A New Locking-Free Thick/Thin Shell Element with Incompatible Approximation in a General Orthogonal Curvilinear Coordinate System

A new locking-free thick/thin shell element with incompatible approximation (SEIA) in a general orthogonal curvilinear coordinate system is proposed for the analysis of the thick/thin shell. The key points for the development of the present element include the definition of the incompatible polynomial displacement approximation in each independent element and the utilization of the fictitious thin layers to ensure the displacement conformity between adjacent elements. Superior to most available shell elements, the SEIA avoids the shear and membrane locking naturally without the adoption of numerical expediencies, has concise theoretical derivation and easy numerical implementation, is insensitive to element distortions and thus provides reliable solutions for the thick/thin shell. The present work also initiates a methodology to develop locking-free thick/thin shell elements. Numerical investigations and comparisons demonstrate the convergence and robustness of the present element.