A NUMERICAL MANIFOLD METHOD FOR PLANE MICROPOLAR ELASTICITY

A numerical manifold method (NMM) for plane micropolar elasticity is proposed in this paper to consider the microstructure influence of materials. First, the basic formulations of plane micropolar elasticity are briefly introduced. Then, the equations of stiffness matrix, boundary conditions, and equivalent force in micropolar NMM are derived based on energy minimization principle. Two manifold elements for micropolar elasticity are provided later. From geometry analysis, the proposed SQ-ME model will have about 40% less degree of freedoms than the corresponding finite element method model. Patch tests are used to validate these two manifold elements and the results show these elements could pass patch tests exactly. Furthermore, the micropolar NMM is used to predict the stress concentration of a micropolar membrane containing a small hole. The results are in agreement with the micropolar analytical solution. Finally, convergence analysis is performed and conclusions are derived.