应用数学和力学

1980 Vol. 1, No. 1

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1980, 1(1): 1-3.

Abstract(2218) PDF(631)

Abstract:

Unified Theory of Variational Principles in Non-linear Theory of Elasticity

Guo Zhong-heng

1980, 1(1): 5-23.

Abstract(2431) PDF(703)

Abstract:
The purpose of this paper is to introduce and to discuss several main variational principles in nonlinear theory of elasticity,namely the classic potential energy principle, complementary energy principle, and other two complementary energy pri nciples(Levinson principle and Fraeijs de Veubeke princ...

Finite Element Analysis of Axisymmetric Elastic Body Problems

Chien Wei-zang

1980, 1(1): 25-35.

Abstract(2531) PDF(987)

Abstract:
Linear form functions are commonly used in a long time for a toroidal volume element swept by a triangle revolved about the symmetrical axis for general axisymmetrical stress problems. It is difficult to obtain the rigidity matrix by exact integration, and instead, the method of approximate integrat...

Some Applications of Perturbation Method in Thin Plate Bending Problems

Kiang Fu-ru

1980, 1(1): 37-53.

Abstract(1918) PDF(692)

Abstract:
In this paper,problems of bending of thin plates under the combined action of lateral loading and in-plane forces are studied by means of perturbation method.

On An Eigenvalue Problem Related to the Buckling of Sandwich Beams

Hu Hai-chang

1980, 1(1): 55-62.

Abstract(1874) PDF(521)

Abstract:
This paper gives various properties of eigenvalue problems related to the buckling of sandwich beams. The applications of eigenfunctions are also indicated.

Variation Transformation Analysis(Ⅰ)

Wu Xue-mou

1980, 1(1): 63-69.

Abstract(1889) PDF(647)

Abstract:
This paper is concerned with operator variation from the transformation point of view,and presents some new concepts and new relations.Related problems and concepts include:convex operator,reciprocity set and reciprocity principles,H-generalized solution and operator-differential equation,etc.

Nonlinear Stability of Thin Elastic Circular Shallow Spherical Shell under the Action of Uniform Edge Moment

Yeh Kai-yuan, Liu Zen-huai, Chang Chuan-dzi, Shue Ih-fan

1980, 1(1): 71-87.

Abstract(2269) PDF(671)

Abstract:
In 1939. the importance of the nonlinear feature in the shell buckling problem was first pointed out in a most spectacular manner by von Karman and Tsien,but the mathematical difficulty is so great that progress has been slow after the first attempts.According to our experience, we should face the d...

Various Reciprocal Theorems and Variational Principles in the Theories of Nonlocal Micropolar Linear Elastic Mediums

Tai Tien-min

1980, 1(1): 89-106.

Abstract(2058) PDF(609)

Abstract:
In the first part of our paper, we have extended the concepts of the classical convolution and the "convolution scalar product" given by I. Hlavacek and presented the concepts of the "convolution vector" and the "convolution vector scalar product", which enable us to extend the initial value as well...

An Asymptotic Elastic Plastic Analysis in Plane Strain Deformation near a Crack Tip

Hsueh Dah-wei

1980, 1(1): 107-113.

Abstract(1963) PDF(648)

Abstract:
In this Paper,an asymptotic elastoplastic analysis in plane strain deformation near a crack tip is established. The special case of which is the well-known Irwin's solution in elastic material.

An Iteration Method for Integral Equations Arising from Axisymmetric Loading Problems

Yun Tain-quan

1980, 1(1): 115-123.

Abstract(2074) PDF(618)

Abstract:
Let the concentrated forces and the centers of pressure with unknown density functions x(ξ) and y(ξ) respectively be distributed along the axis z outside the solid, then one can reduce an axismmetric loading problem of solids of revolution to two simultaneous Fredholm integral equations. An iteratio...

“Velocity” Finite Element Method for Dynamic Problem

Yang Zhen-rong

1980, 1(1): 125-138.

Abstract(1911) PDF(679)

Abstract:
After analysing the essential features of successive integration method taking displacement as variable by N. M. Newmark and E. L. Wilson et al, this paper presents a "Velocity" Element Method, taking velocity as variable for the solution of the initial value problem.A simplified scheme is offered f...