Theoretical Analysis of CFRTP Optimal Variable Thickness Beam Subjected to Bending Load and the Influence of Out-of-plane Shear Modulus

Abstract

Carbon-fiber-reinforced thermoplastics (CFRTP) are highly expected to find application in mass-production vehicles due to their high-productivity, thermal bonding characteristics, and recycle performance. In addition, discontinuous CFRTP adopts a ‘variable thickness structure’, which enables a wide range of practical applications including large structural parts. In this study, the optimum variable thickness of a simple supported beam was theoretically obtained by solving the Euler–Lagrange equation. In addition, the robustness of the variable thickness structure was evaluated through parametric study. Due to the low shear modulus of thermoplastic resin, the ratio of in-plane Young’s modulus (E₁) to out-of-plane shear modulus (G₁₃) of CFRTP is larger than that of other materials. To examine its effect, Timoshenko assumption was applied and was compared with the Euler–Bernoulli assumption. Consequently, it was shown that the Timoshenko-based variable thickness structure required minimum thickness on the edge, which was affected by the length of the beam and the E₁-to-G₁₃ ratio. The theoretical weight reduction rate was obtained by applying both material substitution and optimum variable thickness structure. Those values of carbon-fiber-tape-reinforced thermoplastics (CTT) and carbon-fiber-mat-reinforced thermoplastics (CMT) are 70.1% and 67.9%, respectively.