An improved model for unsymmetric plates. (15th November 2020)

• Record Type: Journal Article
• Authors: Wu, Zhangming; Li, Hao; Chen, Yuli
• Is Part Of: Composite structures. Volume 252(2020)
• Publication Date: 2020-11-15
• Subjects: Unsymmetric plates -- Compatibility equation -- Mid-plane strains membrane strains -- Rayleigh–Ritz method; Composite construction -- Periodicals; Composites -- Périodiques; 624.18
• DOI: 10.1016/j.compstruct.2020.112622
• Languages: English
• ISSNs: 0263-8223

Abstract

Abstract: For an unsymmetric plate, a pure bending (plate curvature) inevitably causes a certain amount of stretching to the geometric mid-plane due to the stretching-bending coupling. According to classical thin plate theory, the geometric mid-plane is assumed to remain unstrained under pure bending. In this study, we demonstrate that the classical thin plate theory based on Kirchhoff–Love hypothesis is not accurate enough to model the structural behavior of unsymmetric plates. To overcome this limitation, we propose an improved theoretical model for unsymmetric plates through taking advantages of neutral plane strains in defining the geometric functions instead of mid-plane strains. Subsequently, the new governing equations and energy expression for the cylindrical bending of unsymmetric plates are derived using a modified constitutive equation. An alternative derivation approach based on the general stress equations is also presented for further validation. A direct consideration of stretching-bending coupling in the constitutive equation can significantly reduce the number of unknown parameters in establishing an accurate analytical model for unsymmetric plates. The pure bending problem of unsymmetric plates with small deformation is first studied, for which the improved model proposed in this paper is shown to capture the out-of-plane deformation of unsymmetric plates, accurately. However, many previous works have to take into account the nonlinear von Kármán strains even in the model of this small deformation problem. For the pure plate bending problem with large deformation, few unknown terms are needed for the improved model to give accurate results compared with the conventional mid-plane strain based method. Later, this improved model is applied to predict the stable configurations, the bifurcation/loss-of-bifurcation and the static snap-through phenomena of bistable cross-ply composite laminates. Furthermore, the application of this improved model for the accurate simulation of the nonlinear dynamics of unsymmetric plates is also demonstrated. Applying this proposed improved model, the model is reduced into an analogous one for isotropic or symmetric plates, therefore, the problem of unsymmetric plates can be solved readily and accurately.