ABSTRACT
Previous chapters have introduced a number of MFree methods for solids, fluids, beams, and plates. This chapter formulates MFree methods for shell structures.
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. Many shells are designed using advanced computer-aided design (CAD) technology to be the main load-carrying structure. Advanced CAD design of shell structures must consider both static and dynamic loads. Hence, both static and frequency analysis are very important and are integral parts of the shell design. Because of the complex nature, both structurally and mechanically, numerical means have to be utilized for analyses of shells. Advances in computing technology have made this possible and have led to the widespread use of numerical analysis of complex shells. The finite element method (FEM) remains the most popular numerical technique as evident from numerous publications since the 1970s (Yang et al., 1990). However, FEM requires the design of meshes, which is an extremely tedious, costly, and time-consuming process. In addition, meshing a shell structure into elements carries a number of risks that are often hidden by colorful pictures, as the curved surface of the shell is usually modeled by shell elements that are flat. This kind of geometric simplification in FEM can lead to severely erroneous results, due to the mechanics coupling effects of bending forces and membrane forces.
