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SOLUTION OF THE PLANE STRESS PROBLEMS OF STRAIN-HARDENING MATERIALS DESCRIBED BY POWER-LAW USING THE COMPLEX PSEUDO-STRESS FUNCTION
作者姓名:王子昆  魏雪霞  高信林
作者单位:Xian Jiaotong Univ. Xian,Lanzhou Univ.,Lanzhou,Ganstt Univ. of Tech.,Lanzhou
摘    要:In the present paper,the compatibility equation for the plane stress problems of power-law materials is transformed into a biharmonic equation by introducing the so-calledcomplex pseudo-stress function,which makes it possible to solve the elastic-plastic planestress problems of strain hardening materials described by power-law using the complexvariable function method like that in the linear elasticity theory.By using this generalmethod,the close-formed analytical solutions for the stress,strain and displacementcomponents of the plane stress problems’of power-law materials is deduced in the paper,which can also be used to solve the elasto-plastic plane stress problems of strain-hardeningmaterials other than that described by power-law.As an example,the problem of a power-law material infinite plate containing a circular hole under uniaxial tension is solved byusing this method,the results of which are compared with those of a known asymptoticanalytical solution obtained by the perturbation method.

收稿时间:16 May 1990

Solution of the plane stress problems of strain-hardening materials described by power-law using the complex pseudo-stress function
Wang Zi-kung,Wei Xue-xia,Gao Xin-lin.SOLUTION OF THE PLANE STRESS PROBLEMS OF STRAIN-HARDENING MATERIALS DESCRIBED BY POWER-LAW USING THE COMPLEX PSEUDO-STRESS FUNCTION[J].Applied Mathematics and Mechanics(English Edition),1991,12(5):481-492.
Authors:Wang Zi-kung  Wei Xue-xia  Gao Xin-lin
Institution:(1) Xian Jiaotong Univ., Xian;(2) Lanzhou Univ., Lanzhou;(3) Gansu Univ. of Tech., Lanzhou
Abstract:In the present paper, the compatibility equation for the plane stress problems of power-law materials is transformed into a biharmonic equation by introducing the so-called complex pseudo-stress function, which makes it possible to solve the elastic-plastic plane stress problems of strain hardening materials described by power-law using the complex variable function method like that in the linear elasticity theory. By using this general method, the close-formed analytical solutions for the stress, strain and displacement components of the plane stress problems of power-law materials is deduced in the paper, which can also be used to solve the elasto-plastic plane stress problems of strain-hardening materials other than that described by power-law. As an example, the problem of a power-law material infinite plate containing a circular hole under uniaxial tension is solved by using this method, the results of which are compared with those of a known asymptotic analytical solution obtained by the perturbation method.
Keywords:power-law materials  pseudo-stress function  plane stress problems  the complex variable function method  total deformation theory
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