| 《非线性变形体动力学》：Nonlinear Physical Science focuses on the recent advances of fundamental theories and principles，analytical and symbolic approaches，as well as computational techniques in nonlinear physical science and nonlinear mathematics with engineering applications． |
| chapter 1 introduction 1.1. deformable-body dynamics 1.1.1. cable dynamics 1.1.2. beams and rods 1.1.3. plates and shells 1.1.4. soft webs 1.2. book layout references chapter 2 tensor analysis 2.1. vectors and tensors 2.1.1. vector algebra 2.1.2. base vectors and metric tensors 2.1.3. local base vector transformation 2.1.4. tensor algebra 2.2. second-order tensors 2.2.1. second-order tensor algebra 2.2.2. basic properties 2.2.3. tensor decompositions 2.2.4. tensor functions 2.3. tensor calculus 2.3.1. differentiation 2.3.2. invariant differential operators and integral theorems 2.3.3. riemann-christoffel curvature tensors 2.4. two-point tensor fields 2.4.1. two-point tensors 2.4.2. independent coordinates 2.4.3. correlated coordinates 2.4.4. shifter tensor fields references chapter 3 deformation, kinematics and dynamics 3.1. deformation geometry 3.1.1. curvilinear coordinates 3.1.2. deformation gradient and tensors 3.1.3. green-cauchy strain tensors and engineering strain 3.1.4. principal strains and directions 3.2. kinematics 3.2.1. material derivatives 3.2.2. strain rates 3.3. dynamics 3.3.1. forces and stresses 3.3.2. transport theorem 3.3.3. cauchy stress and couple-stress tensors 3.4. energy conservation references chapter 4 constitutive laws and damage theory 4.1. constitutive equations 4.2. material damage and effective stress 4.3. equivalence principles 4.4. an anisotropic damage theory 4.5. applications 4.5.1. uniaxial tensional models 4.5.2. pure torsion 4.5.3. elastic perfectly-plastic materials references chapter 5 nonlinear cables 5.1. a nonlinear theory of cables 5.2. traveling and rotating cables 5.3. equilibrium of traveling elastic cables 5.3.1. existence conditions 5.3.2. displacements 5.3.3. applications 5.4. nonlinear dynamics of cables 5.4.1. equations of motion 5.4.2. motions of inextensible cables 5.4.3. motions of deformable cables references chapter 6 nonlinear plates and waves chapter 7 nonlinear webs, membranes and shells chapter 8 nonlinear beams and rods subject index |
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