A Locking-free Three-node Shell Finite Element Formulation

A simple triangular shell finite element with fifteen degrees of freedom for the analysis of general shell structures is presented in this work. The element uses a substitute transverse shear strain field to avoid locking, and is formulated on the basis of RSDS-element (Resultant Stress Degenerated Shell Element) approach, which leads to very simple strain-displacement expressions. The substitute shear strain field is derived assuming constant shear strains along the sides of the element, similar to the MITC (Mixed Interpolation in Tensorial Componentes) procedure. All integrations can be performed using only one point Gaussian rule, leaving the element with one non-comunicable zero energy mode, which does not affect the results. This procedure allows the use of symbolic engines to derive analytic expressions for stiffness matrices, reducing computational cost of the analysis by a significative amount.