Abstract This paper proposes monolithic and partitioned methods to calculate the static deformation of a membrane structure due to a given volume of ponding water. The partitioned methods involve coupling of a structural solver for membranes and a volume-conserving solver, modeling static incompressible fluid. Two methods of this type are proposed, either using coupling iterations with convergence accelerator between structural solver and volume-conserving solver or adding the linearized fluid behavior in the structural solver in addition to the external coupling iterations. The monolithic methods solve the system of structural equations under hydrostatic load with the volume conservation behavior of the fluid included in the Newton-Raphson (N-R) iterations of the structural solver. One such method was already discussed in the literature and updates the free surface plane to conserve volume exactly after every N-R iteration. In the second, new monolithic method, the volume conservation constraint is added as an additional equation and solved together with the structural equations. It was found that the partitioned method used with a quasi-Newton convergence accelerator was very robust but slower than the monolithic methods. On the other hand, the new monolithic method proposed in this paper was found to be both computationally efficient and robust.

中文翻译：

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确定因积水引起的膜结构静态变形的整体和分区方法

摘要 本文提出了整体和分区方法来计算膜结构由于积水量给定的静态变形。分区方法包括耦合膜结构求解器和体积守恒求解器，模拟静态不可压缩流体。提出了两种这种类型的方法，要么在结构求解器和体积守恒求解器之间使用带有收敛加速器的耦合迭代，要么在结构求解器中添加线性化流体行为以及外部耦合迭代。整体方法使用包含在结构求解器的 Newton-Raphson (NR) 迭代中的流体的体积守恒行为来求解静水载荷下的结构方程系统。文献中已经讨论了一种这样的方法，它更新自由表面平面以在每次 NR 迭代后精确地保存体积。在第二种新的整体方法中，体积守恒约束作为附加方程添加并与结构方程一起求解。发现与拟牛顿收敛加速器一起使用的分区方法非常稳健，但比整体方法慢。另一方面，发现本文中提出的新的整体方法既具有计算效率又具有鲁棒性。发现与拟牛顿收敛加速器一起使用的分区方法非常稳健，但比整体方法慢。另一方面，发现本文提出的新单片方法计算效率高且鲁棒。发现与拟牛顿收敛加速器一起使用的分区方法非常稳健，但比整体方法慢。另一方面，发现本文提出的新单片方法计算效率高且鲁棒。