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Abstract A support integration method based on the locality of meshfree methods was proposed for Petrov-Galerkin meshfree methods. Positions and weights of quadrature points were obtained through the requirements that the integral of test functions multiplied by polynomials can be evaluated exactly on the support domain. Only two quadrature points are needed in each dimension for each support domain. The computational cost is much decreased in comparison with background mesh integration. This method can calculate nodal forces exactly for linear stress field, so that the integral constraint condition is satisfied to ensure the stability. One-dimensional and two-dimensional examples show that this method has good accuracy and convergence rates.
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Received: 22 November 2010
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2012, Vol. 33 