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Advanced 3D Hamiltonian nodal position finite element method for nonlinear dynamic analysis of rotating solids
Computers & Structures ( IF 4.4 ) Pub Date : 2024-12-19 , DOI: 10.1016/j.compstruc.2024.107634
Fuzhen Yao, Chaofeng Li, Zheng H. Zhu

This paper develops a novel 3D brick element by Nodal Position Finite Element Method (NPFEM) to effectively model rotating solids. It uses nodal positions instead of nodal displacements to formulate element’s strain and kinetic energies. This approach effectively avoids computational errors caused by spurious strains induced by large rigid-body rotations and can automatically account for stiffening effects arising from centrifugal forces. By directly solving for the positions of rotating elastic solids using Hamiltonian canonical equations, the new 3D NPFEM brick element allows elastic deformation to be efficiently and accurately extracted by subtracting the rigid-body motion from these positions. Additionally, the ability of the new 3D NPFEM brick element to model bending deformation is enhanced by directly introducing incompatible modes into the element shape functions. Numerical validation shows that the new 3D NPFEM brick element accurately models and analyzes the elastic deformation of rotating blades. It automatically captures nonlinear frequency responses of rotating solids without requiring special boundary and loading condition treatments commonly used in classic FEM. This advancement offers significant advantages by avoiding errors when modeling complex rotating solids or machines, thereby improving computational efficiency and accuracy.

中文翻译:


用于旋转固体非线性动态分析的高级 3D 哈密顿节点位置有限元方法



本文通过节点位置有限元法 (NPFEM) 开发了一种新型的 3D 砖单元,以有效地对旋转实体进行建模。它使用节点位置而不是节点位移来表示元件的应变和动能。这种方法有效地避免了由大型刚体旋转引起的杂应变引起的计算误差,并且可以自动考虑离心力引起的硬化效应。通过使用哈密顿规范方程直接求解旋转弹性实体的位置,新的 3D NPFEM 砖单元可以通过从这些位置减去刚体运动来高效、准确地提取弹性变形。此外,通过将不兼容的模式直接引入单元形状函数,增强了新的 3D NPFEM 砖单元对弯曲变形进行建模的能力。数值验证表明,新的 3D NPFEM 砖单元可以准确地模拟和分析旋转叶片的弹性变形。它会自动捕获旋转实体的非线性频率响应,而无需传统有限元法中常用的特殊边界和载荷条件处理。这一进步提供了显著的优势,因为它避免了在对复杂的旋转实体或机器进行建模时出现错误,从而提高了计算效率和准确性。
更新日期:2024-12-19
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