Symplectic elasticity /:
Exact analytical solutions in some areas of solid mechanics, in particular problems in the theory of plates, have long been regarded as bottlenecks in the development of elasticity. In contrast to the traditional solution methodologies, such as Timoshenko's approach in the theory of elasticity...
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| Sprache: | English Chinese |
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©2009.
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| Online-Zugang: | DE-862 DE-863 |
| Zusammenfassung: | Exact analytical solutions in some areas of solid mechanics, in particular problems in the theory of plates, have long been regarded as bottlenecks in the development of elasticity. In contrast to the traditional solution methodologies, such as Timoshenko's approach in the theory of elasticity for which the main technique is the semi-inverse method, this book presents a new approach based on the Hamiltonian principle and the symplectic duality system where solutions are derived in a rational manner in the symplectic space. Dissimilar to the conventional Euclidean space with one kind of variables, the symplectic space with dual variables thus provides a fundamental breakthrough. A unique feature of this symplectic approach is the classical bending problems in solid mechanics now become eigenvalue problems and the symplectic bending deflection solutions are constituted by expansion of eigenvectors. The classical solutions are subsets of the more general symplectic solutions. This book explains the new solution methodology by discussing plane isotropic elasticity, multiple layered plate, anisotropic elasticity, sectorial plate and thin plate bending problems in detail. A number of existing problems without analytical solutions within the framework of classical approaches are solved analytically using this symplectic approach. Symplectic methodologies can be applied not only to problems in elasticity, but also to other solid mechanics problems. In addition, it can also be extended to various engineering mechanics and mathematical physics fields, such as vibration, wave propagation, control theory, electromagnetism and quantum mechanics. |
| Beschreibung: | 1 online resource (xxi, 292 pages) : illustrations |
| Bibliographie: | Includes bibliographical references. |
| ISBN: | 9789812778727 9812778721 1282441361 9781282441361 |
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| 245 | 1 | 0 | |a Symplectic elasticity / |c Weian Yao, Wanxie Zhong, Chee Wah Lim. |
| 260 | |a New Jersey : |b World Scientific, |c ©2009. | ||
| 300 | |a 1 online resource (xxi, 292 pages) : |b illustrations | ||
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| 504 | |a Includes bibliographical references. | ||
| 546 | |a Translated from Chinese. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 1. Mathematical preliminaries. 1.1. Linear space. 1.2. Euclidean space. 1.3. Symplectic space. 1.4. Legengre's transformation. 1.5. The Hamiltonian principle and the Hamiltonian canonical equations. 1.6. The Reciprocal theorems -- 2. Fundamental equations of elasticity and variational principle. 2.1. Stress analysis. 2.2. Strain analysis. 2.3. Stress-strain relations. 2.4. The fundamental equations of elasticity. 2.5. The principle of virtual work. 2.6. The principle of minimum total potential energy. 2.7. The principle of minimum total complementary energy. 2.8. The Hellinger-Reissner variational principle with two kinds of variables. 2.9. The Hu-Washizu variational principle with three kinds of variables. 2.10. The principle of superposition and the uniqueness theorem. 2.11. Saint-Venant principle -- 3. The Timoshenko beam theory and its extension. 3.1. The Timoshenko beam theory. 3.2. Derivation of Hamiltonian system. 3.3. The method of separation of variables. 3.4. Reciprocal theorem for work and adjoint symplectic orthogonality. 3.5. Solution for non-homogeneous equations. 3.6. Two-point boundary conditions. 3.7. Static analysis of Timoshenko beam. 3.8. Wave propagation analysis of Timoshenko beam. 3.9. Wave induced resonance -- 4. Plane elasticity in rectangular coordinates. 