Abstract
The Galerkin boundary node method (GBNM) is developed for two-dimensional solid mechanics problems. The GBNM is a boundary only meshless method that combines an equivalent variational form of boundary integral formulations for governing equations with the moving least-squares (MLS) approximations for construction of the trial and test functions. In this method, boundary conditions can be implemented directly and easily despite the MLS shape functions lack the delta function property, and the resulting formulation inherits the symmetry and positive definiteness of the variational problems. The optimal asymptotic error estimates of this approach for displacements and stresses are derived in detail in Sobolev spaces. Numerical tests are also given to demonstrate the developed algorithms.
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