A continuity re-relaxed thin shell formulation for static and dynamic analyses of linear problems

摘要

This paper presents a curvature-constructed triangular element for static, free vibration and explicit dynamic analyses of shell structures by using a continuity re-relaxed technique. In the present method, the formulation is based on the classical thin shell theory, and only the translational displacements are treated as the filed variables that are assumed piecewisely linear. A set of three-node triangular background cells is adopted to discretize the problem domain. The curvature field in an element is constructed using the continuity re-relaxed technique, which can relax the continuity requirement of the trial function. The membrane strain filed is formulated same as the practice of standard FEM. Based on the principle of virtual work, the discertized system equations are finally formed. As the rotational displacements are not considered as the basic degrees of freedom, the essential boundary conditions of this part are imposed in the process of forming the curvature field. In order to validate the efficiency and accuracy of the present method, several numerical examples are studied. The results demonstrate that the present formulation can achieve very stable and accurate solutions with the less consuming of CPU time.