VIRTUAL ELEMENT METHOD FOR SOLVING 2D GEOMETRIC NONLINEAR PROBLEMS UPON S-R DECOMPOSITION THEOREM

The strain-Rotation (S-R) decomposition theorem provides a reliable and reasonable theoretical basis for geometric nonlinear analyses. However, the mesh distortion is inevitable in a large deformation analysis when using the finite element method. The virtual element method (VEM) proposed recently is applicable to general polygonal meshes. In the study, the first order VEM is used to solve 2D geometric nonlinear problem upon S-R decomposition theorem, aiming to overcome the impact of mesh distortion. One project operator is derived for the linear elastic problem from the admissible displacement space to the polynomial displacement space, by redefining the basis function of the polynomial displacement space. The incremental variation equation based on the updated co-moving coordinate formulation and the potential energy rate principle is computed according to the computation rule of the bilinear form in VEM. The discretization equation is obtained with the matrix expression, and a solution program is coded in MATLAB. The proposed method is employed in the deformation analysis on a cantilever beam under distributed loads and on a thick cylinder under uniform internal pressures, by using a general polygonal mesh and a distorted mesh. Comparison on the results by the method proposed, and those from the published literatures and of ANSYS shows that the method proposed is valid regardless of the mesh distortion and, has a sufficient numerical precision. In conclusion, the method proposed is robust to solve 2D geometric nonlinear problems based on S-R decomposition theorem.