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Structural Engineering and Mechanics Volume 26, Number 5, July30 2007 , pages 591-615 DOI: https://doi.org/10.12989/sem.2007.26.5.591 |
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A BEM implementation for 2D problems in plane orthotropic elasticity |
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N. Kadioglu and S. Ataoglu
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| Abstract | ||
| An improvement is introduced to solve the plane problems of linear elasticity by reciprocal theorem for orthotropic materials. This method gives an integral equation with complex kernels which will be solved numerically. An artificial boundary is defined to eliminate the singularities and also an algorithm is introduced to calculate multi-valued complex functions which belonged to the kernels of the integral equation. The chosen sample problem is a plate, having a circular or elliptical hole, stretched by the forces parallel to one of the principal directions of the material. Results are compatible with the solutions given by Lekhnitskii for an infinite plane. Five different orthotropic materials are considered. Stress distributions have been calculated inside and on the boundary. There is no boundary layer effect. For comparison, some sample problems are also solved by finite element method and to check the accuracy of the presented method, two sample problems are also solved for infinite plate. | ||
| Key Words | ||
| elasticity; orthotropy; finite plates having elliptical and circular holes; multi-valued function; boundary element; reciprocity theorem; singularity. | ||
| Address | ||
| N. Kadioglu and S. Ataoglu: Division of Mechanics, Civil Engineering Department, Faculty of Civil Engineering, Istanbul Technical University, Maslak 34469 Istanbul, Turkey | ||