Introduction to the variational formulation in mechanics : fundamentals and applications /: fundamentals and applications. (2020)
- Record Type:
- Book
- Title:
- Introduction to the variational formulation in mechanics : fundamentals and applications /: fundamentals and applications. (2020)
- Main Title:
- Introduction to the variational formulation in mechanics : fundamentals and applications
- Further Information:
- Note: Edgardo O. Taroco, Pablo J. Blanco, and Raúl A. Feijóo, HeMoLab - Hemodynamics Modeling Laboratory, LNCC/MCTIC - National Laboratory for Scientific Computing, Brazil, INCT-MACC - National Institute of Science and Technology in Medicine Assisted by Scientific Computing, Brazil.
- Authors:
- Taroco, Edgardo O (Edgardo Omar), 1935-
Blanco, Pablo J (Pablo Javier), 1979-
Feijóo, R (Raul) - Contents:
- Intro; Title Page; Copyright Page; Contents; Preface; Part I Vector and Tensor Algebra and Analysis; Chapter 1 Vector and Tensor Algebra; 1.1 Points and Vectors; 1.2 Second-Order Tensors; 1.3 Third-Order Tensors; 1.4 Complementary Reading; Chapter 2 Vector and Tensor Analysis; 2.1 Differentiation; 2.2 Gradient; 2.3 Divergence; 2.4 Curl; 2.5 Laplacian; 2.6 Integration; 2.7 Coordinates; 2.8 Complementary Reading; Part II Variational Formulations in Mechanics; Chapter 3 Method of Virtual Power; 3.1 Introduction; 3.2 Kinematics; 3.2.1 Body and Deformations; 3.2.2 Motion: Deformation Rate 3.2.3 Motion Actions: Kinematical Constraints3.3 Duality and Virtual Power; 3.3.1 Motion Actions and Forces; 3.3.2 Deformation Actions and Internal Stresses; 3.3.3 Mechanical Models and the Equilibrium Operator; 3.4 Bodies without Constraints; 3.4.1 Principle of Virtual Power; 3.4.2 Principle of Complementary Virtual Power; 3.5 Bodies with Bilateral Constraints; 3.5.1 Principle of Virtual Power; 3.5.2 Principle of Complementary Virtual Power; 3.6 Bodies with Unilateral Constraints; 3.6.1 Principle of Virtual Power; 3.6.2 Principle of Complementary Virtual Power 3.7 Lagrangian Description of the Principle of Virtual Power3.8 Configurations with Preload and Residual Stresses; 3.9 Linearization of the Principle of Virtual Power; 3.9.1 Preliminary Results; 3.9.2 Known Spatial Configuration; 3.9.3 Known Material Configuration; 3.10 Infinitesimal Deformations and Small Displacements; 3.10.1 BilateralIntro; Title Page; Copyright Page; Contents; Preface; Part I Vector and Tensor Algebra and Analysis; Chapter 1 Vector and Tensor Algebra; 1.1 Points and Vectors; 1.2 Second-Order Tensors; 1.3 Third-Order Tensors; 1.4 Complementary Reading; Chapter 2 Vector and Tensor Analysis; 2.1 Differentiation; 2.2 Gradient; 2.3 Divergence; 2.4 Curl; 2.5 Laplacian; 2.6 Integration; 2.7 Coordinates; 2.8 Complementary Reading; Part II Variational Formulations in Mechanics; Chapter 3 Method of Virtual Power; 3.1 Introduction; 3.2 Kinematics; 3.2.1 Body and Deformations; 3.2.2 Motion: Deformation Rate 3.2.3 Motion Actions: Kinematical Constraints3.3 Duality and Virtual Power; 3.3.1 Motion Actions and Forces; 3.3.2 Deformation Actions and Internal Stresses; 3.3.3 Mechanical Models and the Equilibrium Operator; 3.4 Bodies without Constraints; 3.4.1 Principle of Virtual Power; 3.4.2 Principle of Complementary Virtual Power; 3.5 Bodies with Bilateral Constraints; 3.5.1 Principle of Virtual Power; 3.5.2 Principle of Complementary Virtual Power; 3.6 Bodies with Unilateral Constraints; 3.6.1 Principle of Virtual Power; 3.6.2 Principle of Complementary Virtual Power 3.7 Lagrangian Description of the Principle of Virtual Power3.8 Configurations with Preload and Residual Stresses; 3.9 Linearization of the Principle of Virtual Power; 3.9.1 Preliminary Results; 3.9.2 Known Spatial Configuration; 3.9.3 Known Material Configuration; 3.10 Infinitesimal Deformations and Small Displacements; 3.10.1 Bilateral Constraints; 3.10.2 Unilateral Constraints; 3.11 Final Remarks; 3.12 Complementary Reading; Chapter 4 Hyperelastic Materials at Infinitesimal Strains; 4.1 Introduction; 4.2 Uniaxial Hyperelastic Behavior; 4.3 Three-Dimensional Hyperelastic Constitutive Laws 4.4 Equilibrium in Bodies without Constraints4.4.1 Principle of Virtual Work; 4.4.2 Principle of Minimum Total Potential Energy; 4.4.3 Local Equations and Boundary Conditions; 4.4.4 Principle of Complementary Virtual Work; 4.4.5 Principle of Minimum Complementary Energy; 4.4.6 Additional Remarks; 4.5 Equilibrium in Bodies with Bilateral Constraints; 4.5.1 Principle of Virtual Work; 4.5.2 Principle of Minimum Total Potential Energy; 4.5.3 Principle of Complementary Virtual Work; 4.5.4 Principle of Minimum Complementary Energy; 4.6 Equilibrium in Bodies with Unilateral Constraints 4.6.1 Principle of Virtual Work4.6.2 Principle of Minimum Total Potential Energy; 4.6.3 Principle of Complementary Virtual Work; 4.6.4 Principle of Minimum Complementary Energy; 4.7 Min-Max Principle; 4.7.1 Hellinger-Reissner Functional; 4.7.2 Hellinger-Reissner Principle; 4.8 Three-Field Functional; 4.9 Castigliano Theorems; 4.9.1 First and Second Theorems; 4.9.2 Bounds for Displacements and Generalized Loads; 4.10 Elastodynamics Problem; 4.11 Approximate Solution to Variational Problems; 4.11.1 Elastostatics Problem; 4.11.2 Hellinger-Reissner Principle … (more)
- Publisher Details:
- Hoboken, NJ : John Wiley & Sons
- Publication Date:
- 2020
- Copyright Date:
- 2020
- Extent:
- 1 online resource (xvii, 588 pages)
- Subjects:
- 620.1001/51564
Mechanics, Applied -- Mathematics
Mechanics, Applied -- Mathematics
Electronic books - Languages:
- English
- ISBNs:
- 9781119600954
1119600952
9781119600947
1119600944
9781119600923
1119600928 - Related ISBNs:
- 9781119600909
1119600901 - Notes:
- Note: Includes bibliographical references and index.
Note: Description based on online resource; title from digital title page (viewed on January 23, 2020). - 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.
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- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD.DS.478521
- Ingest File:
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