应用数学和力学

1997 Vol. 18, No. 11

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Inverse Asymptotic Solution Method for Finite Deformation Elasto-Plasticity

Chen Zhida

1997, 18(11): 959-966.

Abstract(1707) PDF(489)

Abstract:
The development of modern mechanics in recent years has made many importanf progresses in the concepts and methods for nonlinear large deformation mechanics[1][2][3] etc, The present paper is aimed to show how the natural co-moving system method and Stokes-Chen's deco mposition theorem can be effectively applied asy mptotically to solving problems of finite defor mation elasto-plasticity by inverse asy mptotic method for engineering design purpose.Rigid punch problem is examplified in the paper.

Electro-Elastic Green’s Functions for a Piezoelectric Half-Space and Their Application

Liu Jinxi, Wang Biao, Du Shanyi

1997, 18(11): 967-973.

Abstract(2178) PDF(456)

Abstract:
In this paper, as is studied are the electro-elastic solutions for a piezoelectric halfspace subjected Io a line force, a line charge and a line dislocation, i. e.. Green sfunclions on the basis of Stroh formalism and the concept of analytical continuation,explicit expressions for Green's functions are derived. As a direct application of theresults obtained, an infinite piezoelectric solid containing a semi-infinite crack isexammed. Attention iffocused on the stress and electric displacement fields of a cracktip. The stress and electric displacement intensity.factors are given explicitly.

The Globalization of Durand-Kerner Algorithm

Wang Deren, Zhao Fengguang

1997, 18(11): 975-986.

Abstract(2030) PDF(454)

Abstract:
Making use of the theory of continuous ho motopy and the relation between symmetric polynomial and polynomial in one variable the authors devoted this article to constructing a regularly homotopic curve with probability one, Discrete tracing along this homotopic curve leads to a class of Durand-Kerner algorithm with step parameters.The convergence of this class of algorithms is given, whick solves the conjecture about the global property of Durand-Kerner algorithm,The problem for steplength selection is thoroughly discussed,Finally,sufficient numerical examples are used to verify our theory.

Formulation of a Semi-Analytical Approach Based on Gurtin Variational Principle for Dynamic Response of General Thin Plates

Peng Jianshe, Zhang Jingyu, Yang Jie

1997, 18(11): 987-991.

Abstract(2233) PDF(470)

Abstract:
A semi-analytical approach for the dynamic response of general thin plates which employes finite element discretization in space domain and a series of repre-sentation in time domain is developed on the basis of Gurtin variatioual principles.The form ulation of time series is also investigated so that the dynamic response of plates with adequate accuracy.

Crack Propagation in the Power-Law Nonlinear Viscoelastic Material

Zhang Shuangyin, Xiong Dianyuan

1997, 18(11): 993-999.

Abstract(2416) PDF(749)

Abstract:
An analysis on crack creep propagation problem of power-law nonlinear viscoelastic materials is presented, The creepincom pressibility assumption is used,To simulate fracture behavior of craze region, it is assumed that in the fracture process zone near the crack tip, the cohesive stress б_f acts upon the crack surfaces and resists crack opening. Through a perturbation method, i, e.,by superposing the Mode-I applied force onto a referential uniform stress state, which has a trivial solution and gives no effect on the solution of the original problem,the nonlinear viscoelastic problem is reduced to linear problem, For weak non-linear materials, for which,the power-law ind,ea n≌1, the expressions of stress and crack surface displace went are derived. Then, the fracture process zone local energy criterion is proposed and on the basis of which the for mulae of crac-king incubation time t^* and crack slow propagation velocity a are derived.

Exact Solution for Laminated Continuous Open Cylindrical Shells

Fan Jiarang, Sheng Hongyu

1997, 18(11): 1000-1013.

Abstract(2031) PDF(511)

Abstract:
Discarding any assumptions about displacement models and stress distribution and introducing δ-function into the present study,the state equation for the continuous orthropic open cylindrical shells is established. An identical exact solution is presented for the statics of thin,moderately thick and thick laminated continuous open cylindrical shells.Numerical results are obtained and compared with those calculated using SAPS.

Separating Coupled Physic Quantity by Potential Operator

Zhang Shenxue

1997, 18(11): 1014-1020.

Abstract(1769) PDF(425)

Abstract:
In the present paper, using the method of separating coupled physic quantity bypotential operator, we derive two special minmum principles in coupled thermo-elastodynamics are deduced.

Optimum Design of Adhesive Bonding of Resin-Base Composites

Wu Miaosheng, Zhou Zhulin

1997, 18(11): 1021-1025.

Abstract(2395) PDF(928)

Abstract:
In this paper, based on the experimental and theoretical analysis, the primciple ofoptimum design for single lap joint of resin matrix, together with omposites ispresented the adhesive selection, the bonding length and the.hickness of the adhesivelayer and the adherend design. It is shown that by the optinum design the strength ofadhesive bonding is increased while the weight of the composites products is decreasedso that the quality of the products is improved.

An Eigenvalue Method on Group Decision

Qiu Wanhua

1997, 18(11): 1026-1031.

Abstract(2362) PDF(701)

Abstract:
In this paper. a new group decision eigenvalue method abbreviated as GEM isproposed. It overcomes the non-consistence of judgement matrix and will open up anew route for the selection of experts in the decision system.

The Fundamental Equations of Dynamics Using Representation of Quasi-Coordinates in the Space of Non-Linear Non-Holonomic Constraints

Qiu Rong

1997, 18(11): 1032-1040.

Abstract(2138) PDF(540)

Abstract:
The dot product of the bases vectors on the super-surface of the non-linear nonholonomic constraints with one order, expressed by quasi-coorfinates, and Mishirskiiequalions are regarded as the fundamental equations of dynamics with non-linear andnon-holononlic constraints in one order for the system of the variable mass. From thesethe variant ddferential-equations of dynamics expressed by quasi-coordinates arederived. The fundamental equations of dynamics are compatible with the principle ofJourdain. A case is cited.

Interpolation Perturbation Method for Solving Nonlinear Problems

Yuan Yiwu

1997, 18(11): 1041-1048.

Abstract(2217) PDF(593)

Abstract:
In this paper, using the interpolation perturbation method, the author seeks to solve several nonlinear problems.Numerical examples show that the method of this paper attains good accuracy.