Element-free Galerkin method for static and dynamic analysis of spatial shell structures

The implementation of the element free Galerkin method (EFG) for static and free vibration analysis of general shell structures is presented in this paper. The formulation of the discrete system equations is derived from the governing equations of stress resultant geometrically exact shell theory based on the Cosserat surface. A discrete singularity-free mapping between the five- and the six-degrees-of-freedom formulation is constructed by exploiting the geometry connection between the orthogonal group and the unit sphere. Moving least-squares approximation is used in both the construction of shape functions based on arbitrarily distributed nodes as well as in the surface approximation of general spatial shell geometry. Discrete system equations are obtained by incorporating these interpolations into the Galerkin weak form. The formulation is verified through numerical examples of static stress analysis and frequency analysis of spatial shell structures. The phenomena of shear locking and membrane locking are illustrated by showing the membrane and shear energy as fractions of the total energy. Essential boundary conditions are efficiently imposed through a penalty technique for both static analysis and frequency analysis. The formulation is tested on several benchmark problems and the results compare favorably with closed-form solutions and that of finite element analyses.