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

Automated summary

A new displacement-based Trefftz plate element is developed for size-dependent bending analysis of thin plate structures, incorporating the modified couple stress theory and generalized conforming theory, with satisfactory numerical performance.