应用数学和力学

1993 Vol. 14, No. 8

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The Impact Torsional Buckling for the Rigid Plastic Cylindrical Shell

Wang De-yu, Zhang Shan-yuan, Yang Gui-tong

1993, 14(8): 659-664.

Abstract(2023) PDF(620)

Abstract:
By using the energy criterion in [3],the impact torsional buckling for the rigid plastic cylindrical shell is studied.The linear dynamic torsional buckling equations for the rigid plastic shell is drived,and the critical impact velocity is given.

Method of Strongly Singular Integral Equation for the Torsion of Cylinder with Edge Crack

Wang Jin-song, Tang Ren-ji

1993, 14(8): 665-671.

Abstract(2069) PDF(464)

Abstract:
From the dislocation type solution of the torsion of single crack,by using the concept of finite part integrals,we reduce the torsion problem of cylinder with a single crack into an integral equation with strong singularity.The numerical method is also obtained and several numerical examples are calculated successfully at the end of this paper.

Singularity under a Concentrated Force in Elasticity

Wang Quan, Wang Da-jun

1993, 14(8): 679-677.

Abstract(2461) PDF(836)

Abstract:
We first discuss singularity problem of a sort of partial differential equation involving d funetion.Using this result we then have the answer to various singularity problems in elasticity due to the presentation of a concentrated force.Lastly corresponding conclusions in vibration problem are drawn.

Large Deformation Symmetrical Elasticity Problems Solved by the Variational Method

Zhao Yu-xiang, Gu Xiang-zhen, Song Xi-tai

1993, 14(8): 679-685.

Abstract(1995) PDF(533)

Abstract:
In this paper,based on the mathematical theory of classical mechanics and Chen's theorem^[1],the variational method^[2] is used in the study of large deformation symmetrical elasticity problems.The generalized variational principles of potential energy and complementary energy,based on the instantaneous configuration are obtained,and the equivalence between the two principles is proved Besides,the generalized variational principles of dynamical problems based on the instantaneous configuration are also given.

Consolidation Theory of Unsaturated Soil Based on the Theory of Mixture (Ⅱ)

Chen Zheng-han

1993, 14(8): 687-698.

Abstract(2461) PDF(663)

Abstract:
The present paper uses the mathematics model for consolidation of unsaturated soil developed in ref.[I] to solve boundary value problems.The analytical solutions for one-dimensional consolidation problem are gained by making use of Laplace transform and finite Fourier transform.The displacement and the pore water pressure as well as the pore gas pressure are found from governing equations simul taneously.The theoretical formulae of coefficient and degree of consolidation are also given in the paper.With the help of the method of Galerkin Weighted Residuals,the finite element equations for two-dimensional consolidation problem are derived.A FORTRAN program named CSU8 using 8-node isoparameter element is designed.A plane strain consol idation problem is solved using the program,and some distinguishing features on consolidation of unsaturated soil and certain peculiarities on numerical analysis are revealed.These achievements make it convenient to apply the theory proposed by the author in engineering practice.

Fractal Sets in Control Systems

Cheng Dai-zhan

1993, 14(8): 699-706.

Abstract(1850) PDF(525)

Abstract:
In this paper the Hausdorff measure of sets of integral and fractional dimensions is introduced and applied to control systems.A new concept,namely,pseudo-self-similar set is also introduced.The existence and uniqueness of such sets are then proved,and the formula for calculating the dimension of self-similar sets is extended to the psuedo-self-similar case.Using the previous theorem,we show that the reachable set of a control system may have fractional dimensions.We hope that as a new approach the geometry of fractal sets will be a proper tool to analyze the controllability and observability of nonlinear systems.

On Crack-Tip Strain Energy Release Rate in Non-Principal Directions of Elasticity for Simple Layer Plate of Composite Materials

Yang Wei-yang, Zhang Shao-qin

1993, 14(8): 707-713.

Abstract(2130) PDF(616)

Abstract:
In this paper,the fracture problem in non-principal directions of elasticity for a simple layer plate of linear-elastic orthotropic composite materials is studied.The formulae of transformation between characteristic roots,coefficients of elastic compliances in non-principal directions of elasticity and corresponding parameters in principal directions of elasticity are derived.Then,the computing formulae of strain energy release rate under skew-symmetric loading in terms of engineering parameters for principal directions of elasticity are obtained by substituting crack-tip stresses and displacements into the basic formula of the strain energy release rate.

Nonlinear Three-Dimension Analysis for Axially Sym-metrical Circular Plates and Multilayered Plates

Jiang Xiao-yu, Zhang Xiang-zhou

1993, 14(8): 715-727.

Abstract(2180) PDF(671)

Abstract:
Analytic nonlinear three-dimension solutions are presented for axially symmetrical homogeneous isotropic circular plates and multilayered plates with rigidly clamped boundary conditions and under transverse load.The geometric nonlinearity from a moderately large deflection is considered.A developmental perturbation method is used to solve the complicated nonlinear three-dimension differential equations of equilibrium.The basic idea of this perturbation method is using the two-dimension solutions as a basic form of the corresponding three-dimension solutions,and then processing the perturbation procedure to obtain the three-dimension perturbation solutions.The nonlinear three-dimension results in analytic expressions and in numerical forms for ordinary plates and multilayered plates are presented.All of the plate stresses are shown in figures.The results show that this perturbation method used to analyse nonlinear three-dimension problems of plates is effective.

Nonsingular Kernel Boundary Element Method for Thin-Plate Bending Problems

Wang Zuo-hui

1993, 14(8): 729-733.

Abstract(2099) PDF(489)

Abstract:
In this paper,the nonsingular fundamental solutions are obtained from Fourier series under some given conditions.These solutions can be taken as the kernels of integral equation.So a new boundary element method is presented,with which all kinds of thin-plate bending problems can be solved,even with complicated loadings and sinuous boundaries.The calculation is much simpler and more accurate.

The Elastodynamic Solution for a Solid Sphere and Dynamic Stress-Focusing Phenomenon

Wang Xi

1993, 14(8): 739-746.

Abstract(2255) PDF(477)

Abstract:
This paper presents an analytical method of solving the elastodynamic problem of a solid sphere.The basic solution of the elastodynamic problem is decomposed into a quasi-static solution satisfying the inhomogeneous compound boundary conditions and a dynamic solution satisfying the homogeneous compound boundary conditions.By utilizing the variable transform,the dynamic equation may be transformed into Bassel equation.By defining a finite Hankel transform,we can easily obtain the dynamic solution for the inhomogeneous dynamic equation.Thereby,the exact elastodynamic solution for a solid sphere can be obtained.From results carried out,we have observed that there exists the dynamic stress-focusing phenomenon at the center of a solid sphere under shock load and it results in very high dynamic stress-peak.

A New Method for Analyzing Surface Cracks

Zeng Zhao-jing, Dai Shu-he

1993, 14(8): 747-752.

Abstract(2238) PDF(481)

Abstract:
The authors have developed a new line-spring boundary element method in the present paper,which combines the advantage of the line-spring model with that of the boundary element method.This method reduces the three-dimension problem of the surface cracks into a quasi-one-dimension problem and can be used to analyze the surface cracked plate under various loading conditions.In this paper theoretical analyses and numerical verifications are carried out.The calculated results are reported,which indicate that the present method is efficient and can be used to analyze the surface crack problem on a personal computer.