Free Vibration Analysis of Curved Shell Structures with Various Boundary Conditions by Using A Meshfree Method

Abstract

In this paper, the free vibration of curved shell structures with various boundary conditions is examined by using a meshfree method. The meshfree method in this study is based on the radial point interpolation method (RPIM). The RPIM shape function is chosen because it satisfies the Kronecker delta property allowing for the direct imposition of essential boundary conditions. The field variables and the geometry of the curved shell are interpolated through the RPIM shape function. The curved shell formulation is constructed based on the first-order shear deformation theory (FSDT), which considers the transverse shear strain. In a meshfree approach to investigate curved shell structures, a convected coordinate system is employed. This convected coordinate system is tied to the curved surface and used to map an arbitrary curved shell in 3D space into 2D space. To obtain the numerical solution, the calculation is performed first in this convected coordinate system and then mapped back to the global coordinate system. The accuracy and ability of the meshfree method have been shown through many numerical examples. The natural frequencies of curved shells with different geometry and boundary conditions are in good agreement with other available reference solutions.