Non-conforming Trefftz Finite Element Implementation of Orthotropic Kirchhoff Plate Model Based on Consistent Couple Stress Theory

This work proposes a new 4-node non-conforming plate element for static and dynamic analyses of small-scale orthotropic thin plates within the consistent couple stress theory. By applying the Kirchhoff thin plate bending constraint to the three-dimensional consistent couple stress elasticity, the non-classical orthotropic thin plate model is established and the Trefftz functions are derived. Then, the new element is formulated in a straightforward manner based on the generalized conforming theory, by taking the obtained Trefftz functions as the basic function for construction and employing a novel set of point conforming conditions to enforce the compatibility requirement in weak sense. Several benchmark examples are examined and the results show that the element has good numerical accuracy and mesh-distortion tolerance in prediction of the size-dependent bending behavior of the small-scale orthotropic thin plates.