Motion error based robust topology optimization for compliant mechanisms under material dispersion and uncertain forces

Summary This work addresses the topology optimization approach to design robust compliant mechanisms with respect to uncertainties in the output stiffness, when compared to the traditional deterministic approach. To this end, two formulations are proposed: probabilistic and nonprobabilistic. The probabilistic formulation minimizes a joint objective function of expected output displacement plus a measure of its standard deviations, for given statistical distribution of the output stiffness. The nonprobabilistic formulation is written as minimization of a joint function of the median of output displacements, plus the width of the intervals that contains the extreme values of the output displacements, for a given interval of output stiffness. The Monte Carlo simulation method is used to evaluate expected values and standard deviations of output displacements in the probabilistic formulation and to assess results obtained with the deterministic approach. It is shown that both formulations lead to designs where output displacements are less sensitive to variations of output stiffness when compared to the traditional deterministic approach. Furthermore, as an additional benefit, it is observed that large variations of output stiffness can hinder the appearance of one‐node connected hinges, usually found in the deterministic design of compliant mechanisms.

Section: Introductionmentioning

confidence: 99%

Robust topology optimization of compliant mechanisms with uncertainties in output stiffness

Cardoso

Silva

Beck

2019

“…However, it should be emphasized that the material dispersion and uncertain external forces are inevitable in practical engineering and some mechanisms, such as the microelectromechanical systems (MEMS), are sensitive to the variations in material properties and applied loads . Under such circumstances, some researchers proposed the reliability‐based or robust topology optimization concepts in the design of the compliant mechanisms . Guo et al introduced a robust index of compliance under uncertain boundary as the optimization objective and conduct the topology optimization by virtue of the level set approach.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, the aforementioned reliability‐based and robust topology optimization approaches may not be fulfilling in the situation that the output motion accuracy is the most important parameters to designers and engineers. Pedersen et al presented the minimum of motion error as the objective to design a compliant mechanism with an expected output motion in the deterministic assumptions firstly, then Wang et al proposed a robust topology optimization method that minimizes motion error of the output port considering uncertain material properties and external input forces.…”

Section: Introductionmentioning

confidence: 99%

“…24,25 Under such circumstances, some researchers proposed the reliability-based or robust topology optimization concepts in the design of the compliant mechanisms. [26][27][28][29] Guo et al 30 introduced a robust index of compliance under uncertain boundary as the optimization objective and conduct the topology optimization by virtue of the level set approach. Liu et al 31 proposed a BESO topology optimization method which took the correlations of the probability and fuzziness of the applied load direction into account and conducted the uncertain degree of mean compliance as the objective.…”

Section: Introductionmentioning

confidence: 99%

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A nonprobabilistic reliability–based topology optimization method of compliant mechanisms with interval uncertainties

Wang

Liang

Chen

et al. 2019

Self Cite

Summary On account of the inevitable multisource uncertainty factors in compliant mechanisms, which seriously affect the accuracy of output motion, a nonprobabilistic reliability–based topology optimization (NRBTO) framework for compliant mechanisms with interval uncertainties is introduced. Combined with the solid isotropic material with penalization (SIMP) model and the set‐theoretical interval method, the uncertainty quantification analysis is conducted to obtain mathematical approximations and boundary laws of considered mean compliance. By normalization treatment of the limit‐state function, a new quantified measure of the nonprobabilistic reliability is then defined. The compliance‐based NRBTO design method ensures the output motion realizing its target value accurately considering the uncertainty factors. The sensitivities of the nonprobabilistic reliability index with respect to design variables are calculated by the adjoint vector method. Two engineering examples are eventually presented to illustrate the applicability and the validity of the present problem statement as well as the proposed numerical techniques.

“…Long et al introduced a formulation of RTO for structures considering the damage location and load uncertainty. Wang et al developed an RTO for compliant mechanisms with material and load uncertainties. Considering the uncertainty of boundary variations, Guo et al developed an RTO method based on a level‐set framework.…”

Section: Introductionmentioning

confidence: 99%

Level‐set topology optimization for robust design of structures under hybrid uncertainties

Zheng

Luo

Jiang

et al. 2018

This paper will develop a new robust topology optimization (RTO) method based on level sets for structures subject to hybrid uncertainties, with a more efficient Karhunen-Loève hyperbolic Polynomial Chaos-Chebyshev Interval method to conduct the hybrid uncertain analysis. The loadings and material properties are considered hybrid uncertainties in structures. The parameters with sufficient information are regarded as random fields, while the parameters without sufficient information are treated as intervals. The Karhunen-Loève expansion is applied to discretize random fields into a finite number of random variables, and then, the original hybrid uncertainty analysis is transformed into a new process with random and interval parameters, to which the hyperbolic Polynomial Chaos-Chebyshev Interval is employed for the uncertainty analysis. RTO is formulated to minimize a weighted sum of the mean and standard variance of the structural objective function under the worst-case scenario. Several numerical examples are employed to demonstrate the effectiveness of the proposed RTO, and Monte Carlo simulation is used to validate the numerical accuracy of our proposed method. KEYWORDS hybrid uncertainties, hyperbolic Polynomial Chaos-Chebyshev Interval method, robust design, topology optimization Int J Numer Methods Eng. 2019;117:523-542.wileyonlinelibrary.com/journal/nme