4.1. The fundamental equations of plane elasticity. 4.2. Hamiltonian system in rectangular domain. 4.3. Separation of variables and transverse Eigen-problems. 4.4. Eigen-solutions of zero Eigenvalue. 4.5. Solutions of Saint-Venant problems for rectangular beam. 4.6. Eigen-solutions of nonzero Eigenvalues. 4.7. Solutions of generalized plane problems in rectangular domain -- 5. Plane anisotropic elasticity problems. 5.1. The fundamental equations of plane anisotropic elasticity problems. 5.2. Symplectic solution methodology for anisotropic elasticity problems. 5.3. Eigen-solutions of zero Eigenvalue. 5.4. Analytical solutions of Saint-Venant problems. 5.5. Eigen-solutions of nonzero Eigenvalues. 5.6. Introduction to Hamiltonian system for generalized plane problems -- 6. Saint-Venant problems for laminated composite plates. 6.1. The fundamental equations. 6.2. Derivation of Hamiltonian system. 6.3. Eigen-solutions of zero Eigenvalue. 6.4. Analytical solutions of Saint-Venant problem -- 7. Solutions for plane elasticity in polar coordinates. 7.1. Plane elasticity equations in polar coordinates. 7.2. Variational principle for a circular sector. 7.3. Hamiltonian system with radial coordinate treated as "Time". 7.4. Eigen-solutions for symmetric deformation in radial Hamiltonian system. 7.5. Eigen-solutions for anti-symmetric deformation in radial Hamiltonian system. 7.6. Hamiltonian system with circumferential coordinate treated as "Time" -- 8. Hamiltonian system for bending of thin plates. 8.1. Small deflection theory for bending of elastic thin plates. 8.2. Analogy between plane elasticity and bending of thin plate. 8.3. Multi-variable variational principles for thin plate bending and plane elasticity. 8.4. Symplectic solution for rectangular plates. 8.5. Plates with two opposite sides simply supported. 8.6. Plates with two opposite sides free. 8.7. Plate with two opposite sides clamped. 8.8. Bending of sectorial plates. | |
| 520 | |a Exact analytical solutions in some areas of solid mechanics, in particular problems in the theory of plates, have long been regarded as bottlenecks in the development of elasticity. In contrast to the traditional solution methodologies, such as Timoshenko's approach in the theory of elasticity for which the main technique is the semi-inverse method, this book presents a new approach based on the Hamiltonian principle and the symplectic duality system where solutions are derived in a rational manner in the symplectic space. Dissimilar to the conventional Euclidean space with one kind of variables, the symplectic space with dual variables thus provides a fundamental breakthrough. A unique feature of this symplectic approach is the classical bending problems in solid mechanics now become eigenvalue problems and the symplectic bending deflection solutions are constituted by expansion of eigenvectors. The classical solutions are subsets of the more general symplectic solutions. This book explains the new solution methodology by discussing plane isotropic elasticity, multiple layered plate, anisotropic elasticity, sectorial plate and thin plate bending problems in detail. A number of existing problems without analytical solutions within the framework of classical approaches are solved analytically using this symplectic approach. Symplectic methodologies can be applied not only to problems in elasticity, but also to other solid mechanics problems. In addition, it can also be extended to various engineering mechanics and mathematical physics fields, such as vibration, wave propagation, control theory, electromagnetism and quantum mechanics. | ||
| 650 | 0 | |a Elasticity. |0 http://id.loc.gov/authorities/subjects/sh85041516 | |
| 650 | 0 | |a Symplectic spaces. |0 http://id.loc.gov/authorities/subjects/sh2004000709 | |
| 650 | 2 | |a Elasticity |0 https://id.nlm.nih.gov/mesh/D004548 | |
| 650 | 6 | |a Élasticité. | |
| 650 | 6 | |a Espaces symplectiques. | |
| 650 | 7 | |a SCIENCE |x Mechanics |x General. |2 bisacsh | |
| 650 | 7 | |a SCIENCE |x Mechanics |x Solids. |2 bisacsh | |
