A new deformation-based unified theory with analytical solutions for three-dimensional thermal stresses in composite plates

Abstract

The primary aim of this present study is to derive analytical solutions for three-dimensional (3D) thermal stresses in composite plates. In pursuit of this goal, an innovative deformation-based unified theory (DUT) for composite plates is developed. This theory incorporates four unknown displacement components, with each elucidated by well-defined physical elasticity causes and effects. The in-depth analyses of transverse bending and shear deformation and basic assumptions of plate structures lead to the introduction of a higher-order displacement component, in addition to three conventional displacement components at a point on the reference plane. Featuring a novel displacement component, DUT overcomes the thickness locking mechanism (TLM) by improving inherent kinematic assumptions in the traditional plate theories, thereby laying a firm theoretical foundation for the excellent studies of transverse normal displacements, strains, stresses, thermal stresses and thermal strains. Grounded in objective reasoning and derivation of fundamental assumptions, DUT enables the introduction of thickness and modified functions in the form of general mathematical expressions. This flexibility in selecting thickness and modified functions allows the theory and analytical model to be simplified and transformed to any existing plate theories, such as the classical plate theory (CPT), first-order shear deformation theory (FSDT), and third-order shear deformation theory (TSDT). Additionally, a novel method for determining the thermal strain energy associated with 3D thermal stresses in composite plates is formulated by introducing Green’s nonlinear normal strain, aiming to accurately capture the effects of thermal expansion. Analytical solutions for 3D thermal stresses in composite plates are established by applying Hamilton’s principle. Comprehensive numerical analysis and verification of different plate theories are carried out within the scope of DUT. The general and innovative analysis for modeling and investigating the thermo-mechanical coupling response of composite plates subjected to 3D thermal stresses is characterized by the presence of clarity, unity, elegance, and effectiveness, thus establishing a noteworthy advancement to the theory of plates.