Strongly Curved Finite Element for Shell Analysis

A new curved element has been introduced for the purpose of modeling the membrane and bending behavior of strongly curved shells with arbitrary contours. The particular method used herein allows slight slope discontinuities between elements but this disadvantage was offset by savings in computational time and storage requirements. Work is in progress to derive efficient methods to improve interelement slope and twist continuities. A typical derivation for the bending and membrane stiffness matrices of thin shells is given for the new element. Classical linear shell theory was used in the derivation and the shallowness assumption was not used. Numerical results for four contrasting problems: (1) membrane behavior of a sphere; (2) bending behavior of a complete cylinder with clamped ends; (3) nonlinear deployment of an ellipsoid segment; and (4) pressurization of a complete torus, were given to illustrate the potential of the proposed element.