Abstract
The meshless local Petrov-Galerkin approach based on a regular local boundary integral equation is successfully extended to solve nonlinear boundary value problems. The present method is truly meshless, as no mesh connectivity is needed for interpolating the solution variables and for integrating the weak form. Compared to the original MLPG method, the present method does not need the derivatives of the shape functions in constructing the stiffness matrix for those nodes with no displacement specified on their local boundaries. Numerical examples show that high rates of convergence with mesh refinement are achievable, and the computational results are quite accurate.
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