Abstract
The PU (partition-of-unity) based FE-RPIM QUAD4 (4-node quadrilateral) element was proposed for statics problems. In this element, hybrid shape functions are constructed through multiplying QUAD4 shape function with radial point interpolation method (RPIM). In the present work, the FE-RPIM QUAD4 element is further applied for structural dynamics. Numerical examples regarding to free and forced vibration analyses are presented. The numerical results show that: (1) If CMM (consistent mass matrix) is employed, the FE-RPIM QUAD4 element has better performance than QUAD4 element under both regular and distorted meshes; (2) The DLMM (diagonally lumped mass matrix) can supersede the CMM in the context of the FE-RPIM QUAD4 element even for the scheme of implicit time integration.
Highlights
The FEM [1] has been widely adopted to model structural dynamics
In the computation for dynamic problems, both the consistent mass matrix (CMM) and the diagonally lumped mass matrix (DLMM) will be employed in the context of FE-radial point interpolation method (RPIM) QUAD4 element, while only the CMM will be employed in the context of QUAD4, TRIG3, and QUAD8
If the problem domain is discretized into 1 element with 11 × 11 nodes, the solution based on the spectral finite element method (SFEM) is 23.9414, which is even slightly better than that based on the FE-RPIM QUAD4 element (23.8170)
Summary
The FEM (finite element method) [1] has been widely adopted to model structural dynamics. Compared to FEM, higher accuracy can be obtained by FE-LSPIM QUAD4 element, because global approximations with high order are constructed. In contrast to meshless method, FE-LSPIM QUAD4 shape functions have Kronecker-delta character, which means special treatment is not needed for essential boundary condition implementation. According to the report from Xu and Rajendran [49], FE-RPIM QUAD4 element has higher accuracy than FE-LSPIM QUAD4 element for linear and geometry nonlinear static problems if the same number of polynomial terms are employed.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
