Extended refined zigzag theory accounting for two-dimensional thermoelastic deformations in thick composite and sandwich beams

The Extended Refined Zigzag Theory (RZT-E) is introduced for the linear elastic analysis of composite and sandwich beams under static and thermal loads. Building on the Refined Zigzag Theory (RZT), RZT-E incorporates a cubic and zigzag variation for axial displacement and a parabolic and zigzag approximation for transverse displacement, enabling higher-order deformation effects and thickness-stretch modes. These enhancements improve accuracy, particularly for beams with varying material properties and thermal gradients. The mechanical loading includes arbitrary transverse normal and shear tractions applied to the top and bottom surfaces, while thermal loads are modelled using a piecewise linear through-thickness function, accounting for zigzag variations from transient thermal analyses. The formulation involves seven independent kinematic variables, regardless of the number of layers, and employs the virtual work principle to derive seven equilibrium equations with consistent boundary conditions. Analytical solutions are provided for simply supported beams under transverse surface load, shear tractions, and varying thermal loads. Transverse shear and normal stresses are calculated using two-dimensional Cauchy equilibrium equations during post-processing. RZT-E shows improved accuracy over RZT, particularly for cases with significant material or thermal variations. It eliminates the need for shear correction factors and is ideally suited for the development of efficient C ⁰-continuous finite elements.