Tailoring bistability of mechanically prestressed sandwich laminate with various planforms

Bistable structures have two non-adjacent equilibrium configurations with minimum total potential energies. Unsymmetrical cross-ply laminate can show bistability if its initial curvature is within a specified range or an inelastic curvature is induced through various actions such as thermal curing, mechanical prestressing, etc. This paper adopts an alternative method to achieve bistability in three-layered sandwich laminates using a mechanically prestressed core. By adjusting the applied prestrain, this sandwich structure can be designed to exhibit bistable or monostable characteristics. A semi-analytical model based on the Rayleigh-Ritz method is developed for bistable laminates with different planform geometries. In the semi-analytical framework, the kinematic variables are approximated using Lagrange polynomials. The accuracy of the semi-analytical model was ascertained by comparing the semi-analytical solutions with those obtained from finite element analyses. In addition, a simplified analytical model is proposed to verify the deformed shape of a square prestressed laminate. Using the semi-analytical model, the post-critical and negative stiffness behavior of bistable sandwich laminates, with various planform geometries, have been studied. Numerical investigations carried out in this work have revealed that the postcritical behavior and negative stiffness characteristics of sandwich prestressed laminates can be tailored by carefully controlling several factors. These factors include the prestrain ratio applied to the core, elastic moduli of the core, the slenderness of the face sheets, and the planform shape of the laminate. Furthermore, the studies show the feasibility to control the bistable response of the laminate by manipulating the prestrain ratio within the core. By adjusting the prestrain ratio, the structural response of the laminate can be tuned, allowing it to exhibit stable configurations under specific conditions. This capability of controlling and inducing bistable or pseudo-bistable states opens up new possibilities for designing advanced materials and structures with tailored mechanical properties and enhanced functionality.