Improved proportional topology optimization algorithm for minimum volume problem with stress constraints

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Wenming Cheng ◽  
Hui Wang ◽  
Min Zhang ◽  
Run Du
Keyword(s):  
Topology Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Weighting Function ◽  
Target Material ◽  
Stress Constraints ◽  
Convergence Speed ◽  
Minimum Volume ◽  
Content Type ◽  
Density Filter

Purpose The purpose of this paper is to propose an improved proportional topology optimization (IPTO) algorithm for tackling the stress-constrained minimum volume optimization problem, which can meet the requirements that are to get rid of the problems of numerical derivation and sensitivity calculation involved in the process of obtaining sensitivity information and overcome the drawbacks of the original proportional topology optimization (PTO) algorithm. Design/methodology/approach The IPTO algorithm is designed by using the new target material volume update scheme and the new density variable update scheme and by introducing the improved density filter (considering the weighting function based on the Gaussian distribution) and Heaviside-type projection operator on the basis of the PTO algorithm. The effectiveness of the IPTO algorithm is demonstrated by solving the stress-constrained minimum volume optimization problems for two numerical examples and being compared with the PTO algorithm. Findings The results of this paper show that the uses of the proposed strategies contribute to improving the optimized results and the performance (such as the ability to obtain accurate solutions, robustness and convergence speed) of the IPTO algorithm. Compared with the PTO algorithm, the IPTO algorithm has the advantages of fast convergence speed, enhancing the ability to obtain accurate solutions and improving the optimized results. Originality/value This paper achieved the author’s intended purpose and provided a new idea for solving the stress-constrained optimization problem under the premise of avoiding obtaining sensitivity information.

h-adaptive topology optimization considering variations of material properties and energy error density recovery

2020 ◽  
Vol 37 (9) ◽  
pp. 3209-3241
Author(s):  
Jéderson da Silva ◽  
Jucélio Tomás Pereira ◽  
Diego Amadeu F. Torres
Keyword(s):  
Topology Optimization ◽  
Material Properties ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Computational Cost ◽  
Error Estimator ◽  
Content Type ◽  
Energy Error ◽  
Error Density ◽  
Discretization Errors

Purpose The purpose of this paper is to propose a new scheme for obtaining acceptable solutions for problems of continuum topology optimization of structures, regarding the distribution and limitation of discretization errors by considering h-adaptivity. Design/methodology/approach The new scheme encompasses, simultaneously, the solution of the optimization problem considering a solid isotropic microstructure with penalization (SIMP) and the application of the h-adaptive finite element method. An analysis of discretization errors is carried out using an a posteriori error estimator based on both the recovery and the abrupt variation of material properties. The estimate of new element sizes is computed by a new h-adaptive technique named “Isotropic Error Density Recovery”, which is based on the construction of the strain energy error density function together with the analytical solution of an optimization problem at the element level. Findings Two-dimensional numerical examples, regarding minimization of the structure compliance and constraint over the material volume, demonstrate the capacity of the methodology in controlling and equidistributing discretization errors, as well as obtaining a great definition of the void–material interface, thanks to the h-adaptivity, when compared with results obtained by other methods based on microstructure. Originality/value This paper presents a new technique to design a mesh made with isotropic triangular finite elements. Furthermore, this technique is applied to continuum topology optimization problems using a new iterative scheme to obtain solutions with controlled discretization errors, measured in terms of the energy norm, and a great resolution of the material boundary. Regarding the computational cost in terms of degrees of freedom, the present scheme provides approximations with considerable less error if compared to the optimization process on fixed meshes.

