An immersed boundary 3D shell element is presented here that is based on Mindlin-Reissner shell theory assumptions and uses quadratic B-spline approximation for the solution. It enables mesh independent analysis wherein the surface representing the shell geometry is defined independently and not by the mesh. The shell geometry is immersed in a uniform background mesh whose elements are 3D B-spline shell elements. By making the geometric model independent of the mesh, the typical difficulties associated with mesh generation can be avoided. The quadratic 3D B-spline shell elements in the mesh can represent the displacement field as a tangent continuous piece-wise polynomial approximation. The nodes of the element have three translational and no rotational degrees of freedom. The element is formulated under small-deformation and plane stress assumptions. Constructing the element based on shell theory enables the use of effective properties to model thin fiber reinforced laminated composite shell-like structures. The element formulation and the mesh independent approach are validated against a series of common shell element benchmark problems.

这里介绍了一个浸入式边界 3D 壳单元，它基于 Mindlin-Reissner 壳理论假设，并使用二次 B 样条近似来求解。它支持网格独立分析，其中表示壳几何的表面是独立定义的，而不是由网格定义的。壳几何体浸入均匀的背景网格中，其元素是 3D B 样条壳单元。通过使几何模型独立于网格，可以避免与网格生成相关的典型困难。网格中的二次 3D B 样条壳单元可以将位移场表示为切线连续分段多项式逼近。单元的节点具有三个平移自由度和无旋转自由度。该单元是在小变形和平面应力假设下制定的。基于壳理论构建单元能够使用有效属性来模拟薄纤维增强层压复合材料壳状结构。单元公式和网格独立方法针对一系列常见的壳单元基准问题进行了验证。