Multiscale Analysis of Sandwich Beams with Polyurethane Foam Core: A Comparative Study of Finite Element Methods and...

Area of Science:

• Materials Science
• Computational Mechanics
• Mechanical Engineering

Background:

• Sandwich beams with polyurethane foam (PUF) cores are essential in various engineering applications.
• Multiscale analysis requires robust numerical methods for accurate material property prediction.
• Finite Element Methods (FEMs) are widely used, but meshless methods offer potential advantages.

Purpose of the Study:

• To perform a comprehensive multiscale analysis of sandwich beams with PUF cores.
• To numerically compare the performance of FEM and the Radial Point Interpolation Method (RPIM).
• To investigate the integration of RPIM with homogenization techniques for multiscale analysis.

Main Methods:

• Phase 1: Homogenization of PUF with varying volume fractions using FEM and four RPIM versions.
• Phase 2: Application of homogenized properties to large-scale sandwich beam problems (homogeneous and functionally graded cores).
• Numerical comparison of stress distributions and computational efficiency between FEM and RPIM formulations.

Main Results:

• RPIM formulations with higher-order integration can approximate FEM solutions but may incur high computational costs.
• RPIM effectively approximates FEM results for large-scale sandwich beam analysis.
• Lower nodal connectivity RPIM formulations offer an efficient balance between computational cost and accuracy.
• RPIM shows a tendency for lower stress values near domain edges, converging with other methods.

Conclusions:

• RPIM is a viable and efficient alternative to FEM for multiscale analysis in elasticity problems.
• The integration of RPIM with homogenization techniques is effective for complex material structures.
• RPIM demonstrates potential for practical applications in analyzing sandwich beam structures.