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This paper presents new regularized boundary integral equations (BIEs) for elastic displacement gradients in three dimensions and then combines them by the generalized Hooke’s law to calculate the boundary stress. In the new regularized BIEs, two special tangential vectors are designed with the normal vector to construct a transformation system. Ba...
Bifurcations in a cubic system with a degenerate saddle point are investigated using the technique of blow-up, the method of planar perturbation theory and qualitative analysis. It has been found that after appropriate perturbations, at least 12 limit cycles can bifurcate from a degenerate saddle point in a type of cubic systems.
To begin with, a regularized boundary integral equation with indirect formulation is adopted to deal with the singular integrals and the boundary unknown quantities can be calculated accurately. When it comes to the physical quantities at the interior points, an efficient non-linear transformation is utilized to evaluate the nearly singular integra...
The accurate evaluation of nearly singular boundary integrals is an important issue in boundary element analysis, and the importance of this problem is next to the singular boundary integrals. Although many ways of evaluating nearly singular integrals have been developed in recent years, and obtained varying degree of success, questions still remai...
A kind of new partitioning algorithm is presented. The algorithm solves the eigenvalue, inverse matrix and determinant of the generalized cycle matrixes and a system of linear equations with the generalized cycle coefficient matrix. The original problem is partitioned into a series of independent subproblems. Compared with the original problem, the...
The exact form of exterior boundary value problems for plane potential problem is established with variational principle. Based on this, to avoid using the Green's formula on infinite domain, an infinitely differentiable function with compact subset is constructed and some important results to an especial solution of the inhomogeneous field equatio...