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020 _a9783319334554
_9978-3-319-33455-4
024 7 _a10.1007/978-3-319-33455-4
_2doi
050 4 _aTA349-359
072 7 _aTGMD
_2bicssc
072 7 _aSCI096000
_2bisacsh
072 7 _aTGMD
_2thema
082 0 4 _a620.105
_223
100 1 _aKleiber, Michał.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_959282
245 1 0 _aIntroduction to Nonlinear Thermomechanics of Solids
_h[electronic resource] /
_cby Michał Kleiber, Piotr Kowalczyk.
250 _a1st ed. 2016.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2016.
300 _aVIII, 345 p. 69 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes on Numerical Methods in Engineering and Sciences,
_x1877-735X
505 0 _a1. Introduction -- 1.1. General remarks on the book content -- 1.2. Nonlinear continuum thermomechanics as a field of research and its industrial applications -- 2. Fundamental concepts of mechanics -- 2.1. Statics of a bar -- 2.2. Trusses -- 2.3. Two-dimensional continuum generalization -- 3. Fundamentals of tensor algebra and analysis -- 3.1. Introduction -- 3.1.1. Euclidean space and coordinate systems -- 3.1.2. Scalars and vectors -- 3.1.3. Basis of vector space -- 3.2. Tensors -- 3.2.1. Definitions -- 3.2.2. Operations on tensors -- 3.2.3. Isotropic tensors -- 3.3. Second order tensors -- 3.3.1. Definitions and properties -- 3.3.2. Tensor eigenproblem -- 3.3.3. Spectral decomposition of symmetric tensor -- 3.3.4. Polar decomposition of tensor -- 3.4. Tensor functions and fields -- 3.4.1. Integration and differentiation of tensor fields -- 3.4.2. Gauss–Ostrogradski theorem -- 3.5. Curvilinear coordinate systems -- 3.6. Notations used in tensor description -- 4. Motion, deformation and strain in material continuum -- 4.1. Motion of bodies -- 4.2. Strain -- 4.2.1. Definitions -- 4.2.2. Physical meaning of strain in one dimension -- 4.2.3. Physical meaning of strain components -- 4.2.4. Some other strain tensor properties -- 4.3. Area and volumetric deformation -- 4.4. Strain rate and strain increments -- 4.4.1. Time derivative of a tensor field. Lagrangian and Eulerian description of motion -- 4.4.2. Increments and rates of strain tensor measures -- 4.4.3. Strain increments and rates in one dimension -- 4.5. Strain compatibility equations -- 5. Description of stress state -- 5.1. Introduction -- 5.1.1. Forces, stress vectors and stress tensor in continuum -- 5.1.2. Principal stress directions. Extreme stress values -- 5.2. Description of stress in deformable body -- 5.2.1. Cauchy and Piola–Kirchhoff stress tensors -- 5.2.2. Objectivity and invariance of stress measures -- 5.3. Increments and rates of stress tensors -- 5.4. Work of internal forces. Conjugate stress–strain pairs -- 6. Conservation laws in continuum mechanics -- 6.1. Mass conservation law -- 6.2. Momentum conservation law -- 6.3. Angular momentum conservation law -- 6.4. Mechanical energy conservation law -- 7. Constitutive equations -- 7.1. Introductory remarks -- 7.2. Elastic materials -- 7.2.1. Linear elasticity -- 7.2.2. Nonlinear elasticity -- 7.3. Viscoelastic materials -- 7.3.1. One-dimensional models -- 7.3.2. Continuum formulation -- 7.3.3. Energy dissipation in viscoelastic materials -- 7.4. Elastoplastic materials -- 7.4.1. One-dimensional models -- 7.4.2. Three-dimensional formulation in plastic flow theory -- 8. Fundamental system of solid mechanics equations -- 8.1. Field equations and initial-boundary conditions -- 8.2. Incremental form of equations -- 8.3. Some special cases -- 8.4. Example of analytical solution -- 9. Fundamentals of thermomechanics and heat conduction problem -- 9.1. Laws of thermodynamics -- 9.1.1. The first law of thermodynamics -- 9.1.2. The second law of thermodynamics -- 9.2. Heat conduction problem -- 9.3. Fundamental system of solid thermomechanics equations. Thermomechanical Couplings -- 9.4. Thermal expansion in constitutive equations of linear elasticity -- 