ABSTRACT
Previous chapters have introduced a number of meshfree methods for solids, fluids, beams, and plates. This chapter formulates two meshfree methods for shell structures: element-free Galerkin (EFG) and edge-based smoothed point interpolation method (ES-PIM). Spatial thin shell structures are used very extensively in many engineering structures,
including aircraft, pressure vessels, storage tanks, and so on, due to their outstanding efficiency in utilizing materials. Because of the complex nature, both structurally and in mechanics, numerical means have to be utilized for analyses of shells during the design process. The finite element method (FEM) remains the most popular numerical technique for such analyses [1,20]. However, FEM often requires quality meshes, creating which is a tedious, costly, and time-consuming process. Meshfree methods present a promising alternative to FEM, as they offer opportunities to
relieve the manual meshing process in modeling a structure. This is particularly important for shells, as shell structures are very complex both in field variable variation and in geometric configuration. Meshfree methods can offer a very important capability in representing the complex curved geometry of shell structures. The meshfree approximations both in field variables and in the structure itself can provide more accurate results compared to the standard FEM. Very few works have been reported in the development of meshfree methods for shell
structures. The first contribution in this regard was made by Krysl and Belytschko [2] based on the thin shell theory using moving least squares (MLS) approximation with Lagrange multipliers for essential boundary conditions. Noguchi et al. [3] developed a formulation for thick shell using MLS approximation with penalty method for handling essential boundary conditions. Li et al. [4] formulated a meshfree method based on the reproducing kernel particle method for thin shells with large deformation. In this work, the essential boundary condition is imposed by modifying shape functions for nodes near and on the essential boundaries. Other works are reported in [5,6] on EFG, and recently on ES-PIM [19]. This chapter covers the following two topics:
. Formulation of the EFG method for shell structures. The materials on EFG presented here are based on the works in [5,6], where both the field variables and geometry of the shell are all approximated using the MLS approximation.
