An efficient 4-node facet shell element for the modified couple stress elasticity

This work proposes a simple but robust 4-node 24-DOF facet shell element for static analysis of small-scale thin shell structures. To accommodate the size effects, the modified couple stress theory is employed as the theoretical basis. The element is constructed via two main innovations. First, the trial functions that can a priori satisfy related governing differential equations are adopted as the basic functions for formulating the element interpolations. Second, the generalized conforming theory and the penalty function method are employed to meet the C-1 continuity requirement in weak sense for ensuring the computation convergence property. Several benchmarks of shells with different geometries are tested to assess the new facet shell element's capability. The numerical results reveal that the element can effectively simulate the size-dependent mechanical behaviors of small-scale thin shells, exhibiting satisfactory numerical accuracy and low susceptibility to mesh distortion. Moreover, as the shell element uses only six degrees of freedom per node, it can be incorporated into the commonly available finite element programs very readily.