| Abstract: | Although they furnish accurate displacements, conventional displacement-based lower order finite elements fail to predict accurate stress resultants and stresses in certain classes of plate and shell problems that involve free edges, steep stress gradients and singularities. In order to tackle such problems, a triangular higher-order shell element based on the nodal basis approach has been developed. The nodes of the element are located at optimal points and its more superior shape functions derived from orthogonal Proriol polynomials. To illustrate the improved performance of the higher-order element as compared to commonly used lower order shell elements in predicting the variations of stress resultants and stresses, three example problems involving a simply supported skew plate, a corner supported square plate, and a clamped cylindrical shell are solved. The stress resultants and the stresses furnished by the higher-order element for the problems considered are found to be accurate with the satisfaction of the natural boundary conditions and devoid of any oscillations. When compared to lower order elements, the higher-order element requires a simple mesh design and lesser degrees of freedom resulting in a considerable reduction in the computational effort, especially for large scale nonlinear analysis. |
