Analysis of Shell-Like Structures Using Structured Mesh

Shell-like structures are modeled in traditional finite element method using shell elements. The geometry for such structures is modeled using surfaces that represent the mid-plane. A mesh consisting of planar or curved shell elements is then generated for the surface which can be challenging for complex surface geometries and the resultant mesh sometimes poorly approximates the geometry. In order to avoid the problems associated with mesh generation, several meshless methods and structured grid methods have been proposed in the past two decades. In this paper, a structured grid method called Implicit Boundary Finite Element Method (IBFEM) has been used for the analysis of shell-like structures. Three dimensional elements that use uniform B-spline approximation schemes for representing the solution are used to represent the displacement field. The surfaces representing shell passes through these elements and the equations of these surfaces are used to represent the geometry exactly. B-spline approximations can provide higher order solutions that have tangent and curvature continuity. Numerical examples are presented to demonstrate the performance of shell elements using IBFEM and B-spline approximation. The results are compared with traditional shell element solutions.