An improved sparrow search algorithm based on levy flight and opposition-based learning

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Danni Chen ◽  
JianDong Zhao ◽  
Peng Huang ◽  
Xiongna Deng ◽  
Tingting Lu
Keyword(s):  
Parameter Optimization ◽  
Optimization Problem ◽  
Heuristic Algorithms ◽  
Search Algorithm ◽  
Convergence Speed ◽  
Support Vector ◽  
Lévy Flight ◽  
Levy Flight ◽  
Content Type ◽  
Opposition Based Learning

Purpose Sparrow search algorithm (SSA) is a novel global optimization method, but it is easy to fall into local optimization, which leads to its poor search accuracy and stability. The purpose of this study is to propose an improved SSA algorithm, called levy flight and opposition-based learning (LOSSA), based on LOSSA strategy. The LOSSA shows better search accuracy, faster convergence speed and stronger stability. Design/methodology/approach To further enhance the optimization performance of the algorithm, The Levy flight operation is introduced into the producers search process of the original SSA to enhance the ability of the algorithm to jump out of the local optimum. The opposition-based learning strategy generates better solutions for SSA, which is beneficial to accelerate the convergence speed of the algorithm. On the one hand, the performance of the LOSSA is evaluated by a set of numerical experiments based on classical benchmark functions. On the other hand, the hyper-parameter optimization problem of the Support Vector Machine (SVM) is also used to test the ability of LOSSA to solve practical problems. Findings First of all, the effectiveness of the two improved methods is verified by Wilcoxon signed rank test. Second, the statistical results of the numerical experiment show the significant improvement of the LOSSA compared with the original algorithm and other natural heuristic algorithms. Finally, the feasibility and effectiveness of the LOSSA in solving the hyper-parameter optimization problem of machine learning algorithms are demonstrated. Originality/value An improved SSA based on LOSSA is proposed in this paper. The experimental results show that the overall performance of the LOSSA is satisfactory. Compared with the SSA and other natural heuristic algorithms, the LOSSA shows better search accuracy, faster convergence speed and stronger stability. Moreover, the LOSSA also showed great optimization performance in the hyper-parameter optimization of the SVM model.

Topology optimization of structures subject to self-weight loading under stress constraints

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Renatha Batista dos Santos ◽  
Cinthia Gomes Lopes
Keyword(s):  
Topology Optimization ◽  
Stress Constraints ◽  
Topological Derivative ◽  
The Self ◽  
Von Mises Stress ◽  
Stress Constraint ◽  
Content Type ◽  
Derivative Method ◽  
Von Mises ◽  
Weight Loading

PurposeThe purpose of this paper is to present an approach for structural weight minimization under von Mises stress constraints and self-weight loading based on the topological derivative method. Although self-weight loading topology has been the subject of intense research, mainly compliance minimization has been addressed.Design/methodology/approachThe resulting minimization problem is solved with the help of the topological derivative method, which allows the development of efficient and robust topology optimization algorithms. Then, the derived result is used together with a level-set domain representation method to devise a topology design algorithm.FindingsNumerical examples are presented, showing the effectiveness of the proposed approach in solving a structural topology optimization problem under self-weight loading and stress constraint. When the self-weight loading is dominant, the presence of the regularizing term in the formulation is crucial for the design process.Originality/valueThe novelty of this research work lies in the use of a regularized formulation to deal with the presence of the self-weight loading combined with a penalization function to treat the von Mises stress constraint.

A deterministic semi-infinite global optimization method to design slotless permanent magnet machines

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Zahia Amrouchi ◽  
Frederic Messine ◽  
Clement Nadal ◽  
Mohand Ouanes
Keyword(s):  
Global Optimization ◽  
Permanent Magnet ◽  
Analytical Model ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Angular Position ◽  
Torque Ripple ◽  
Deterministic Global Optimization ◽  
Content Type ◽  
Torque Ripples

