Trefftz-unsymmetric finite element for bending analysis of orthotropic plates

This work develops a new four-node quadrilateral displacement-based Trefftz-type plate element for bending analysis of orthotropic plates within the framework of the unsymmetric finite element method (FEM). In the present formulation, the modified isoparametric interpolations are employed to formulate the element's test functions in which the deflection is effectively enriched by the nodal rotation degrees of freedom (DOFs). Meanwhile, the element's trial functions are determined based on the Trefftz functions that can a prior satisfy the governing equations of orthotropic Mindlin-Reissner plates. Numerical benchmark tests reveal that the new unsymmetric plate element is free of shear locking problem and can produce satisfactory results for both the displacement and stress resultant. In particular, it exhibits quite good tolerances to the gross mesh distortion.

Automated summary

This study introduces a new four-node quadrilateral displacement-based Trefftz-type plate element for bending analysis of orthotropic plates within the unsymmetric finite element method framework. It effectively enriches deflection by nodal rotation degrees of freedom and uses Trefftz functions to satisfy governing equations. The new plate element shows good performance, free of shear locking problem, and tolerant to mesh distortion.