Hybrid Trefftz Plane Elements with Drilling Degrees of Freedom

摘要

We introduce efficient and accurate plane elements with drilling degrees of freedom based on the hybrid Trefftz method. By variational formulation, hybrid Trefftz method connects two independent displacement fields : the internal displacement field satisfying governing equations of plane elasticity problems and the boundary displacement field consistent at the inter-element boundaries. In this study, we derive element stiffness of triangular and quadrilateral elements using hybrid Trefftz variational formulation which is based on the total potential energy principle and boundary integrations for stiffness matrices. At the same time, we approximate the boundary displacement field by Allman type displacement field for drilling degrees of freedom. However, we can easily apply it to arbitrary polygon elements because all the domain integrals are changed into boundary integrals. With these plane elements, we performed a series of tests and got good results in view of accuracy, convergence and robustness.