Multi-load cases topological optimization by weighted sum method based on load case severity degree and ideality

Abstract

Mechanical structures always bear multiple loads under working conditions. Topology optimization in multi-load cases is always treated as a multi-objective optimization problem, which is solved by the weighted sum method. However, different weight factor allocation strategies have led to discrepant optimization results, and when ill loading case problems appear, some unreasonable results are obtained by those alternatives. Moreover, many multi-objective optimization problems have certain optimization objective, and an evaluation formula to measure Pareto solution in the multi-objective optimization problem area is lacking. Regarding these two problems, a new method for calculating the weight factor is proposed based on the definition of load case severity degree. Additionally, an amplified load increment is derived and suggested in the minimum compliance with a volume constraint problem. Ideality is formulized from Pareto front to the ideal solution to evaluate the different optimization results. Benchmark topology optimization examples are solved and discussed. The results show that the load case severity degree is less affected by the different weighted sum functions and can avoid ill loading case phenomena, and the ideality of optimization result obtained by the load case severity degree is the best.

Multi-Objective Topology Optimization for Curved Arm of Multifunctional Billet Tong Based on Characterization of Working Conditions

“…To be able to get a determinate optimal solution, various weighted sum methods, such as the compromise programming method [20], the linear weighting method [38], the weight-square method [24] and the weight-norm method [23], can be applied to convert the multi-objective optimization problem into a single objective optimization problem. No matter which method is applied, the calculation of the weight factor for each objective is critical, since the weights have a significant effect on the final optimization result.…”

“…Increasing the small loads is a straightforward way of dealing with ill-load cases, but the effects induced by increments of small loads and large loads are quite different. Hence, Li, et al [24] introduced the amplification coefficient (AC) to amplify small loads to deal with ill-load cases.…”

“…Hence, topology optimization of the billet tong is a typical topology optimization problem of a continuum structure with multiple loads or working conditions [15]. Since this problem exists in many practical applications, it has been investigated by using the homogenization method [16][17][18], the level-set method [19], the Solid Isotropic Material with Penalization (SIMP) method [20][21][22][23][24][25], the Rational Approximation of Material Properties (RAMP) method [26], the Independent Continuous and Mapping (ICM) method [27,28], the Evolutionary Structural Optimization (ESO) method [29], evolutionary algorithms (EA) [30,31] and a hybrid approach [32]. SIMP is popularly adopted, among others because of its theoretical simplicity and ease of implementation [11,33].…”

Multiobjective Topology Optimization of Spatial‐Structure Joints

“…In practice, joints are generally in complex stress states that include axial, shear, and bending moment stresses. erefore, the static topology optimization problem aims to maximize the stiffness of the structure under multiple-load conditions, also known as the multistiffness topology optimization problem [24]. For static multiload condition topology optimization problems, each load corresponds to an optimal solution aimed at maximizing stiffness.…”

Lightweight and maintainable rotary-wing UAV frame from configurable design to detailed design

“…The researchers used topology optimization methods to optimize a variety of components. 15,16 However, the UAV frame design methods still have problems such as long design period, high manufacturing cost, and difficulty in maintenance. Few researchers used the thin-walled parts derived from the topology optimization method to construct the UAV frame.…”