10. Variational formulations in solid thermomechanics -- 10.1. Variational principles — introduction -- 10.2. Variational formulations for linear mechanics problems -- 10.2.1. Virtual work principle and potential energy -- 10.2.2. Extended variational formulations -- 10.3. Variational formulations for nonlinear mechanics problems -- 10.3.1. Elasticity at large deformations -- 10.3.2. Incremental problem of nonlinear mechanics -- 10.4. Variational formulations for heat conduction problems -- 11. Discrete formulations in thermomechanics -- 11.1. Discrete formulations in heat conduction problems -- 11.1.1. Linear problem of stationary heat conduction -- 11.1.2. General form of the heat conduction problem -- 11.2. Discrete formulations in solid mechanics problems -- 11.2.1. Linear problem of statics -- 11.2.2. Linear problem of dynamics -- 11.2.3. Nonlinear elastic problem with large deformations -- 11.2.4. Incremental form of nonlinear mechanics problem -- 11.3. Weighted residual method -- 12. Fundamentals of finite element method -- 12.1. Introduction -- 12.1.1. FEM formulation for linear heat conduction problem -- 12.1.2. FEM formulation for linear static elasticity problem -- 12.2. FEM approximation at the element level -- 12.2.1. Simple one-dimensional elements -- 12.2.2. Constant strain elements -- 12.2.3. Isoparametric elements -- 13. Solution of FEM equation systems -- 13.1. Introduction -- 13.2. Solution methods for linear algebraic equation systems -- 13.2.1. Elimination methods -- 13.2.2. Iterative methods -- 13.3. Multigrid methods -- 13.4. Solution methods for nonlinear algebraic equation systems -- 13.5. Solution methods for linear and nonlinear systems of first order ordinary differential equations -- 13.6. Solution methods for linear and nonlinear systems of second order ordinary differential equations -- Bibliography -- Index. .
520 _aThe first part of this textbook presents the mathematical background needed to precisely describe the basic problem of continuum thermomechanics. The book then concentrates on developing governing equations for the problem dealing in turn with the kinematics of material continuum, description of the state of stress, discussion of the fundamental conservation laws of underlying physics, formulation of initial-boundary value problems and presenting weak (variational) formulations. In the final part the crucial issue of developing techniques for solving specific problems of thermomechanics is addressed. To this aim the authors present a discretized formulation of the governing equations, discuss the fundamentals of the finite element method and develop some basic algorithms for solving algebraic and ordinary differential equations typical of problems on hand. Theoretical derivations are followed by carefully prepared computational exercises and solutions.
650 0 _aMechanics, Applied.
_93253
650 0 _aSolids.
_93750
650 0 _aMechanics.
_98758
650 0 _aMathematical physics.
_911013
650 0 _aMechanical engineering.
_95856
650 0 _aComputer-aided engineering.
_914016
650 0 _aMathematics—Data processing.
_931594
650 1 4 _aSolid Mechanics.
_931612
650 2 4 _aClassical Mechanics.
_931661
650 2 4 _aTheoretical, Mathematical and Computational Physics.
_931560
650 2 4 _aMechanical Engineering.
_95856
650 2 4 _aComputer-Aided Engineering (CAD, CAE) and Design.
_931735
650 2 4 _aComputational Science and Engineering.
_959283
700 1 _aKowalczyk, Piotr.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_959284
710 2 _aSpringerLink (Online service)
_959285
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783319334547
776 0 8 _iPrinted edition:
_z9783319334561
776 0 8 _iPrinted edition:
_z9783319815176
830 0 _aLecture Notes on Numerical Methods in Engineering and Sciences,
_x1877-735X
_959286
856 4 0 _uhttps://doi.org/10.1007/978-3-319-33455-4
912 _aZDB-2-ENG
912 _aZDB-2-SXE
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