THREE-DIMENSIONAL GEOMETRIC NONLINEARITY ELEMENT-FREE METHOD BASED ON S-R DECOMPOSITION THEOREM

Due to its overcoming the deficiencies of classic finite deformation theories, Strain-Rotation (S-R) decomposition theorem can provide a reliable theoretical support for the geometrically nonlinear simulation. In addition, due to it’s independent of the elements and meshes, the element-free method has more advantages to solve large deformation problems compared to finite element method (FEM), so that the accuracy is guaranteed as a result of avoiding the element distortions. Therefore, a more reasonable and reliable geometric nonlinearity numerical method certainly will be established by combining the S-R decomposition theorem and element-free method. But the studies of element-free methods based on S-R decomposition theorem in current literature are limited to two-dimensional problems. In most cases, three-dimensional mathematical-physical models must be established for the practical problems. Therefore it is very necessary to establish a three-dimensional element-free method based on the S-R decomposition theorem. Present study extends the previously work by authors into three-dimensional case: The incremental variation equation is derived from updated co-moving coordinate formulation and principle of potential energy rate in this paper, and three-dimensional discretization equations are obtained by element-free Galerkin method (EFG). By using the MATLAB programs based on the proposed 3D S-R element-free method in present study, the nonlinear bending problems for three-dimensional cantilever beam and simply supported plates subjected to uniform load are numerical discussed. The reasonability, availability and accuracy of 3D S-R element-free method proposed by present paper are verified through comparison studies, and the numerical method in present work can provide a reliable way to analysis 3D geometric nonlinearity problems.