A Novel Higher-Order Zigzag Function Applied to Refined Unified Beam Theory for the Analysis of Composite Laminated Materials

Highly efficient materials and structures are becoming increasingly common in military, aeronautical, aerospace, mechanical, and civil engineering applications. Composite materials have been developed to address the need to combine two or more materials to achieve superior properties. Many structural elements, such as laminated beams, use composite materials, but an accurate mathematical model of the bending behavior is required due to the abrupt changes in material properties in the interlaminar zones. This accurate model can be achieved using zigzag theory. This theory is one of the most commonly used formulations for modeling laminated beams. This theory is an improvement of the equivalent single-layer theory as an additional term called the “zigzag function” is used to represent the variation in the axial displacement along the cross section. This paper proposes a novel high-order zigzag function in a sinusoidal format. Several higher-order beam theories are combined with the proposed functions, and their performances are compared with those of other functions in the literature. The results reveal excellent agreement between the proposed formulation and the reference solution as well as a more effective combination of zigzag functions and beam theory.