Meshless implementation of arbitrary 3D-shell structures based on a modified first order shear deformation theory

Abstract

A meshless implementation of arbitrary 3D-shell structures based on a modified first order shear deformation theory (FSDT) is investigated in this paper. The FSDT is improved in this manuscript in order to assume a parabolic distribution of the shear strain to correct the constant shear stress in the Mindlin–Reissner theory and to get closer to a realistic distribution of the shear strain through the thickness. The radial point interpolation method is used in the construction of shape functions based on arbitrarily distributed nodes of general spatial shell geometry. The convergence of the proposed model is compared to other well-known formulations found in the literature considering isotropic and functionally graded spatial shell structures. The results obtained using the proposed meshless method demonstrate that the improved FSDT is very successful compared to closed-form solutions and finite element results using different shell theories. The effect of the material distribution on the deflections and stresses is also analyzed.