Finding globally optimal arrangements of multiple point loads in structural design using a single FEA

Abstract

Many structures around us are designed to carry point loads. Such structures are typically sensitive to load arrangements, including load locations, magnitudes, and directions; a slight change in these ingredients could significantly affect the structural response. Therefore, knowing the extremal load arrangements to achieve the best and worst structural performance holds great potential to maximize structural efficiency and avoid structural failure, respectively. Existing studies have attempted to optimize load conditions using iterative optimization algorithms. However, they cannot always guarantee to find the global optimum and may instead obtain the local optima. In this study, we propose a new method, the single FEA method, that can effectively and efficiently find the extremal load conditions of a given structure. The new method considers all possible arrangements of prescribed loads without needing to create and analyze the corresponding finite element models. This is achieved by utilizing a single finite element analysis (FEA) with multiple load cases, where each load case has a unit load applied at one of the candidate load locations. Using the proposed method, we can quickly obtain the extremal load arrangements of the structure to produce the best and worst stiffness performance. A variety of 2D and 3D examples are presented to demonstrate the effectiveness and wide applicability of the new method.