A computational model is proposed for short-fiber reinforced materials with the eigenstrain formulation of the boundary integral equations （BIE） and solved with the newly developed boundary point method （BPM）. The...A computational model is proposed for short-fiber reinforced materials with the eigenstrain formulation of the boundary integral equations （BIE） and solved with the newly developed boundary point method （BPM）. The model is closely derived from the concept of the equivalent inclusion Of Eshelby tensors. Eigenstrains are iteratively determined for each short-fiber embedded in the matrix with various properties via the Eshelby tensors, which can be readily obtained beforehand either through analytical or numerical means. As unknown variables appear only on the boundary of the solution domain, the solution scale of the inhomogeneity problem with the model is greatly reduced. This feature is considered significant because such a traditionally time-consuming problem with inhomogeneity can be solved most cost-effectively compared with existing numerical models of the FEM or the BEM. The numerical examples are presented to compute the overall elastic properties for various short-fiber reinforced composites over a representative volume element （RVE）, showing the validity and the effectiveness of the proposed computational modal and the solution procedure.展开更多
In the conventional differential quadrature （DQ） method the functional values along a mesh line are used to approximate derivatives and its application is limited to regular regions. In this paper, a local different...In the conventional differential quadrature （DQ） method the functional values along a mesh line are used to approximate derivatives and its application is limited to regular regions. In this paper, a local differential quadrature （LDQ） method was developed by using irregular distributed nodes, where any spatial derivative at a nodal point is approximated by a linear weighted sum of the functional values of nodes in the local physical domain. The weighting coefficients in the new approach are determined by the quadrature rule with the aid of nodal interpolation. Since the proposed method directly approximates the derivative, it can be consistently well applied to linear and nonlinear problems and the mesh-free feature is still kept. Numerical examples are provided to validate the LDQ method.展开更多
基金Project supported by the National Natural Science Foundation of China (No.10772106)
文摘A computational model is proposed for short-fiber reinforced materials with the eigenstrain formulation of the boundary integral equations （BIE） and solved with the newly developed boundary point method （BPM）. The model is closely derived from the concept of the equivalent inclusion Of Eshelby tensors. Eigenstrains are iteratively determined for each short-fiber embedded in the matrix with various properties via the Eshelby tensors, which can be readily obtained beforehand either through analytical or numerical means. As unknown variables appear only on the boundary of the solution domain, the solution scale of the inhomogeneity problem with the model is greatly reduced. This feature is considered significant because such a traditionally time-consuming problem with inhomogeneity can be solved most cost-effectively compared with existing numerical models of the FEM or the BEM. The numerical examples are presented to compute the overall elastic properties for various short-fiber reinforced composites over a representative volume element （RVE）, showing the validity and the effectiveness of the proposed computational modal and the solution procedure.
文摘In the conventional differential quadrature （DQ） method the functional values along a mesh line are used to approximate derivatives and its application is limited to regular regions. In this paper, a local differential quadrature （LDQ） method was developed by using irregular distributed nodes, where any spatial derivative at a nodal point is approximated by a linear weighted sum of the functional values of nodes in the local physical domain. The weighting coefficients in the new approach are determined by the quadrature rule with the aid of nodal interpolation. Since the proposed method directly approximates the derivative, it can be consistently well applied to linear and nonlinear problems and the mesh-free feature is still kept. Numerical examples are provided to validate the LDQ method.
