Design optimization of hopper cars employing functionally graded honeycomb sandwich panels

In this paper, a novel multiscale and multi-stage structural design optimization procedure is developed for the weight minimization of hopper cars. The procedure is tested under various loading conditions according to guidelines established by regulatory bodies, as well as a novel load case that considers fluid-structure interaction by means of explicit finite elements employing Smoothed Particle Hydrodynamics. The first stage in the design procedure involves topology optimization whereby optimal beam locations are determined within the design space of the hopper car wall structure. This is followed by cross-sectional sizing of the frame to concentrate mass in critical regions of the hopper car. In the second stage, hexagonal honeycomb sandwich panels are considered in lower load regions, and are optimized by means of Multiscale Design Optimization (MSDO). The MSDO drew upon the Kreisselmeier–Steinhausser equations to calculate a penalized cost function for the mass and compliance of a hopper car Finite Element Model (FEM) at the mesoscale. For each iteration in the MSDO, the FEM was updated with homogenized sandwich composite properties according to four design variables of interest at the microscale. A cost penalty is summed with the base cost by comparing results of the FEM with the imposed constraints. Efficacy of the novel design methodology is compared according to a baseline design employing conventional materials. By invoking the proposed methodology in a case study, it is demonstrated that a mass savings as high as 16.36% can be yielded for a single hopper car, which translates into a reduction in greenhouse gas emissions of 13.09% per car based on available literature.