Advanced 3D Hamiltonian nodal position finite element method for nonlinear dynamic analysis of rotating solids

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.