Comparison of symbolic and numerical integration methods for an assumed‐stress hybrid shell element

Hybrid shell elements have long been regarded with reserve by the commercial finite element developers despite the high degree of reliability and accuracy associated with such formulations. The fundamental reason is the inherent higher computational cost of the hybrid approach as compared to the displacement‐based formulations. However, a noteworthy factor in favour of hybrid elements is that numerical integration to generate element matrices can entirely be avoided by the use of symbolic integration. In this paper, the use of the symbolic computational approach is presented for an assumed‐stress hybrid shell element with drilling degrees of freedom, and the significant time saving achieved is demonstrated through an example.