Conforming radial point interpolation method for spatial shell structures on the stress-resultant shell theory

The implementation of the conforming radial point interpolation method (CRPIM) for spatial thick shell structures is presented in this paper. The formulation of the discrete system equations is derived from a stress-resultant geometrically exact theory of shear flexible shells based on the Cosserat surface. A discrete singularity-free mapping between the five degrees of freedom of the Cosserat surface and the normal formulation with six degrees of freedom is constructed by exploiting the geometry connection between the orthogonal group and the unit sphere. A radial basis function 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 geometries. The major advantage of the CRPIM is that the shape functions possess a delta function property and the interpolation function obtained passes through all the scattered points in the influence domain. Thus, essential boundary conditions can be easily imposed, as in finite element method. A range of shape parameters is studied to examine the performance of CRPIM for shells, and optimal values are proposed. The phenomena of shear locking and membrane locking are illustrated by presenting the membrane and shear energies as fractions of the total energy. Several benchmark problems for shells are analyzed to demonstrate the validity and efficiency of the present CRPIM. The convergence rate of the results using a Gaussian (EXP) radial basis is relatively high compared to those using a multi-quadric (MQ) radial basis for the shell problems.