An efficient 3-node triangular plate element for static and dynamic analyses of microplates based on modified couple stress theory with micro-inertia

Within the modified couple stress elasticity, a novel nonconforming 3-node triangular plate element is derived from the d’Alembert–Lagrange principle for simulating the size-dependent static and dynamic bending behaviors of thin microplates and studying the effects of micro-inertia. This is accomplished via two main steps. First, the Trefftz functions that are derived from the governing equations of the problem concerned are adopted as the basis functions for constructing the element’s displacement interpolation. Second, according to the generalized conforming theory, the SemiLoof constraints are used to enforce the C¹ compatibility requirement for guaranteeing the computation convergence. The benchmark tests are carried out and the results reveal that the new element exhibits satisfactory numerical accuracy and captures the size dependences effectively in the static, free vibration and forced vibration analyses. Moreover, the findings also show that the micro-inertia affects the dynamic response of the plate mainly through the natural frequency. In general, the influences on higher order modes are more obvious than that on lower order modes.