Immersed boundary thin shell analysis using 3D B-Spline background mesh

摘要

An immersed boundary shell element formulation based on Kirchhoff-Love shell theory is presented here that uses a background mesh consisting of uniform 3D B-spline elements within which the geometry and the boundaries are embedded. In this theory, rotation is assumed to be identical to slope which introduces second derivatives of deflection in the weak form. As a result, elements that provide tangent continuous approximation of the displacement are needed. A 3D shell element is formulated under small deformation assumptions that has three translational degrees of freedom (DOF) per node and uses quadratic B-Spline shape functions. The displacement field is transformed to a local coordinate system attached to the shell surface and defined such that the shell theory assumptions are satisfied. Essential boundary conditions are applied using the step boundary method where approximate step functions are utilized to construct trial and test solutions that satisfy the boundary conditions. Benchmark problems that are commonly used to test shell elements are used to validate the 3D Bspline thin shell element presented here.