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BL
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| Record Number
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891230
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| Main Entry
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Peng, Yijiang
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| Title & Author
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Advances in the base force element method /\ Yijiang Peng, Yinghua Liu.
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| Publication Statement
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Singapore :: Springer,, 2019.
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| Page. NO
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1 online resource
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| ISBN
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9789811357763
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: 9789811357770
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: 9811357765
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: 9811357773
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9789811357756
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9811357757
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| Bibliographies/Indexes
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Includes bibliographical references.
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| Contents
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Intro; Preface; References; Acknowledgements; Contents; 1 Introduction; 1.1 Development of Finite Element Method; 1.2 Development of Complementary Energy Principle for Large Elastic Deformation; 1.3 Development of Base Force Element Method; 1.4 Characteristics of Base Force Element Method; 1.5 Main Contents of This Book; References; 2 Basic Formula on Base Forces; 2.1 Definition of Base Forces; 2.2 Function of Base Forces; 2.3 Relation Between Base Forces and Various Stress Tensors; 2.4 Conjugate Variable of Base Forces; 2.5 Basic Equation Expressed by Gradient of Displacement and Base Forces
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10 Base Force Element Method for Nonlinear Problems of Materials10.1 Basic Equations; 10.2 Equivalent Stress of a BFEM Element; 10.3 Expression of Nodal Displacement; 10.4 Method for Solving Nonlinear Equations; 10.5 Procedure of the Base Force Element Method for Elastoplastic Problems; 10.6 Numerical Examples; 10.7 Conclusions; 11 3D Base Force Element Method for Linear Elastic Problems; 11.1 Stress of a Polyhedral Element; 11.2 Compliance Matrix of a Polyhedral Element; 11.3 Governing Equations of Structure; 11.4 Node Displacement; 11.5 Numerical Examples; 11.6 Conclusions; References
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2.6 Boundary ConditionsReferences; 3 Complementary Energy Principle on Base Forces; 3.1 Complementary Energy Principle by Y.C. Gao; 3.2 Some Questions; 3.3 Examples; 3.4 Another Version of the Principle; 3.5 The Relation of Complementary Energy and Potential Energy; References; 4 2D Base Force Element Method for Linear Elastic Problems; 4.1 2D Basic Equations; 4.2 Compliance Matrix; 4.3 Governing Equations; 4.4 Numerical Examples; 4.5 Conclusions; References; 5 Base Force Element Method for Convex Polygonal Mesh; 5.1 Compliance Matrix; 5.2 Governing Equations
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5.3 Expression of Stress for a Convex Polygon Element5.4 Expression of Node Displacement of Convex Polygon Element; 5.5 Numerical Example; 5.6 Conclusions; References; 6 Base Force Element Method for Concave Polygonal Mesh; 6.1 Development of 2D BFEM with Concave Polygonal Meshes; 6.2 Numerical Examples; 6.3 Conclusions; References; 7 2D Base Force Element Method for Geometrically Nonlinear Problems; 7.1 Setting of the Problem; 7.2 Complementary Energy of an Element; 7.3 Nonlinear Governing Equations of BFEM; 7.4 Expression of Element Stress; 7.5 Expression of Node Displacement
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7.6 Numerical Examples7.7 Conclusions; References; 8 BFEM on Convex Polygonal Mesh for Geometrically Nonlinear Problems; 8.1 Basic Formulae; 8.2 Basic Formulae Model of BFEM for Arbitrary Mesh Problems; 8.3 Explicit Expressions for Stress of Element and Displacement of Node; 8.4 Numerical Examples; 8.5 Conclusions; Reference; 9 BFEM on Concave Polygonal Mesh for Geometrically Nonlinear Problems; 9.1 Complementary Energy of a Concave Polygonal Element; 9.2 Stress of Concave Polygonal Element and Displacement of Node; 9.3 Numerical Examples; 9.4 Conclusions; Reference
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| Abstract
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This book describes the main concepts of and recent advances in the base forces element method (BFEM). It combines theories, methods, models, numerical results, and an analysis of the BFEM. Each chapter starts with an introduction and derivation of a new mathematical model for the proposed method. Subsequently, the methods are described and numerical examples demonstrating the significance of the proposed method are presented. The closing chapter summarizes the performance and features of the BFEM and describes the prospects for its application. The book is intended for engineers, scientists and graduate students in applied mechanics and applied mathematics, and for all readers interested in numerical computations and simulations.
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| Subject
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Finite element method.
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| Subject
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Finite element method.
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| Subject
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MATHEMATICS-- Numerical Analysis.
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| Dewey Classification
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518/.25
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| LC Classification
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TA347.F5
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| Added Entry
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Liu, Yinghua
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