解析解を変関数とした変分原理の有限要素法への応用 : 応力拡大係数計算への応用

概要

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In this paper, variational principle using analytical solution for admissible function is derived. Based on this variational principle, the finite element method is applied to evaluating the elastic stress intensity factors at the tip of a sharp crack. Stress or strain field in an element and boundary displacement are used for admissible functions in this variational principle. The stress or strain field in an element is assumed to satisfy equilibrium equations and compatibility equations. On the otherhand, boundary displacement is assumed to satisfy geometrical boundary conditions. To calculate the stress intensity factors using this principle, the whole elements of a structure are classified to regular elements and singular elements. Namely stress field in an element away from a singular point is expressed with only regular part and stress field in an element in vicinity of the singular point is expressed with the sum of regular part and singular part. The present method is applied to several problems. In the case of rectangular plates with cracks, the numerical results show good agreement with those obtained by the former authors. By this method, good results can be obtained without subdividing a structure to fine elements. The stress intensity factors for lack of penetration in a welded cruciform joint are obtained by the present method, and some results are shown in this paper.
社団法人日本船舶海洋工学会の論文