Effective Hybrid/Mixed Finite Elements for Folded-Plate Structures

Abstract

A new formulation in which the assumed stress field is divided into membrane and bending stress fields is developed. A family of effective shell elements of hybrid/mixed finite element method that accounts for transverse shear deformations is proposed based on a modified Hellinger–Reissner variational principle. In this paper, the present shell elements possess different three-field assumptions, which are described by compatible displacement, incompatible displacement, and stress fields. Several benchmark problems are conducted to test both the accuracy and reliability of the proposed shell elements. Numerical analyses show that the present shell elements pass all the patch tests, do not contain any spurious zero energy modes, and have no lock phenomena even for very thin plate and shell. Further insight into the performance of the present shell elements is gained to demonstrate the high accuracy of the elements by several folded-plate structure problems. The numerical results demonstrate the validity, reliability, and applicability of the present elements. The present elements are valid for thick as well as thin shell structures.