| 650 | 7 | |a Elasticity |2 fast | |
| 650 | 7 | |a Symplectic spaces |2 fast | |
| 655 | 0 | |a Electronic books. | |
| 700 | 1 | |a Zhong, Wanxie. | |
| 700 | 1 | |a Lim, Chee Wah, |d 1965- |1 https://id.oclc.org/worldcat/entity/E39PCjMfjvx8CKbwBTfKVV8bwK |0 http://id.loc.gov/authorities/names/no2009148031 | |
| 758 | |i has work: |a Symplectic elasticity (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFYf6bKmTh3cTbmttpHt8C |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
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| adam_text | |
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| author | Yao, Weian, 1963- |
| author2 | Zhong, Wanxie Lim, Chee Wah, 1965- |
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| contents | 1. Mathematical preliminaries. 1.1. Linear space. 1.2. Euclidean space. 1.3. Symplectic space. 1.4. Legengre's transformation. 1.5. The Hamiltonian principle and the Hamiltonian canonical equations. 1.6. The Reciprocal theorems -- 2. Fundamental equations of elasticity and variational principle. 2.1. Stress analysis. 2.2. Strain analysis. 2.3. Stress-strain relations. 2.4. The fundamental equations of elasticity. 2.5. The principle of virtual work. 2.6. The principle of minimum total potential energy. 2.7. The principle of minimum total complementary energy. 2.8. The Hellinger-Reissner variational principle with two kinds of variables. 2.9. The Hu-Washizu variational principle with three kinds of variables. 2.10. The principle of superposition and the uniqueness theorem. 2.11. Saint-Venant principle -- 3. The Timoshenko beam theory and its extension. 3.1. The Timoshenko beam theory. 3.2. Derivation of Hamiltonian system. 3.3. The method of separation of variables. 3.4. Reciprocal theorem for work and adjoint symplectic orthogonality. 3.5. Solution for non-homogeneous equations. 3.6. Two-point boundary conditions. 3.7. Static analysis of Timoshenko beam. 3.8. Wave propagation analysis of Timoshenko beam. 3.9. Wave induced resonance -- 4. Plane elasticity in rectangular coordinates. 4.1. The fundamental equations of plane elasticity. 4.2. Hamiltonian system in rectangular domain. 4.3. Separation of variables and transverse Eigen-problems. 4.4. Eigen-solutions of zero Eigenvalue. 4.5. Solutions of Saint-Venant problems for rectangular beam. 4.6. Eigen-solutions of nonzero Eigenvalues. 4.7. Solutions of generalized plane problems in rectangular domain -- 5. Plane anisotropic elasticity problems. 5.1. The fundamental equations of plane anisotropic elasticity problems. 5.2. Symplectic solution methodology for anisotropic elasticity problems. 5.3. Eigen-solutions of zero Eigenvalue. 5.4. Analytical solutions of Saint-Venant problems. 5.5. Eigen-solutions of nonzero Eigenvalues. 5.6. Introduction to Hamiltonian system for generalized plane problems -- 6. Saint-Venant problems for laminated composite plates. 6.1. The fundamental equations. 6.2. Derivation of Hamiltonian system. 6.3. Eigen-solutions of zero Eigenvalue. 6.4. Analytical solutions of Saint-Venant problem -- 7. Solutions for plane elasticity in polar coordinates. 7.1. Plane elasticity equations in polar coordinates. 7.2. Variational principle for a circular sector. 7.3. Hamiltonian system with radial coordinate treated as "Time". 7.4. Eigen-solutions for symmetric deformation in radial Hamiltonian system. 7.5. Eigen-solutions for anti-symmetric deformation in radial Hamiltonian system. 7.6. Hamiltonian system with circumferential coordinate treated as "Time" -- 8. Hamiltonian system for bending of thin plates. 8.1. Small deflection theory for bending of elastic thin plates. 8.2. Analogy between plane elasticity and bending of thin plate. 8.3. Multi-variable variational principles for thin plate bending and plane elasticity. 8.4. Symplectic solution for rectangular plates. 8.5. Plates with two opposite sides simply supported. 8.6. Plates with two opposite sides free. 8.7. Plate with two opposite sides clamped. 8.8. Bending of sectorial plates. |
| ctrlnum | (OCoLC)610176684 |
| dewey-full | 531/.382 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531/.382 |
