A FSDT meshfree method for free vibration analysis of arbitrary laminated composite shells and spatial structures

In this paper, a FSDT meshfree method based on the 3D continuous shell theory and moving-least squares approximation is proposed for the first time to investigate the free vibration behavior of arbitrary laminated composite shells and spatial structures. The novelty lies in that the resultant meshfree model has completely general geometric and kinematic descriptions, which are more readily applied to complex laminated shell geometries. In the formulation, the geometrical representation is based on the mapping technique without simplifying assumptions on the shell geometry, whereas the moving least-squares (MLS) approach and the first shear order theory (FSDT) are employed to build displacement fields. By using the mapping technique, a 3D arbitrary curved surface is expanded in a two-dimensional space, and the displacement approximation is established based on a set of nodes scattered in the Converted coordinate system. The simple Gauss integral are also formed in the Converted coordinate system. The essential boundary conditions are imposed by the full transformation method. According to Hamilton principle, the meshfree governing equations of free vibration of arbitrary laminated shells are obtained. The convergence, accuracy and applicability of the proposed method are demonstrated for the laminated shells of different geometrical shell shapes involving the square plates, shallow shells, open cylindrical shells, conical shells and corrugated plates with different boundary conditions and lamination schemes.