無限体内に存在する熱歪近傍の弾塑性解析 : 固有歪の概念による3次元弾塑性解析 : その1

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In thc previous paper the authors^<1)> presented the problem of stress distributions around a hole or a crack which belongs to the very important one in the field of fracture mechanics. Basic equations were derived from complex stress functions and the calculations were carried out on the basis of the concept of thermo-elasticity theory. In this paper, the problem is extended to that of an elasto-plastic stress field in an infinitely large isotropic matrix around a cuboidal element within which dilatational strains are distributed. Just as in the case of two-dimensional problem, the concept of thermo-elasticity is adopted. Galerkin vector for unit inherent strains which exist in an infinitesimal volume element at a point is derived from the Galerkin vector for concentrated body forces in an infinite, isotropic, elastic medium. When the distribution of the inherent strain in a cuboidal element is expressed by polynomial, the Galerkin vector will be obtained in terms of volume integrals in closed form to any order. Then, the displacement and stress fields are calculated from second and third derivatives of the Galerkin vector respectively. The three dimensional elasto-plastic analysis is conducted using the Initial Strain Method, in which the localized zone with plastic strains is divided into a number of small cuboidal elements each of which has polynomial distribution of initial strains up to second order on the boundaries. The stress field as compensation for plastic behavior are then calculated by regarding the initial strains as inherent strains, and the values of plastic strains are determined by trial-and-error operation. Numerical stress evaluation has been performed for several shapes of cuboids, within which dilatational strains are distributed.
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無限体内に存在する熱歪近傍の弾塑性解析 : 固有歪の概念による3次元弾塑性解析 : その1

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