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| dewey-sort | 3531 3382 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Electronic eBook |
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Mathematical preliminaries. 1.1. Linear space. 1.2. Euclidean space. 1.3. Symplectic space. 1.4. Legengre's transformation. 1.5. The Hamiltonian principle and the Hamiltonian canonical equations. 1.6. The Reciprocal theorems -- 2. Fundamental equations of elasticity and variational principle. 2.1. Stress analysis. 2.2. Strain analysis. 2.3. Stress-strain relations. 2.4. The fundamental equations of elasticity. 2.5. The principle of virtual work. 2.6. The principle of minimum total potential energy. 2.7. The principle of minimum total complementary energy. 2.8. The Hellinger-Reissner variational principle with two kinds of variables. 2.9. The Hu-Washizu variational principle with three kinds of variables. 2.10. The principle of superposition and the uniqueness theorem. 2.11. Saint-Venant principle -- 3. The Timoshenko beam theory and its extension. 3.1. The Timoshenko beam theory. 3.2. Derivation of Hamiltonian system. 3.3. The method of separation of variables. 3.4. Reciprocal theorem for work and adjoint symplectic orthogonality. 3.5. Solution for non-homogeneous equations. 3.6. Two-point boundary conditions. 3.7. Static analysis of Timoshenko beam. 3.8. Wave propagation analysis of Timoshenko beam. 3.9. Wave induced resonance -- 4. Plane elasticity in rectangular coordinates. 4.1. The fundamental equations of plane elasticity. 4.2. Hamiltonian system in rectangular domain. 4.3. Separation of variables and transverse Eigen-problems. 4.4. Eigen-solutions of zero Eigenvalue. 4.5. Solutions of Saint-Venant problems for rectangular beam. 4.6. Eigen-solutions of nonzero Eigenvalues. 4.7. Solutions of generalized plane problems in rectangular domain -- 5. Plane anisotropic elasticity problems. 5.1. The fundamental equations of plane anisotropic elasticity problems. 5.2. Symplectic solution methodology for anisotropic elasticity problems. 5.3. Eigen-solutions of zero Eigenvalue. 5.4. Analytical solutions of Saint-Venant problems. 5.5. Eigen-solutions of nonzero Eigenvalues. 5.6. Introduction to Hamiltonian system for generalized plane problems -- 6. Saint-Venant problems for laminated composite plates. 6.1. The fundamental equations. 6.2. Derivation of Hamiltonian system. 6.3. Eigen-solutions of zero Eigenvalue. 6.4. Analytical solutions of Saint-Venant problem -- 7. Solutions for plane elasticity in polar coordinates. 7.1. Plane elasticity equations in polar coordinates. 7.2. Variational principle for a circular sector. 7.3. Hamiltonian system with radial coordinate treated as "Time". 7.4. Eigen-solutions for symmetric deformation in radial Hamiltonian system. 7.5. Eigen-solutions for anti-symmetric deformation in radial Hamiltonian system. 7.6. Hamiltonian system with circumferential coordinate treated as "Time" -- 8. Hamiltonian system for bending of thin plates. 8.1. Small deflection theory for bending of elastic thin plates. 8.2. Analogy between plane elasticity and bending of thin plate. 8.3. Multi-variable variational principles for thin plate bending and plane elasticity. 8.4. Symplectic solution for rectangular plates. 8.5. Plates with two opposite sides simply supported. 8.6. Plates with two opposite sides free. 8.7. Plate with two opposite sides clamped. 8.8. Bending of sectorial plates.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Exact analytical solutions in some areas of solid mechanics, in particular problems in the theory of plates, have long been regarded as bottlenecks in the development of elasticity. In contrast to the traditional solution methodologies, such as Timoshenko's approach in the theory of elasticity for which the main technique is the semi-inverse method, this book presents a new approach based on the Hamiltonian principle and the symplectic duality system where solutions are derived in a rational manner in the symplectic space. Dissimilar to the conventional Euclidean space with one kind of variables, the symplectic space with dual variables thus provides