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受对称与非对称载荷作用的轴对称机械结构弹塑性应力分析的边界元法

黄庆平  
【摘要】:The reduction of the number of dimensions is one of the principal advantages of boundary element method. For an axisymmetric body the number of dimension can be reduced by transforming the boundary integral equation for 3-D coordinates into Polar coordinates.This will be of significance for less cost of computation in many mechanical engineering problems.In this thesis;the formulation and numerical implementation for the elastoplastic analysis of an axisymmetric body subjected to axi symmetric and nonaxisymmetric load are presented.And some problems within this topic have been discussed in detail. The principal points of the thesis can be summarized as follows:1. An improved integral expression for domain stresses in 3-D e lastoplastic problems had been put forward to avoid evaluating the Cauchy principal value in domain integral. The idea presented here can be applied to other field variabtes conveniently where the derivatives of the domain function are required.2. All kernel functions and boundary functions in the formulations for 3-D problems(the boundary integral equation and integral expression for domain stresses) are expressed in polat coordinates by tensor transformalion. With proper Fourier expansion of the boundary functions (displacement and traction);the formulations for an axisymmetric body subjected to a nonaxisymmetric load in elastoplastic analysis are deduced. The expressions of the kernel functions in the thesis are much simple than what used previously.3. The evaluation of the surface stresses has been given in the thesis.4. In order to avoid evaluating the Chauchy principal value in the boundary integral equation/ same special solutions of the equilibrium equation for the Fourier coefficients of harmonic 'n' have been derived.5. Two simple iteration formulations which have been used widely by Aitken process and amended Aitken process are discussed in detail and a new iteration formulation has been proved to be better in convergence.6. A numerical scheme of BEM for an axisymmetric body subjected to a non-axisymmetric load in elastoplastic analysis has been included in this thesis.7. With many concrete examples which show that not only feasibility of the method but also it is better in accuracy and efficiency, this provides the evidence of BEM in mechanical engineering applications.


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