Modeling Structural Dynamics Using FE-Meshfree QUAD4 Element with Radial-Polynomial Basis Functions

Area of Science:

• * Computational mechanics
• * Structural dynamics
• * Finite element analysis

Background:

• * The partition-of-unity (PU) based finite element (FE) method combined with the radial point interpolation method (RPIM) created the FE-RPIM QUAD4 element for static problems.
• * This hybrid element uses shape functions that multiply standard QUAD4 shape functions with RPIM.
• * The current study extends the application of this element to structural dynamics.

Purpose of the Study:

• * To investigate the performance of the FE-RPIM QUAD4 element in structural dynamics.
• * To compare its efficiency with the standard QUAD4 element.
• * To evaluate the impact of different mass matrix formulations (consistent vs. diagonally lumped) on the element's dynamic analysis capabilities.

Main Methods:

• * Development and implementation of the FE-RPIM QUAD4 element for dynamic analysis.
• * Free and forced vibration numerical simulations.
• * Comparative analysis using both consistent mass matrix (CMM) and diagonally lumped mass matrix (DLMM).

Main Results:

• * The FE-RPIM QUAD4 element demonstrated superior performance compared to the standard QUAD4 element when using a consistent mass matrix (CMM), particularly with distorted meshes.
• * The diagonally lumped mass matrix (DLMM) proved to be a viable and efficient alternative to CMM for the FE-RPIM QUAD4 element, even with implicit time integration schemes.

Conclusions:

• * The FE-RPIM QUAD4 element is effective for structural dynamics problems, offering improved accuracy and robustness over standard elements.
• * The use of a diagonally lumped mass matrix (DLMM) provides a computationally efficient approach for dynamic analysis with this element, without significant loss of accuracy.