A novel stiffness prediction method with constructed microscopic displacement field for periodic composite plates

Abstract

A novel method for predicting effective stiffnesses of composite plates with in-plane periodicity is proposed according to two-scale strain energy equivalence. The macroscale energy is reached with the Reissner-Mindlin plate theory, while the microscale energy is obtained through the newly constructed displacement functions of a unit cell within the framework of the three-dimensional elasticity theory. The new displacement functions consist of homogenized displacements, two decoupled expansion terms, and a higher-order perturbed displacement term. The elaborate finite element formulations are presented for realizing the present method in Comsol Multiphysics. Several numerical experiments demonstrate the effectiveness of the new stiffness prediction method.

Keywords:

• Periodic
• composite plate
• stiffness prediction
• asymptotic homogenization
• energy equivalence
• Reissner–Mindlin

Declaration of interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Funding

This work was funded by the National Natural Science Foundation of China (grant nos. 12002019, 12172023, and 11872090) and the China Postdoctoral Science Foundation (grant no. 2021T140040).