This work presents a fully Lagrangian Finite Element Method (FEM) with nodal integration for the simulation of fluid–structure interaction (FSI) problems. The Particle Finite Element Method (PFEM) is used to solve the incompressible fluids and to track their evolving free surface, while the solid bodies are modeled with the standard FEM. The coupled problem is solved through a monolithic approach to ensure a strong FSI coupling. Accuracy and convergence of the proposed nodal integration method are proved against several benchmark tests, involving complex interactions between unsteady free-surface fluids and solids undergoing large displacements. A very good agreement with the numerical and experimental results of the literature is obtained. The numerical results of the nodal integration algorithm are also compared to those given by a standard Gaussian method, and their upper-bound convergent behavior is also discussed.

这项工作提出了一种完整的带节点积分的拉格朗日有限元方法（FEM），用于模拟流固耦合（FSI）问题。粒子有限元方法（PFEM）用于求解不可压缩的流体并跟踪其演化的自由表面，而实体则使用标准FEM进行建模。耦合问题通过单片解决，以确保牢固的FSI耦合。通过几个基准测试证明了所提出的节点积分方法的准确性和收敛性，涉及不稳定的自由表面流体与经历大位移的固体之间的复杂相互作用。获得与文献的数值和实验结果非常好的一致性。