A boundary integral equation approach for the calculation of gradients and higher order derivatives in solid mechanics problems

摘要

An asymptotically convergent boundary integral technique is presented for the analytical calculation of the gradients in the solid mechanics problems. Upon introducing the perturbed trial function for the boundary unknowns into the differentiated integral equations, it is proved that the former intractable hyper-singular integral equations turn out to become asymptotically convergent. The current approach is able not only to calculate the gradients at the point close to or just at the boundary, but also to obtain the higher order derivatives conveniently. Compared with other suggested techniques, the current one has the advantages of efficiency and generality. The demonstrative numerical examples show that the results have very good accuracy compared with the close form solution. Besides, the problem of properly selection of the shape functions to represent the deflection along the free or symmetric side in the Kirchhoff plate bending problems is also discussed.