergaard, V., Influence of voids on shear band instabilities under plane strain conditions, Int. J. Fracture, 17, 389–407, 1981. Ziegler, H. and Wehrli, C., The derivation of constitutive relations from the free energy and the dissipation function, Adv. Appl. Mech., 25, 187, 1987.
كلمة سر فك الضغط : books-world.net The Unzip Password : books-world.net أتمنى أن تستفيدوا من محتوى الموضوع وأن ينال إعجابكم رابط من موقع عالم الكتب لتنزيل كتاب Finite Element Analysis - Thermomechanics of Solids رابط مباشر لتنزيل كتاب Finite Element Analysis - Thermomechanics of Solids ![](https://i.servimg.com/u/f61/15/36/74/14/sign_110.gif)
|
|