Stress analysis in plane orthotropic material by the boundary element method

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The boundary element method is a more suitable technique than the finite element method for problems having large stress gradients. One such problem is the stresses around mechanical Fasteners. To solve a problem by the boundary element method requires a solution of an integral equation. The integrand of the integral equation is a product of a known Green's function and an unknown function. Unlike isotropic material, the plane orthotropic material can have three forms of Green's function depending upon the relationship of the four material constants. To solve the integral equations numerically, the unknown function is approximated by a piecewise continuous linear function. The boundary is approximated by a sum of straight line segments. The result of the two approximations is integrals over straight line segments, the integrand of which is a product of linear polynomials and one of the three Green's functions. These integrals arc evaluated analytically. By exploiting the common features in the three forms of Green's function a very efficient algorithm can be designed. Numerical results arc presented for a circular hole in an infinite medium and in a coupon. The results show good correlation with analytical results for all kinds of orthotropic materials. © 1988.

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International Journal of Solids and Structures