Purpose In this work, a method to design a slotless permanent magnet machine (SPMM) based on the joint use of an analytical model and deterministic global optimization algorithms is addressed. The purpose of this study is to propose to include torque ripples as an extra constraint in the optimization phase involving de facto the study of a semi-infinite optimization problem. Design/methodology/approach Based on the use of a well-known analytical model describing the electromagnetic behavior of an SPMM, this analytical model has been supplemented by the calculus of the dynamic torque and its ripples to carry out a more accurate optimized sizing method of such an electromechanical converter. As a consequence, the calculated torque depends on a continuous variable, namely, the rotor angular position, resulting in the definition of a semi-infinite optimization problem. The way to solve this kind of semi-infinite problem by discretizing the rotor angular position by using a deterministic global optimization solver, that is to say COUENNE, via the AMPL modeling language is addressed. Findings In this study, the proposed approach is validated on some numerical tests based on the minimization of the magnet volume. Efficient global optimal solutions with torque ripples about 5% (instead of 30%) can be so obtained. Research limitations/implications The analytical model does not use results from the solution of two-dimensional field equations. A strong assumption is put forward to approximate the distribution of the magnetic flux density in the air gap of the SPMM. Originality/value The problem to design an SPMM can be efficiently formulated as a semi-infinite global optimization problem. This kind of optimization problems are hard to solve because they involve an infinity of constraints (coming from a constraint on the torque ripple). The authors show in this paper that by using analytical models, a discretization method and a deterministic global optimization code COUENNE, this problem is efficiently tackled. Some numerical results show that the deterministic global solution of the design can be reached even if the step of discretization is small.

A novel approach of reliability-based topology optimization for continuum structures under interval uncertainties

2019 ◽  
Vol 25 (9) ◽  
pp. 1455-1474 ◽  
Author(s):  
Lei Wang ◽  
Haijun Xia ◽  
Yaowen Yang ◽  
Yiru Cai ◽  
Zhiping Qiu
Keyword(s):  
Topology Optimization ◽  
Reliability Index ◽  
Large Scale ◽  
Optimization Problems ◽  
Uncertainty Propagation ◽  
Content Type ◽  
Continuum Structures ◽  
Novel Approach ◽  
Design Variables ◽  
Interval Uncertainties

Purpose The purpose of this paper is to propose a novel non-probabilistic reliability-based topology optimization (NRBTO) method for continuum structural design under interval uncertainties of load and material parameters based on the technology of 3D printing or additive manufacturing. Design/methodology/approach First, the uncertainty quantification analysis is accomplished by interval Taylor extension to determine boundary rules of concerned displacement responses. Based on the interval interference theory, a novel reliability index, named as the optimization feature distance, is then introduced to construct non-probabilistic reliability constraints. To circumvent convergence difficulties in solving large-scale variable optimization problems, the gradient-based method of moving asymptotes is also used, in which the sensitivity expressions of the present reliability measurements with respect to design variables are deduced by combination of the adjoint vector scheme and interval mathematics. Findings The main findings of this paper should lie in that new non-probabilistic reliability index, i.e. the optimization feature distance which is defined and further incorporated in continuum topology optimization issues. Besides, a novel concurrent design strategy under consideration of macro-micro integration is presented by using the developed RBTO methodology. Originality/value Uncertainty propagation analysis based on the interval Taylor extension method is conducted. Novel reliability index of the optimization feature distance is defined. Expressions of the adjoint vectors between interval bounds of displacement responses and the relative density are deduced. New NRBTO method subjected to continuum structures is developed and further solved by MMA algorithms.

Multi-objective fatigue life optimization using Tabu Genetic Algorithms

2015 ◽  
Vol 6 (6) ◽  
pp. 677-688
Author(s):  
Kim C. Long ◽  
William S Duff ◽  
John W Labadie ◽  
Mitchell J Stansloski ◽  
Walajabad S Sampath ◽  
...  
Keyword(s):  
Tabu Search ◽  
Real World ◽  
Optimization Problem ◽  
High Efficiency ◽  
Optimization Problems ◽  
Superior Performance ◽  
Bench Mark ◽  
Reliability Optimization ◽  
Content Type ◽  
Multi Objective

