Immersed Boundary Shell Element Based on Higher Order Shear Deformation Theories for Laminated Composite Shells

ABSTRACT A mesh that conforms to the geometry is needed for the traditional Finite Element Method (FEM), which is often difficult to generate for complex geometry. It is easier to generate a uniform Cartesian background mesh in which the geometry is embedded. The immersed boundary finite element method (IBFEM) uses a background mesh to approximate the solution while using equations to accurately represent the geometry for finite element analysis. For shell‐like structures, a surface representing the mid‐surface of the shell is utilized, which passes through the 3D elements of the background mesh. In this article, Higher‐Order Shear Deformation Theories (HSDT) are modified for use with immersed boundary shell elements to model laminated composite shells. The rotations and slopes are expressed as derivatives of the displacement field approximated over 3D elements of a background mesh. This requires the displacement field to be tangent‐continuous. Therefore, quadratic or higher‐order B‐spline shape functions that ensure a tangent‐continuous displacement field are utilized to formulate the element. Only three degrees of freedom per node are needed for the immersed boundary shell elements. The shell element presented here is formulated assuming that the strains are infinitesimal. For validating the elements and the modified higher order shear deformation theories, several commonly used laminated composite benchmark problems are used to assess its accuracy. The results obtained using this approach are compared with analytical solutions or with solutions from 3D FEA and isogeometric analysis (IGA) for validation.