数学弹性力学研究的若干进展

数学弹性力学研究的若干进展
作 者: 王敏中 高存法 高阳
出版社: 科学出版社
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作者简介

暂缺《数学弹性力学研究的若干进展》作者简介

内容简介

《数学弹性力学研究的若干进展》收集了第一作者和他的合作者在数学弹性力学理论研究中的一些论文,涉及的内容有:各向异性弹性力学问题的通解;矩阵的广义逆与应力函数;Saint-Venant问题、广义平面应力问题和Sternberg集中力定义的弱假设——梁、板的精化理论;局部边界积分方程等价于弹性中值定理;某些裂纹、夹杂与空间问题的精确解;多种物理因素(热、磁、压电……)作用下弹性力学问题的通解等。

图书目录

目录

1.关于胡海昌解的完备性 1

2.柱体平衡圣维那解的一个弱假设 10

3.在极坐标中构造平面弹性力学特解的一种方法 17

4.发散积分的有限部分在弹性力学中的应用 21

5.On the Assumption of Saint-Venant's Problem 33

6.受一般载荷的楔:佯谬的解决 41

7.关于以应力表示的弹性力学边值问题 55

8.Brebbia's Indirect Representation and the Completeness of Papkovich-Neuber's and Boussinesq-Galerkin's Solutions in Elasticity 68

9.半空间的热弹性问题||弹性通解方法的应用 73

10.两种材料组成弹性体的界面裂纹问题 90

11.半无限长圆管内 Stokes 流的入口流 96

12.General Complete Solutions of the Equations of Spatial and Axisymmetric Stokes Flow 106

13.Decay Rates for the Hollow Circular Cylinder 119

14.各向异性弹性力学一般边值问题的广义 Stroh 公式 136

15.The Anisotropic Elastic Semi-Infinite Strip 157

16.横观各向同性弹性体轴对称问题的通解及其完备性 176

17.双孔介质弹性动力学通解及其完备性 192

18.广义逆矩阵和应力函数 197

19.Complete Solution of the Linear Magnetoe-lasticity and the Magnetic Fields in a Magnetized Elastic Half-Space 205

20.Completeness and Nonuniqueness of General Solutions of Transversely Isotropic Elasticity 219

21.Stress Functions in Two-Dimensional, Three-Dimensional and n-Dimensional Elasticity 234

22.Collinear Permeable Cracks in Thermopiezoelectric Materials 241

23.Equivalence Between the Local Boundary Integral Equation and the Mean Value Theorem in the Theory of Elasticity 257

24.The Decomposed Form of the Three-Dimensional Elastic Plate 267

25.关于“平面弹性悬臂梁剪切挠度问题” 278

26.The Ellipsoidal Inhomogeneity with Imperfect Interface 284

27.具有孔洞的双周期热弹性平面问题的复势 297

28.A Note on the Limit Definition of Concentrated Loads 311

29.The Quasi Eshelby Property for Rotational Symmetrical Inclusions of Uniform Eigencurvatures within an Infinite Plate 320

30.Comment on “Stress Boundary Conditions for Plate Bending” by F.Y.M.Wan [Int.J.Solids Struct.40(2003) 4107-4123] 334

31.On the Canonical Elastic Moduli of Linear Plane Anisotropic Elasticity 336

32.The Equivalence of the Refined Theory and the Decomposition Theorem of Rectangular Beams 349

33.Three-dimensional Green's Functions for Infinite Anisotropic Piezoelectric Media 367

34.Recent General Solutions in Linear Elasticity and Their Applications 374

35.Elastic Fields for the Ellipsoidal Cavity Problem 431

36.On the Generalized Plane Stress Problem, the Gregory Decomposition and the Filon Mean Method 449

37.General Representations of Polynomial Elastic Fields 482

38.Inhomogeneity Problem with a Sliding Interface under Remote Shearing Stress 502

39.On the Assumptions of the Generalized Plane Stress Problem and the Filon Average 513

40.某些数学方法在弹性力学中的应用 525