Purpose – The purpose of this paper is to present a real world application of an innovative hybrid system reliability optimization algorithm combining Tabu search with an evolutionary algorithm (TSEA). This algorithm combines Tabu search and Genetic algorithm to provide a more efficient search method. Design/methodology/approach – The new algorithm is applied to an aircraft structure to optimize its reliability and maintain its structural integrity. For retrofitting the horizontal stabilizer under severe stall buffet conditions, a decision support system (DSS) is developed using the TSEA algorithm. This system solves a reliability optimization problem under cost and configuration constraints. The DSS contains three components: a graphical user interface, a database and several modules to provide the optimized retrofitting solutions. Findings – The authors found that the proposed algorithm performs much better than state-of-the-art methods such as Strength Pareto Evolutionary Algorithms on bench mark problems. In addition, the proposed TSEA method can be easily applied to complex real world optimization problem with superior performance. When the full combination of all input variables increases exponentially, the DSS become very efficient. Practical implications – This paper presents an application of the TSEA algorithm for solving nonlinear multi-objective reliability optimization problems embedded in a DSS. The solutions include where to install doublers and stiffeners. Compromise programming is used to rank all non-dominant solutions. Originality/value – The proposed hybrid algorithm (TSEA) assigns fitness based upon global dominance which ensures its convergence to the non-dominant front. The high efficiency of this algorithm came from using Tabu list to guidance the search to the Pareto-optimal solutions.

Topology Optimization Design of Bars Structure Based on SKO Method

2013 ◽  
Vol 394 ◽  
pp. 515-520 ◽  
Author(s):  
Wen Jun Li ◽  
Qi Cai Zhou ◽  
Xu Hui Zhang ◽  
Xiao Lei Xiong ◽  
Jiong Zhao
Keyword(s):  
Global Optimization ◽  
Topology Optimization ◽  
Optimization Design ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Topology Optimization Problem ◽  
Proposed Model ◽  
Continuum Structure ◽  
The Impact

There are less topology optimization methods for bars structure than those for continuum structure. Bionic intelligent method is a powerful way to solve the topology optimization problems of bars structure since it is of good global optimization capacity and convenient for numerical calculation. This article presents a SKO topology optimization model for bars structure based on SKO (Soft Kill Option) method derived from adaptive growth rules of trees, bones, etc. The model has been applied to solve the topology optimization problem of a space frame. It uses three optimization strategies, which are constant, decreasing and increasing material removed rate. The impact on the optimization processes and results of different strategies are discussed, and the validity of the proposed model is proved.

An Efficient Topology Optimization Method for Structures with Uniform Stress

2018 ◽  
Vol 15 (08) ◽  
pp. 1850073 ◽  
Author(s):  
Sheng Chu ◽  
Liang Gao ◽  
Mi Xiao
Keyword(s):  
Topology Optimization ◽  
Decision Problem ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Bisection Method ◽  
Uniform Stress ◽  
Topology Optimization Problem ◽  
Self Organized ◽  
Volume Minimization ◽  
Single Objective

This paper focuses on two kinds of bi-objective topology optimization problems with uniform-stress constraints: compliance-volume minimization and local frequency response–volume minimization problems. An adaptive volume constraint (AVC) algorithm based on an improved bisection method is proposed. Using this algorithm, the bi-objective uniform-stress-constrained topology optimization problem is transformed into a single-objective topology optimization problem and a volume-decision problem. The parametric level set method based on the compactly supported radial basis functions is employed to solve the single-objective problem, in which a self-organized acceleration scheme based on shape derivative and topological sensitivity is proposed to adaptively adjust the derivative of the objective function and the step length during the optimization. To solve the volume-decision problem, an improved bisection method is proposed. Numerical examples are tested to illustrate the feasibility and effectiveness of the self-organized acceleration scheme and the AVC algorithm based on the improved bisection method. An extended application to the bi-objective stress-constrained topology optimization of a structure with stress concentration is also presented.

