Generalized conforming Trefftz element for size-dependent analysis of thin microplates based on the modified couple stress theory

In this work, a new displacement-based Trefftz plate element is developed for size-dependent bending analysis of the thin structures in context modified couple stress theory. This achieved via two steps. First, functions, that are derived by introducing assumptions into three-dimensional governing equations elasticity, adopted as basis functions designing element's displacement interpolations. Second, generalized conforming theory employed to meet interelement compatibility requirements weak sense ensuring convergence property. The resulting 4-node performs like nonconforming models on coarse meshes and gradually converges one with mesh refinement. Numerical tests reveal can efficiently capture mechanical responses microplates exhibits satisfactory numerical accuracy distortion tolerance. Moreover, has only three degrees freedom (DOF) per node, it be easily incorporated commonly available finite programs.