a fundamental breakthrough. A unique feature of this symplectic approach is the classical bending problems in solid mechanics now become eigenvalue problems and the symplectic bending deflection solutions are constituted by expansion of eigenvectors. The classical solutions are subsets of the more general symplectic solutions. This book explains the new solution methodology by discussing plane isotropic elasticity, multiple layered plate, anisotropic elasticity, sectorial plate and thin plate bending problems in detail. A number of existing problems without analytical solutions within the framework of classical approaches are solved analytically using this symplectic approach. Symplectic methodologies can be applied not only to problems in elasticity, but also to other solid mechanics problems. 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| genre | Electronic books. |
| genre_facet | Electronic books. |
| id | ZDB-4-EBA-ocn610176684 |
| illustrated | Illustrated |
| indexdate | 2025-04-11T08:36:42Z |
| institution | BVB |
| isbn | 9789812778727 9812778721 1282441361 9781282441361 |
| language | English Chinese |
| oclc_num | 610176684 |
| open_access_boolean | |
| owner | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| physical | 1 online resource (xxi, 292 pages) : illustrations |
| psigel | ZDB-4-EBA FWS_PDA_EBA ZDB-4-EBA |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | World Scientific, |
| record_format | marc |
| spelling | Yao, Weian, 1963- https://id.oclc.org/worldcat/entity/E39PCjBFjtFbcX6TCtY4bdGDVP http://id.loc.gov/authorities/names/no2009148023 Symplectic elasticity / Weian Yao, Wanxie Zhong, Chee Wah Lim. New Jersey : World Scientific, ©2009. 1 online resource (xxi, 292 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references. Translated from Chinese. Print version record. 1. Mathematical preliminaries. 1.1. Linear space. 1.2. Euclidean space. 1.3. Symplectic space. 1.4. Legengre's transformation. 1.5. The Hamiltonian principle and the Hamiltonian canonical equations. 1.6. The Reciprocal theorems -- 2. Fundamental equations of elasticity and variational principle. 2.1. Stress analysis. 2.2. Strain analysis. 2.3. Stress-strain relations. 2.4. The fundamental equations of elasticity. 2.5. The principle of virtual work. 2.6. The principle of minimum total potential energy. 2.7. The principle of minimum total complementary energy. 2.8. The Hellinger-Reissner variational principle with two kinds of variables. 2.9. The Hu-Washizu variational principle with three kinds of variables. 2.10. The principle of superposition and the uniqueness theorem. 2.11. Saint-Venant principle -- 3. The Timoshenko beam theory and its extension. 3.1. The Timoshenko beam theory. 3.2. Derivation of Hamiltonian system. 3.3. The method of separation of variables. 3.4. Reciprocal theorem for work and adjoint symplectic orthogonality. 3.5. Solution for non-homogeneous equations. 3.6. Two-point boundary conditions. 3.7. Static analysis of Timoshenko beam. 3.8. Wave propagation analysis of Timoshenko beam. 3.9. Wave induced resonance -- 4. Plane elasticity in rectangular coordinates. 4.1. The fundamental equations of plane elasticity. 4.2. Hamiltonian system in rectangular domain. 4.3. Separation of variables and transverse Eigen-problems. 4.4. Eigen-solutions of zero Eigenvalue. 4.5. Solutions of Saint-Venant problems for rectangular beam. 4.6. Eigen-solutions of nonzero Eigenvalues. 4.7. Solutions of generalized plane problems in rectangular domain -- 5. Plane anisotropic elasticity problems. 5.1. The fundamental equations of plane anisotropic elasticity problems. 5.2. Symplectic solution methodology for anisotropic elasticity problems. 5.3. Eigen-solutions of zero Eigenvalue. 5.4. Analytical solutions of Saint-Venant problems. 5.5. Eigen-solutions of nonzero Eigenvalues. 5.6. Introduction to Hamiltonian system for generalized plane problems -- 6. Saint-Venant problems for laminated composite plates. 6.1. The fundamental equations. 6.2. Derivation of Hamiltonian system. 6.3. Eigen-solutions of zero Eigenvalue. 