A theory and finite element formulation of shells at finite deformations involving thickness change: Circumventing the use of a rotation tensor (Q1804527)

A nonlinear shell theory, including transverse strains perpendicular to the midsurface and transverse shear strains, is developed. A quadratic displacement field over the shell thickness with seven degrees of freedom is considered; however, the use of a rotation tensor is avoided. In the case of linear constitutive equations, a possible reduction to six degrees of freedom is discussed and a finite element formulation, based on a hybrid variational principle, is presented. The accuracy of the theory and its wide range of applicability are demonstrated by several examples.