A hybrid Trefftz plane elasticity element with drilling degrees of freedom

We suggest a linear plane element that is accurate and easy to use. The new element is based on the hybrid Trefftz method. To give the drilling degrees of freedom and to enhance the performance of the element, we take the hybrid Trefftz method based on the total potential energy principle and adopt Allman’s quadratic displacement field as a boundary displacement field. To stabilize the drilling degrees of freedom, we restrict the rotation field by a penalty term. The penalty term ties up the drilling rotation with the true rotation derived from the internal displacement field, which is made up of Trefftz functions. With the proposed formulation, we can make up polygonal elements in a unified framework. The performance of the new element reveals an advantage in modeling and analyzing, as well as good accuracy and robustness.