scholarly journals Revisiting non-convexity in topology optimization of compliance minimization problems

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mohamed Abdelhamid ◽  
Aleksander Czekanski
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Global Optimum ◽  
Continuation Methods ◽  
Comprehensive Treatment ◽  
Mathematical Treatment ◽  
Content Type ◽  
Compliance Minimization ◽  
Intermediate Density ◽  
Filtering Techniques

PurposeThis is an attempt to better bridge the gap between the mathematical and the engineering/physical aspects of the topic. The authors trace the different sources of non-convexification in the context of topology optimization problems starting from domain discretization, passing through penalization for discreteness and effects of filtering methods, and end with a note on continuation methods.Design/methodology/approachStarting from the global optimum of the compliance minimization problem, the authors employ analytical tools to investigate how intermediate density penalization affects the convexity of the problem, the potential penalization-like effects of various filtering techniques, how continuation methods can be used to approach the global optimum and how the initial guess has some weight in determining the final optimum.FindingsThe non-convexification effects of the penalization of intermediate density elements simply overshadows any other type of non-convexification introduced into the problem, mainly due to its severity and locality. Continuation methods are strongly recommended to overcome the problem of local minima, albeit its step and convergence criteria are left to the user depending on the type of application.Originality/valueIn this article, the authors present a comprehensive treatment of the sources of non-convexity in density-based topology optimization problems, with a focus on linear elastic compliance minimization. The authors put special emphasis on the potential penalization-like effects of various filtering techniques through a detailed mathematical treatment.

An approach to cost-benefit analysis by competitive advantages with stochastic data

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mohammad Khodabakhshi ◽  
Mehdi Ahmadi
Keyword(s):  
Stochastic Optimization ◽  
Competitive Advantage ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Cost Benefit Analysis ◽  
Cost Benefit ◽  
Benefit Analysis ◽  
Content Type ◽  
Stochastic Data ◽  
Benefits And Costs

Purpose The paper aims to present an approach to cost-benefit analysis with stochastic data. Determining the type and the values of alternative’s factors are probably the most important issue in this approach. Therefore, in the proposed approach, a competitive advantage model was built to measure the values of alternative’s factors. Then, a satisfactory cost-benefit analysis model with random data was proposed to evaluate the alternatives. The cost-benefit analysis of each alternative was carried out to obtain the real and satisfactory cost-benefit of the decision-maker. Design/methodology/approach This paper is orientationally expressed as a mathematical problem in which the optimization problem needs to analyze the approach. This paper is written based on uncertainty linear optimization. Optimization under uncertainty refers to this branch of optimization where there are uncertainties involved in the data or the model and is popularly known as stochastic optimization problems. Findings As was seen in the purpose part, in this paper, an approach is presented to cost-benefit analysis by the use of competitive advantage with stochastic data. In this regards, a stochastic optimization problem to assess competitive advantage is proposed. This optimization problem recognizes the values of alternative’s factors which is the most important step in cost-benefit analysis. An optimization problem is proposed to cost benefit analysis, as well. Practical implications To investigate different aspects of the proposed approach, a case study with random data of 21 economic projects was considered. Originality/value Cost–benefit analysis is a systematic approach to estimating the strengths and weaknesses of alternatives used to determine options which provide the best approach to achieving benefits while preserving savings. Cost–benefit analysis is related to cost-effectiveness analysis. Benefits and costs are expressed in monetary terms and are adjusted for the time value of money; all flows of benefits and costs over time are expressed on a common basis in terms of their net present value, regardless of whether they are incurred at different times. As seen the paper using competitive advantage tries to determine the values of alternative’s factor. As competitive advantage model analyze the advantages and disadvantages of alternatives, this paper by the use of this idea tries to determine the costs and benefits. Two stochastic optimization problems in the middle of this approach are proposed, which assess competitive advantage and cost–benefit analysis, respectively.

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