6.4. Analytical solutions of Saint-Venant problem -- 7. Solutions for plane elasticity in polar coordinates. 7.1. Plane elasticity equations in polar coordinates. 7.2. Variational principle for a circular sector. 7.3. Hamiltonian system with radial coordinate treated as "Time". 7.4. Eigen-solutions for symmetric deformation in radial Hamiltonian system. 7.5. Eigen-solutions for anti-symmetric deformation in radial Hamiltonian system. 7.6. Hamiltonian system with circumferential coordinate treated as "Time" -- 8. Hamiltonian system for bending of thin plates. 8.1. Small deflection theory for bending of elastic thin plates. 8.2. Analogy between plane elasticity and bending of thin plate. 8.3. Multi-variable variational principles for thin plate bending and plane elasticity. 8.4. Symplectic solution for rectangular plates. 8.5. Plates with two opposite sides simply supported. 8.6. Plates with two opposite sides free. 8.7. Plate with two opposite sides clamped. 8.8. Bending of sectorial plates. Exact analytical solutions in some areas of solid mechanics, in particular problems in the theory of plates, have long been regarded as bottlenecks in the development of elasticity. In contrast to the traditional solution methodologies, such as Timoshenko's approach in the theory of elasticity for which the main technique is the semi-inverse method, this book presents a new approach based on the Hamiltonian principle and the symplectic duality system where solutions are derived in a rational manner in the symplectic space. Dissimilar to the conventional Euclidean space with one kind of variables, the symplectic space with dual variables thus provides a fundamental breakthrough. A unique feature of this symplectic approach is the classical bending problems in solid mechanics now become eigenvalue problems and the symplectic bending deflection solutions are constituted by expansion of eigenvectors. The classical solutions are subsets of the more general symplectic solutions. This book explains the new solution methodology by discussing plane isotropic elasticity, multiple layered plate, anisotropic elasticity, sectorial plate and thin plate bending problems in detail. A number of existing problems without analytical solutions within the framework of classical approaches are solved analytically using this symplectic approach. Symplectic methodologies can be applied not only to problems in elasticity, but also to other solid mechanics problems. In addition, it can also be extended to various engineering mechanics and mathematical physics fields, such as vibration, wave propagation, control theory, electromagnetism and quantum mechanics. Elasticity. http://id.loc.gov/authorities/subjects/sh85041516 Symplectic spaces. http://id.loc.gov/authorities/subjects/sh2004000709 Elasticity https://id.nlm.nih.gov/mesh/D004548 Élasticité. Espaces symplectiques. SCIENCE Mechanics General. bisacsh SCIENCE Mechanics Solids. bisacsh Elasticity fast Symplectic spaces fast Electronic books. Zhong, Wanxie. Lim, Chee Wah, 1965- https://id.oclc.org/worldcat/entity/E39PCjMfjvx8CKbwBTfKVV8bwK http://id.loc.gov/authorities/names/no2009148031 has work: Symplectic elasticity (Text) https://id.oclc.org/worldcat/entity/E39PCFYf6bKmTh3cTbmttpHt8C https://id.oclc.org/worldcat/ontology/hasWork Print version: Yao, Weian, 1963- Symplectic elasticity. New Jersey : World Scientific, ©2009 9789812778703 (DLC) 2009280194 (OCoLC)496282564 |
| spellingShingle | Yao, Weian, 1963- Symplectic elasticity / 1. Mathematical preliminaries. 1.1. Linear space. 1.2. Euclidean space. 1.3. Symplectic space. 1.4. Legengre's transformation. 1.5. The Hamiltonian principle and the Hamiltonian canonical equations. 1.6. The Reciprocal theorems -- 2. Fundamental equations of elasticity and variational principle. 2.1. Stress analysis. 2.2. Strain analysis. 2.3. Stress-strain relations. 2.4. The fundamental equations of elasticity. 2.5. The principle of virtual work. 2.6. The principle of minimum total potential energy. 2.7. The principle of minimum total complementary energy. 2.8. The Hellinger-Reissner variational principle with two kinds of variables. 2.9. The Hu-Washizu variational principle with three kinds of variables. 