High-Precision Elastoplastic Four-Node Quadrilateral Shell Element

In order to enhance the accuracy of calculations for four-node quadrilateral shell elements, modifications have to be made to the computation of the membrane strain rate and transverse shear strain rate. For membrane strain rate calculations, the interpolation of the quadratic displacement of the nodes along the edges of the quadrilateral shell element is implemented, along with the introduction of a degree of freedom for rotation around the normal. Additionally, the elimination of the zero-energy mode of additional stiffness is achieved through a penalty function. When computing the transverse shear strain rate, the covariant component is expressed in the tensor of the natural coordinate system, followed by the elimination of shear self-locking in the element coordinate system. The strain-updating calculation and stress-updating calculation for the quadrilateral shell element, utilizing the model and J2 flow theory, respectively, are suitable for small deformations, geometric nonlinearity, and elastic–plastic problems. The improved quadrilateral shell element successfully undergoes in-plane and bending fragment inspections, demonstrating good reliability and calculation accuracy for the dynamic analysis of planar shells, curved shells, and twisted shells.