Distribution law of strain energy density for stiffness design of GFRP, UT/GFRP, and VRB/GFRP hybrid hat‐shaped beams

Abstract

AbstractThe structural optimization for stiffness performances with hundreds or thousands of design parameters is a complex and time‐consuming process. This is because, on the one hand, the direct relationship between the stiffness and the many design parameters is unknown, and on the other hand, the sensitivity of a single design parameter to the global stiffness is hardly obtained. Therefore, transforming the global stiffness performance to the strain energy density (SED) distribution over the whole structure can significantly simplify the optimization problem. In this work, the relationships among the design parameters, SED distribution and stiffnesses of glass fiber reinforced plastic (GFRP), uniform thickness metal (UT)/GFRP, and variable‐thickness rolled blanks (VRB)/GFRP hat‐shaped beams are investigated through numerical simulations. It is found that the higher SED of the all hat‐shaped beam structure indicates a worse stiffness performance under both bending and torsional conditions. When the SED of the GFRP hat‐shaped beam increases 6.65%, its bending stiffness decreases 10.8%. It is also found that the smaller SED distribution variance of the all hat‐shaped beam structures indicates a better stiffness performance. When the SED distribution variances of the VRB and GFRP in the VRB/GFRP hybrid beam are, respectively, reduced by 70.78% and 85.56%, the bending stiffness of the hybrid beam is increased by 50.83%. The above relations and conclusions indicate that the structural stiffness optimization problem with many design parameters can be replaced with the structural SED distribution variance minimization problem, which would not need the unavailable sensitivities of the design parameters to the global stiffness. Besides, compared to the GFRP hat‐shaped beam, with the same mass, volume or cost, the bending stiffnesses of the VRB/GFRP hat‐shaped beam, respectively, increases by 196.1%, 476.5%, and 676.4%, and its torsional stiffnesses, respectively, increases by 70.9%, 233.0%, and 348.4%. This means the combination of VRB and GFRP in the beam structure can reach a better stiffness performance and a higher lightweight level.