An efficient grid-based direct-volume integration BEM for 3D geometrically nonlinear elasticity

The boundary element method is regarded as an efficient method for solving problems with complex domains. However most successful applications of the BEM have been thus far limited to linear analyses. A major difficulty with the BEM solution of a nonlinear problem is the handling of the volume integral resulting from the nonlinear terms. In this work, a grid-based direct-volume integration BEM has been developed for 3D geometrically nonlinear elastic problems. The volume integrals are evaluated using a regular Cartesian grid, and thus only the boundary discretization of the problem domain is required. The efficiency of the method is enhanced by using acceleration schemes for both surface and volume integration. Several 3-D example calculations have been performed to demonstrate the effectiveness of the three-dimensional formulas and the numerical implementation.