Robust compliance topology optimization based on the topological derivative concept

Abstract

In this paper, we present an approach for robust compliance topology optimization under volume constraint. The compliance is evaluated considering a point-wise worst-case scenario. Analogously to sequential optimization and reliability assessment, the resulting robust optimization problem can be decoupled into a deterministic topology optimization step and a reliability analysis step. This procedure allows us to use topology optimization algorithms already developed with only small modifications. Here, the deterministic topology optimization problem is addressed with an efficient algorithm based on the topological derivative concept and a level-set domain representation method. The reliability analysis step is handled as in the performance measure approach. Several numerical examples are presented showing the effectiveness of the proposed approach. a maximum failure probability of the system [7][8][9]. In the case of robust optimization, the goal is to obtain an optimum design that is least sensitive to variations and uncertainties of the variables [10][11][12][13]. In the case of risk-based optimization, the failure probability of the system is used to evaluate the total cost of failures, which together with other costs compose the objective function of the problem [14].Topology optimization of continuum structures considering uncertainties has already been addressed in the literature. In the context of reliability-based design optimization, volume minimization with stress constraints has been studied in [8,15,16], while design of microelectromechanical systems has been presented in [9,17]. Regarding the robust optimization, compliance-based topology design under uncertain loads has been studied in [11,[18][19][20], synthesis of compliant mechanism together with design of structures with minimum compliance has been tackled in [21,22], whereas boundary uncertainties have been investigated in [23]. Some applications of risk-based optimization to problems concerning structural optimization have been presented in [14,24], while a general review of select applications has been presented in [25].It has been observed that uncertainties consideration may lead to solutions conceptually different from deterministic optimization. This fact supports the application of optimization under uncertainties in several cases of practical interest. However, in general, uncertainty-based optimization requires much more computation effort than its deterministic counterpart. This fact limits the range of practical applications of uncertainty-based optimization.In this context, the goal of this paper is to present an approach for robust compliance topology optimization that is both general and computationally efficient. The compliance is evaluated considering a point-wise worst-case scenario, found within an event set of possible outcomes of the random parameters. Analogously to sequential optimization and reliability assessment [26], the resulting robust optimization problem can be decoupled into a deterministic topology optimization s...

Robust topology optimization methodology for continuum structures under probabilistic and fuzzy uncertainties

“…where the parameter can be set to a large value to ensure accuracy; this value is selected as 10,000 in this study. For Equation (19), the variables and random variables x can be considered constants, and the Karush-Kuhn-Tucker optimality condition is as follows:…”

Topology optimization of industrial robots: Application to a five-bar mechanism

“…This methodology is based on the choice of optimal robot configurations or trajectories for which extreme performance will be attained. This procedure was inspired from [70,71].…”

Reliability‐based topology optimization of structures under stress constraints

“…In the case of robust design optimization, the goal is to obtain an optimum design that is least sensitive to uncertainties in the problem parameters. () In the case of RBDO, the constraints of the optimization problem are stated as to impose a target reliability level for the system under design. ()…”

“…In the case of robust design optimization, the goal is to obtain an optimum design that is least sensitive to uncertainties in the problem parameters. [8][9][10][11] In the case of RBDO, the constraints of the optimization problem are stated as to impose a target reliability level for the system under design. [12][13][14] More recently, RBDO approaches have been applied to topology optimization, originating the field of reliability-based topology optimization (RBTO).…”

“…Recent works concerning RBTO applied to the volume minimization of structures with stress constraints were presented by Luo et al 12 and Silva and Cardoso, 20 whereas the design of microelectromechanical systems has been presented in the works of Maute and Frangopol 14 and Kim et al 21 The goal of this paper is to present an approach based on the topological derivative concept for RBTO, where a structure of minimum weight subject to von Mises stress constraints under load and material uncertainties is sought. Following the original ideas presented in the work of Torii et al 10 in the context of compliance minimization under uncertainties, the RBTO problem is formulated using the performance measure approach (PMA), 13 and the sequential optimization and reliability assessment (SORA) approach 22 is employed. This strategy allows for decoupling the RBTO problem into 2 steps, namely, a deterministic topology optimization step and a reliability analysis step.…”