论文标题
一致的高阶层壳壳配方
A Consistent Higher-Order Isogeometric Shell Formulation
论文作者
论文摘要
壳分析是一个完善的领域，但是对于此类模拟，实现最佳的高阶收敛速率是一个艰难的挑战。我们提出了一个iSOOGETRIC KIRCHHOFF-LOVE SHELL框架，该框架以一致的高阶准确方式处理每个数值方面。特别地，单个修剪的B型序列表面提供了足够光滑的几何形状，而非对称的Nitsche方法强制执行边界条件。对于（多个）修剪曲线，在参数空间中跨度跨度的切合结跨度的更高阶段的精确修复为（多）修剪曲线提供了一个强大的更高阶段的准确正交正交正常，并且扩展的B-Spline概念控制了所得方程系统的条件。除了这些组件确保对高阶准确性的所有要求之外，呈现的壳配方基于切向差分计算，级别集合功能定义了修剪曲线。数值实验证实该方法会产生高阶收敛速率，因为该解决方案足够光滑。
Shell analysis is a well-established field, but achieving optimal higher-order convergence rates for such simulations is a difficult challenge. We present an isogeometric Kirchhoff-Love shell framework that treats every numerical aspect in a consistent higher-order accurate way. In particular, a single trimmed B-spline surface provides a sufficiently smooth geometry, and the non-symmetric Nitsche method enforces the boundary conditions. A higher-order accurate reparametrization of cut knot spans in the parameter space provides a robust, higher-order accurate quadrature for (multiple) trimming curves, and the extended B-spline concept controls the conditioning of the resulting system of equations. Besides these components ensuring all requirements for higher-order accuracy, the presented shell formulation is based on tangential differential calculus, and level-set functions define the trimming curves. Numerical experiments confirm that the approach yields higher-order convergence rates, given that the solution is sufficiently smooth.