2.10. The principle of superposition and the uniqueness theorem. 2.11. Saint-Venant principle -- 3. The Timoshenko beam theory and its extension. 3.1. The Timoshenko beam theory. 3.2. Derivation of Hamiltonian system. 3.3. The method of separation of variables. 3.4. Reciprocal theorem for work and adjoint symplectic orthogonality. 3.5. Solution for non-homogeneous equations. 3.6. Two-point boundary conditions. 3.7. Static analysis of Timoshenko beam. 3.8. Wave propagation analysis of Timoshenko beam. 3.9. Wave induced resonance -- 4. Plane elasticity in rectangular coordinates. 4.1. The fundamental equations of plane elasticity. 4.2. Hamiltonian system in rectangular domain. 4.3. Separation of variables and transverse Eigen-problems. 4.4. Eigen-solutions of zero Eigenvalue. 4.5. Solutions of Saint-Venant problems for rectangular beam. 4.6. Eigen-solutions of nonzero Eigenvalues. 4.7. Solutions of generalized plane problems in rectangular domain -- 5. Plane anisotropic elasticity problems. 5.1. The fundamental equations of plane anisotropic elasticity problems. 5.2. Symplectic solution methodology for anisotropic elasticity problems. 5.3. Eigen-solutions of zero Eigenvalue. 5.4. Analytical solutions of Saint-Venant problems. 5.5. Eigen-solutions of nonzero Eigenvalues. 5.6. Introduction to Hamiltonian system for generalized plane problems -- 6. Saint-Venant problems for laminated composite plates. 6.1. The fundamental equations. 6.2. Derivation of Hamiltonian system. 6.3. Eigen-solutions of zero Eigenvalue. 6.4. Analytical solutions of Saint-Venant problem -- 7. Solutions for plane elasticity in polar coordinates. 7.1. Plane elasticity equations in polar coordinates. 7.2. Variational principle for a circular sector. 7.3. Hamiltonian system with radial coordinate treated as "Time". 7.4. Eigen-solutions for symmetric deformation in radial Hamiltonian system. 7.5. Eigen-solutions for anti-symmetric deformation in radial Hamiltonian system. 7.6. Hamiltonian system with circumferential coordinate treated as "Time" -- 8. Hamiltonian system for bending of thin plates. 8.1. Small deflection theory for bending of elastic thin plates. 8.2. Analogy between plane elasticity and bending of thin plate. 8.3. Multi-variable variational principles for thin plate bending and plane elasticity. 8.4. Symplectic solution for rectangular plates. 8.5. Plates with two opposite sides simply supported. 8.6. Plates with two opposite sides free. 8.7. Plate with two opposite sides clamped. 8.8. Bending of sectorial plates. Elasticity. http://id.loc.gov/authorities/subjects/sh85041516 Symplectic spaces. http://id.loc.gov/authorities/subjects/sh2004000709 Elasticity https://id.nlm.nih.gov/mesh/D004548 Élasticité. Espaces symplectiques. SCIENCE Mechanics General. bisacsh SCIENCE Mechanics Solids. bisacsh Elasticity fast Symplectic spaces fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85041516 http://id.loc.gov/authorities/subjects/sh2004000709 https://id.nlm.nih.gov/mesh/D004548 |
| title | Symplectic elasticity / |
| title_auth | Symplectic elasticity / |
| title_exact_search | Symplectic elasticity / |
| title_full | Symplectic elasticity / Weian Yao, Wanxie Zhong, Chee Wah Lim. |
| title_fullStr | Symplectic elasticity / Weian Yao, Wanxie Zhong, Chee Wah Lim. |
| title_full_unstemmed | Symplectic elasticity / Weian Yao, Wanxie Zhong, Chee Wah Lim. |
| title_short | Symplectic elasticity / |
| title_sort | symplectic elasticity |
| topic | Elasticity. http://id.loc.gov/authorities/subjects/sh85041516 Symplectic spaces. http://id.loc.gov/authorities/subjects/sh2004000709 Elasticity https://id.nlm.nih.gov/mesh/D004548 Élasticité. Espaces symplectiques. SCIENCE Mechanics General. bisacsh SCIENCE Mechanics Solids. bisacsh Elasticity fast Symplectic spaces fast |
| topic_facet | Elasticity. Symplectic spaces. Elasticity Élasticité. Espaces symplectiques. SCIENCE Mechanics General. SCIENCE Mechanics Solids. Symplectic spaces Electronic books. |
| work_keys_str_mv | AT yaoweian symplecticelasticity AT zhongwanxie symplecticelasticity AT limcheewah symplecticelasticity |