We present a novel isogeometric discretization approach for the Kirchhoff-Love shell formulation based on the Hellinger-Reissner variational principle. For mitigating membrane locking, we discretize the independent strains with spline basis functions that are one degree lower than those used for the displacements. To enable computationally efficient condensation of the independent strains, we first discretize the variations of the independent strains with approximate dual splines to obtain a projection matrix that is close to a diagonal matrix. We then diagonalize this strain projection matrix via row-sum lumping. The combination of approximate dual test functions with row-sum lumping enables the direct condensation of the independent strain fields at the quadrature point level, while maintaining higher-order accuracy at optimal rates of convergence. We illustrate the numerical properties and the performance of our approach through numerical benchmarks, including a curved Euler-Bernoulli beam and the examples of the shell obstacle course.

翻译：本文提出了一种基于Hellinger-Reissner变分原理的Kirchhoff-Love壳单元新型等几何离散方法。为缓解薄膜闭锁现象，我们采用比位移场低一阶的样条基函数对独立应变场进行离散。为实现独立应变场的高效计算凝聚，首先采用近似对偶样条离散独立应变场的变分形式，获得接近对角矩阵的投影矩阵，随后通过行和集中法对该应变投影矩阵进行对角化处理。近似对偶测试函数与行和集中法的结合，使得独立应变场能在积分点层面直接凝聚，同时保持最优收敛速率下的高阶精度。通过数值基准测试（包括曲梁Euler-Bernoulli算例和壳障碍课程案例），我们验证了该方法的数值特性与计算性能。