Introduction to nonlinear thermomechanics of solids. (2016)

• Record Type: Book
• Further Information: Note: Michał Kleiber, Piotr Kowalczyk.
• Authors: Kleiber, Michał; Kowalczyk, P (Piotr), 1963-
• Contents: 1. 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.
• Publisher Details: Switzerland : Springer
• Publication Date: 2016
• Extent: 1 online resource (viii, 345 pages), illustrations
• Subjects: 531/.3; Engineering; Nonlinear mechanics; Finite element method; Tensor algebra; Finite element method; Nonlinear mechanics; Tensor algebra; Science -- Mechanics -- General; Science -- Mathematical Physics; Technology & Engineering -- Mechanical; Computers -- CAD-CAM; Computers -- Computer Science; Classical mechanics; Mathematical physics; Mechanical engineering; Computer-aided design (CAD); Maths for scientists; Mechanics; Mechanics, Applied; Mechanical engineering; Computer aided design; Computer science; Science -- Mechanics -- Solids; Mechanics of solids; Electronic books
• Languages: English
• ISBNs: 9783319334554; 3319334557; 3319334549; 9783319334547
• Related ISBNs: 9783319334547
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed June 30, 2016).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.