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집중력의 확산현상과 구조의 불연속에 기인되는 응력집중현상의 유한요소법에 의한 해석
A finite element model of a problem gives a piecewise approximation to the governing equations. The basic premise of the finite element method in that a solution region can be analytically modeled or approximated by replacing it with an assemblage of discrete elements. In this paper, to analyze the stress diffusion of the cantilevered plate subjected to concentrated load and the stress concentration of the plate with a circular hole in its center, the governing equation is derived by energy method. The two dimensional finite elements of the triangular element and the rectangular element with two degrees of freedom at each node are used for this problem and are defined by speci-fying geometry, internal displacement functions, strain-displace ment relations and stress displacement relations. To analyze the stress diffusion of the cantilevered plate the rectangular element is used and this element has the comp-atibilities of the displacements. To analyze the stress concen-tration of the plate with a circular hole in its center the triangular element is used and this triangular element is suita-ble for the shapes of the irregular boundaries. The stress diffusion factors of the cantilevered plate sub-jected to concentrated load, and the stress concentration factors of the plate with a circular hole in its center are obtained. The results are plotted graphically and the parts of these results are compared with Ref.(6), Ref(8) and Ref.(16). They agree good enough to accept the problem of engineerings in this field.
有限要素法에 依한 圓筒形 構造의 應力 集中 및 擴散 現象에 關한 硏究
Diffustion phenomena of a concentrated load and the stress concentration phenomena due to the structural incontinuity are studied by finite element method. In this study, a circular cylinder is treated. Under the axial load, the membrane action is dominate and the well known 24 D.O.F. cylindrical membrane finite element is used. The assembly of this element can successfully represent the original structure geometrically. The internal displacement function is such organized that the inter element compatibility condition is pully satisfied. In the study of the diffustion phenomena of a concentrated load acting at a point on the circumference, it is found that the resisting stress can equally distribute beyond the region of axial distance equal to the cylinder diameter. The quantitative results are computed and plotted. Along the circumferential direction, stress distributation is also computed and plotted. In the study of the stress concentration phenomena due to the presence of a hole on the cylinder wall the stress concentration factor versus the location of the hole is computed and plotted. It is found that the hole effect on the stress concentration disappears beyond the neighboring region of the hole size from the edge of the hole. Those reasults are useful for practical design in determining the region where the re-fnforcing is necessary.