Robust topology optimization for continuum structures with random loads

Self Cite

This paper presents an adaptive mesh adjustment algorithm for continuum topology optimization method to describe the structural boundary using nonuniform isoparametric element. A criterion on the basis of the node movement is proposed; herein, the densities and coordinates of the nodes are defined to instruct the deformation of finite elements in subsequent optimization iterations. With such a scheme, the topology optimization can start from a regular mesh discretization then gradually yields an optimal design with clear structural boundaries. The element in the transition along the boundary is refined; on the contrary, the pure solid or void element is coarsen. The contribution of this work is to improve the resolution of the structural boundaries and decrease the percentage of transitional regions with the invariant design variable. Several 2D and 3D numerical examples indicate the effectiveness of our proposed method. Seen from the examples, the structural boundary become smoother and the intermediate densities have been reduced up to 70%. In addition, a design process based on the presented method is proposed to make the optimum solutions be fabricated conveniently and accurately by linking it with the 3D design software, ie, SolidWorks, which is also demonstrated in the numerical examples. KEYWORDS mesh adjustment, nonuniform isoparametric element, smooth boundary, topology optimization, 3D design software 1304

Section: Numerical Examplessupporting

confidence: 59%

An adaptive mesh‐adjustment strategy for continuum topology optimization to achieve manufacturable structural layout

Wang

Liu

Wen

2018

Self Cite

“…In order to evaluate numerically the objective function (22) for a given geometry of Ω, we need to evaluate high-order frequency derivatives of F with respect to the angular frequency. Recalling that, for example, we can evaluate dF∕d as…”

Section: Computation Of Angular Frequency Derivativesmentioning

confidence: 99%

“…In this subsection, we derive the topological derivative of the present objective function (22). Since our objective function is a function of F( 0 ) in (4) and its high-order derivatives F (k) ( 0 ) (k = 1, … , N) with respect to the angular frequency , using the chain rule, its topological derivative can be computed as…”

Section: Topological Derivativementioning

confidence: 99%

“…Zheng et al 21 solved the compliance‐minimizing problem with a semi‐analytical RTO method, in which a generic coefficient of variation as a robust index is deployed to improve the numerical accuracy. Liu et al 22 transformed the RTO problem which is hard to solve into an equivalent tractable one, without losing the original robust intention. Carrasco et al 23 validated a multilevel stochastic programming approach for RTO in designing three‐dimensional truss structure.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A robust topology optimization for enlarging working bandwidth of acoustic devices

Qin

Isakari

Taji

et al. 2021

We propose a novel robust topology optimization for designing acoustic devices that are effective for broadband sound waves. Here, we define the objective function as the weighted sum of the acoustic response to an incident wave consisting of a single frequency and its standard deviation (SD) against the frequency perturbation. By approximating the SD, under the assumption that the incident frequency follows the normal distribution, with the high‐order Taylor expansion of the (conventional) objective function, we deal with significant frequency variations. To calculate such an approximation, we need to calculate the high‐order frequency derivatives of the state variable. Here, we define them by integral representations, which enables us to characterize them even when the state variable is defined in an unbounded domain as is often the case with wave scattering problems. We further show that, based on this definition, the high‐order derivatives can efficiently be computed by a combination of the boundary element method and automatic differentiation. We also present a derivation and calculation of the topological derivative for the newly defined objective function. We install all the proposed techniques into a topology optimization method based on the level‐set method to design wideband acoustic devices. The validity and effectiveness of the proposed topology optimization are confirmed through several numerical examples.

“…In recent years, the topology optimization methods of compliant mechanisms considering geometric nonlinearity, manufacturing uncertainty, stress constraints, multiphysics design requirements, manufacturing uncertainty, and their combination requirements, respectively, have been developed. [41][42][43][44][45][46][47][48]77,78 Despite these significant advances, most studies have been conducted on designing CMs with single input and single output behaviors. Only a few of studies have been conducted on a topological design of single input and multiple output CMs.…”

Section: Introductionmentioning

confidence: 99%

A new method for optimizing the topology of hinge‐free and fully decoupled compliant mechanisms with multiple inputs and multiple outputs

Rong

Luo

et al. 2021

Compliant mechanisms with multiple inputs and multiple outputs have a wide range of applications in precision mechanics, for example, cell manipulations, electronic microscopes, and so on. The movement uncoupling and maximum desired output displacements among these devices all become critical because many inputs and outputs are involved. The topology optimization design of compliant mechanisms, which can solve output coupling and input coupling problems, hinge and gray region problems, and the multiple-objective optimal problem, is an important topic of researches for achieving fully decoupled motion. It is also a challenge area of research due to serious conflicts of between the four of output and input uncoupling constraints, volume constraint, the hinge-free requirement, and the good black/white solution requirement. In order to comprehensively solve these problems, a simple optimization model overcoming these serious conflicts is posed, which includes small change rate constraints of structural compliances corresponding to the driving input loads and output point virtual loads. Then, the multiple output displacement functions of the model are equivalently converted into non-negative functions. The multiple-objective model is converted into a single-objective optimization model by using a bound variable. The method of moving asymptotes (MMA) algorithm is adopted to solve it. Several examples are presented to demonstrate the validity of the proposed method.