Structural Optimization of Thin-Walled Tubular Structures for Progressive Collapse Using Hybrid Cellular Automaton with a Prescribed Response Field

Abstract

The design optimization of thin-walled tubular structures is of relevance in the automotive industry due to their low cost, ease of manufacturing and installation, and high-energy absorption efficiency. This study presents a methodology to design thin-walled tubular structures for crashworthiness applications. During an impact, thin-walled tubular structures may exhibit progressive collapse/buckling, global collapse/buckling, or mixed collapse/buckling. From a crashworthiness standpoint, the most desirable collapse mode is progressive collapse due to its high-energy absorption efficiency, stable deformation, and low peak crush force (PCF). In the automotive industry, thin-walled components have complex structural geometries. These complexities and the several loading conditions present in a crash reduce the possibility of progressive collapse. The Hybrid Cellular Automata (HCA) method has shown to be an efficient continuum-based approach in crashworthiness design. All the current implementations of the HCA method use a scalar set point to design structures with a uniform distribution of a field variable, e.g., stress, strain, internal energy density (IED), mutual potential energy. For example, using IED and mutual potential energy as the field variable result in high stiffness and progressive collapsing structures, respectively. This paper presents a modified version of the HCA method to design thin-walled structures that collapse progressively. In this methodology, the set point has two components, a prescribed response field, which promotes progressive collapse, and a variable offset value, which satisfies the mass constraint. The numerical examples show that this modified HCA method is capable of finding material distributions that exhibit progressive collapse, resulting in significant improvement in specific energy absorption (SEA) with relatively little change in the PCF.