Theoretical solutions of short glass fiber/polyurethane composite beams based on Hamiltonian principle

Shape memory polymers (SMP) and its composites (SMPC) have gained popularity for their potential in intelligent structures fields. Developing a reliable mechanical model to accurately describe mechanical behavior of its intelligent structures is important for both theory and practice. This paper presents a novel mechanical model for describing the mechanical behavior of short glass fiber/polyurethane (GF/PU) composite beams, based on a constitutive model of SMP and incorporating principles from composite mechanics theory, the Hamiltonian principle and Euler-Bernoulli beam theory. The model includes kinematic equations and material parameter equations. Based on the constitutive equations of SMP, coupled with Euler-Bernoulli beam theory and Hamilton's principle, the kinematic equations of GF/PU composite beam are established. Additionally, a correction factor was proposed and employed to modify the material parameter equation of SMP, which was then combined with the mechanics theory of composite materials to establish a material parameter equation for composite beams. Taking a simply supported beam as an example, we solve the model using Fourier method and simulate and analyze the material parameters properties, static and viscous mechanical behaviors properties, and shape memory behavior properties of the GF/PU composite beam. The results show that the GF volume fraction, temperature correction coefficient, regularization parameter, and contact parameter have a significant impact on the material parameters of GF/PU composite materials and the material parameters of composite beams have important effects on their mechanical properties. By adjusting material parameters, ideal mechanical properties can be obtained for the GF/PU composite beam. This study provides a theoretical foundation for intelligent beam design and analysis based on SMP and SMPC.