유한요소-J 적분법을 이용한 3차원 응력강도계수의 계산

Abstract

2차원 균열문제에 대한 J 적분법을 3차원 균열문제에 확대하여 적용하는 방법을 개발하였다. 표면적분인 3차원 J 적분을 균열전선 어느 짧은 구간을 포위한 충분히 가는 원통 적분표면을 선택하여 균열전선과 수직인 평면에서의 2차원 J 적분으로 환원하였다. 유한요소의 수치적분점을 통과하는 적분 경로가 균열전선과 수직인 평면 상에 놓이도록 균열전선을 포위한 15 절점 퇴화요소의 3각형 양측면이 각각 균열전선과 수직이도록 절점을 배치하였다. 몇 개의 3차원 균열문제를 통하여 본 논문에서 개발한 방법의 정확성과 안정성을 입증하였다.

The J-integral method widely used for 2-D crack problems is extended to cover 3-D crack problems. Selecting a cylindrical surface of sufficiently small radius and nearly zero length along the crack front as an integration surface, the 3-D j-integral can be reduced to the 2-D J-integral defined on the plane perpendicular to the crack front. To make the plane perpendicular to the crack front, two triangular faces of the 15-node degenerate elements around the crack front are set to be perpendicular to the crack front. The accuracy and stability of the present method are confirmed through some 3-D example crack problems.

The J-integral method widely used for 2-D crack problems is extended to cover 3-D crack problems. Selecting a cylindrical surface of sufficiently small radius and nearly zero length along the crack front as an integration surface, the 3-D j-integral can be reduced to the 2-D J-integral defined on the plane perpendicular to the crack front. To make the plane perpendicular to the crack front, two triangular faces of the 15-node degenerate elements around the crack front are set to be perpendicular to the crack front. The accuracy and stability of the present method are confirmed through some 3-D example crack problems.