标题： 基于平衡的高效应力恢复方法用于等几何层合曲面结构 显示英文标题

标题： Efficient equilibrium-based stress recovery for isogeometric laminated curved structures

摘要： 这项工作专注于层合复合曲面结构的一种高效应力恢复过程，该过程依赖于等几何分析（IGA）和平衡。 通过厚度方向使用单个单元，并结合校准的分层积分规则或均质化方法，3D实体等几何建模在位移（及其导数）和面内应力方面提供了经济且准确的近似，而厚度方向的应力分量则近似效果较差。 应用进一步的后处理步骤，即使从粗糙的位移解中也可以恢复出准确的面外应力状态。 这是基于强形式平衡方程的直接积分，涉及位移场的高阶导数。 这种连续性要求由IGA形状函数的性质完全满足。 后处理步骤是局部应用的，这使得在平衡中不会出现额外的耦合项，从而允许直接重建，无需进一步迭代以解决不平衡动量方程。 多个数值结果表明，该方法在具有显著半径与厚度比和铺层数的复合材料堆叠中表现出良好的性能。 特别是，在后者的情况下，采用分层技术，其自由度数量与铺层数成正比，计算成本会非常高，而所提出的方法可以被视为一种非常有吸引力的替代选择。 显示英文摘要

摘要： This work focuses on an efficient stress recovery procedure for laminated composite curved structures, which relies on Isogeometric Analysis (IGA) and equilibrium. Using a single element through the thickness in combination with a calibrated layerwise integration rule or a homogenized approach, the 3D solid isogeometric modeling grants an inexpensive and accurate approximation in terms of displacements (and their derivatives) and in-plane stresses, while through-the-thickness stress components are poorly approximated. Applying a further post-processing step, an accurate out-of-plane stress state is also recovered, even from a coarse displacement solution. This is based on a direct integration of the equilibrium equations in strong form, involving high order derivatives of the displacement field. Such a continuity requirement is fully granted by IGA shape function properties. The post-processing step is locally applied, which grants that no additional coupled terms appear in the equilibrium, allowing for a direct reconstruction without the need to further iterate to resolve the out-of-balance momentum equation. Several numerical results show the good performance of this approach particularly for composite stacks with significant radius-to-thickness ratio and number of plies. In particular, in the latter case, where a layerwise technique employing a number of degrees of freedom directly proportional to the number of plies would be much more computationally demanding, the proposed method can be regarded as a very appealing alternative choice.