Non-gradient Robust Topology Optimization Method Considering Loading Uncertainty

To effectively tackle the robust topology optimization (RTO) problem of continuum structure considering the uncertainties of loading magnitude and direction under the premise of avoiding gaining the sensitivity information, a non-gradient RTO method was proposed by combining the improved proportional topology optimization (IPTO) algorithm with multiple methods (including the probabilistic approach, the superposition principle of linear theory, the Monte Carlo method and the weighted combination method). Among these, the probabilistic approach was used to describe the uncertainties of loading magnitude and direction. The weighted combination method was employed to establish the RTO model with the objective function of minimizing the weighted sum of the expectation and standard deviation of structural compliance. The calculation method of the expectation and standard deviation of structural compliance was given by applying the superposition principle of linear theory and the Monte Carlo method. Subsequently, the core equations of the IPTO algorithm (without requiring the sensitivity information) were redesigned to ensure that the structural RTO problem can be tackled. Finally, the numerical examples were used and other RTO methods were compared to demonstrate the effect of the RTO method proposed. The results show that the new RTO method not only can effectively address the structural RTO problem considering loading uncertainty, but also has advantages over other RTO methods in terms of some performance during solving the structural RTO problem. Moreover, the different values of control parameters in the new RTO method also have an effect on structural optimization results.

[1]  Wang Chunjie,et al.  Robust Topology Optimization under Loading Uncertainty with Proportional Topology Optimization Method , 2016, 2016 Eighth International Conference on Measuring Technology and Mechatronics Automation (ICMTMA).

[2]  Junpeng Zhao,et al.  Robust Topology Optimization of Structures Under Loading Uncertainty , 2014 .

[3]  Dong Wang,et al.  Robust topology optimization under multiple independent uncertainties of loading positions , 2020, International Journal for Numerical Methods in Engineering.

[4]  Nozomu Kogiso,et al.  Robust Topology Optimization for Compliant Mechanisms Considering Uncertainty of Applied Loads , 2008 .

[5]  Junpeng Zhao,et al.  Robust topology optimization under loading uncertainty based on linear elastic theory and orthogonal diagonalization of symmetric matrices , 2014 .

[6]  James K. Guest,et al.  Achieving minimum length scale in topology optimization using nodal design variables and projection functions , 2004 .

[7]  Takayuki Nishino,et al.  Robust topology optimization based on finite strain considering uncertain loading conditions , 2020, International Journal for Numerical Methods in Engineering.

[8]  Hae Chang Gea,et al.  Robust topology optimization under multiple independent unknown-but-bounded loads , 2018 .

[9]  Anikó Csébfalvi.  A New Compliance-function-shapeoriented Robust Approach for Volume-constrained Continuous Topology Optimization with Uncertain Loading Directions , 2017 .

[10]  Wang Chunjie,et al.  Algorithm of structural topology optimization under loading uncertainty , 2014 .

[11]  Albert C. To,et al.  Proportional Topology Optimization: A New Non-Sensitivity Method for Solving Stress Constrained and Minimum Compliance Problems and Its Implementation in MATLAB , 2014, PloS one.

[12]  Zhenyu Liu,et al.  Robust topology optimization of continuum structures with loading uncertainty using a perturbation method , 2017 .

[13]  O. Sigmund.  Morphology-based black and white filters for topology optimization , 2007 .

[14]  J. Lógó,et al.  A critical analysis of expected-compliance model in volume-constrained robust topology optimization with normally distributed loading directions, using a minimax-compliance approach alternatively , 2018, Adv. Eng. Softw..

[15]  Jie Liu,et al.  Robust topology optimization for continuum structures with random loads , 2018 .

[16]  Weifeng Gao,et al.  Robust topology optimization under load position uncertainty , 2019, International Journal for Numerical Methods in Engineering.

[17]  Peter D. Dunning,et al.  Robust Topology Optimization: Minimization of Expected and Variance of Compliance , 2013 .

[18]  Giancarlo Valente,et al.  The Default Mode Network and the Working Memory Network Are Not Anti-Correlated during All Phases of a Working Memory Task , 2015, PloS one.

[19]  Hui Wang,et al.  Improved proportional topology optimization algorithm for solving minimum compliance problem , 2020, Structural and Multidisciplinary Optimization.

[20]  Hui Wang,et al.  Improved proportional topology optimization algorithm for minimum volume problem with stress constraints , 2020, Engineering Computations.