Because of descriptive nonlinearity and computational inefficiency,topology optimization with fatigue life under aperiodic loads has developed slowly.A fatigue constraint topology optimization method based on bidirect...Because of descriptive nonlinearity and computational inefficiency,topology optimization with fatigue life under aperiodic loads has developed slowly.A fatigue constraint topology optimization method based on bidirectional evolutionary structural optimization(BESO)under an aperiodic load is proposed in this paper.In viewof the severe nonlinearity of fatigue damagewith respect to design variables,effective stress cycles are extracted through transient dynamic analysis.Based on the Miner cumulative damage theory and life requirements,a fatigue constraint is first quantified and then transformed into a stress problem.Then,a normalized termination criterion is proposed by approximatemaximum stress measured by global stress using a P-normaggregation function.Finally,optimization examples show that the proposed algorithm can not only meet the requirements of fatigue life but also obtain a reasonable configuration.展开更多
Stress-based topology optimization is one of the most concerns of structural optimization and receives much attention in a wide range of engineering designs.To solve the inherent issues of stress-based topology optimi...Stress-based topology optimization is one of the most concerns of structural optimization and receives much attention in a wide range of engineering designs.To solve the inherent issues of stress-based topology optimization,many schemes are added to the conventional bi-directional evolutionary structural optimization(BESO)method in the previous studies.However,these schemes degrade the generality of BESO and increase the computational cost.This study proposes an improved topology optimization method for the continuum structures considering stress minimization in the framework of the conventional BESO method.A global stress measure constructed by p-norm function is treated as the objective function.To stabilize the optimization process,both qp-relaxation and sensitivity weight scheme are introduced.Design variables are updated by the conventional BESO method.Several 2D and 3D examples are used to demonstrate the validity of the proposed method.The results show that the optimization process can be stabilized by qp-relaxation.The value of q and p are crucial to reasonable solutions.The proposed sensitivity weight scheme further stabilizes the optimization process and evenly distributes the stress field.The computational efficiency of the proposed method is higher than the previous methods because it keeps the generality of BESO and does not need additional schemes.展开更多
In this paper,a new algorithm combining the features of bi-direction evolutionary structural optimization(BESO)and reinforcement learning(RL)is proposed for continuum structural topology optimization(STO).In contrast ...In this paper,a new algorithm combining the features of bi-direction evolutionary structural optimization(BESO)and reinforcement learning(RL)is proposed for continuum structural topology optimization(STO).In contrast to conventional approaches which only generate a certain quasi-optimal solution,the goal of the combined method is to provide more quasi-optimal solutions for designers such as the idea of generative design.Two key components were adopted.First,besides sensitivity,value function updated by Monte-Carlo reinforcement learning was utilized to measure the importance of each element,which made the solving process convergent and closer to the optimum.Second,ε-greedy policy added a random perturbation to the main search direction so as to extend the search ability.Finally,the quality and diversity of solutions could be guaranteed by controlling the value of compliance as well as Intersection-over-Union(IoU).Results of several 2D and 3D compliance minimization problems,including a geometrically nonlinear case,show that the combined method is capable of generating a group of good and different solutions that satisfy various possible requirements in engineering design within acceptable computation cost.展开更多
Natural frequency and dynamic stiffness under transient loading are two key performances for structural design related to automotive,aviation and construction industries.This article aims to tackle the multi-objective...Natural frequency and dynamic stiffness under transient loading are two key performances for structural design related to automotive,aviation and construction industries.This article aims to tackle the multi-objective topological optimization problem considering dynamic stiffness and natural frequency using modified version of bi-directional evolutionary structural optimization(BESO).The conventional BESO is provided with constant evolutionary volume ratio(EVR),whereas low EVR greatly retards the optimization process and high EVR improperly removes the efficient elements.To address the issue,the modified BESO with variable EVR is introduced.To compromise the natural frequency and the dynamic stiffness,a weighting scheme of sensitivity numbers is employed to form the Pareto solution space.Several numerical examples demonstrate that the optimal solutions obtained from the modified BESO method have good agreement with those from the classic BESO method.Most importantly,the dynamic removal strategy with the variable EVR sharply springs up the optimization process.Therefore,it is concluded that the modified BESO method with variable EVR can solve structural design problems using multi-objective optimization.展开更多
A smooth bidirectional evolutionary structural optimization(SBESO),as a bidirectional version of SESO is proposed to solve the topological optimization of vibrating continuum structures for natural frequencies and dyn...A smooth bidirectional evolutionary structural optimization(SBESO),as a bidirectional version of SESO is proposed to solve the topological optimization of vibrating continuum structures for natural frequencies and dynamic compliance under the transient load.A weighted function is introduced to regulate the mass and stiffness matrix of an element,which has the inefficient element gradually removed from the design domain as if it were undergoing damage.Aiming at maximizing the natural frequency of a structure,the frequency optimization formulation is proposed using the SBESO technique.The effects of various weight functions including constant,linear and sine functions on structural optimization are compared.With the equivalent static load(ESL)method,the dynamic stiffness optimization of a structure is formulated by the SBESO technique.Numerical examples show that compared with the classic BESO method,the SBESO method can efficiently suppress the excessive element deletion by adjusting the element deletion rate and weight function.It is also found that the proposed SBESO technique can obtain an efficient configuration and smooth boundary and demonstrate the advantages over the classic BESO technique.展开更多
Live bone inherently responds to applied mechanical stimulus by altering its internal tissue composition and ultimately biomechanical properties, structure and function. The final formation may structurally appear inf...Live bone inherently responds to applied mechanical stimulus by altering its internal tissue composition and ultimately biomechanical properties, structure and function. The final formation may structurally appear inferior by design but complete by function. To understand the loading response, this paper numerically investigated structural remodeling of mature sheep femur using evolutionary structural optimization method (ESO). Femur images from Computed Tomography scanner were used to determine the elastic modulus variation and subsequently construct finite element model of the femur with stiffest elasticity measured. Major muscle forces on dominant phases of healthy sheep gait were imposed on the femur under static mode. ESO was applied to progressively alter the remodeling of numerically simulated femur from its initial to final design by iteratively removing elements with low strain energy density (SED). The computations were repeated with two different mesh sizes to test the convergence. The elements within the medullary canal had low SEDs and therefore were removed during the optimization. The SEDs in the remaining elements varied with angle around the circumference of the shaft. Those elements with low SED were inefficient in supporting the load and thus fundamentally explained how bone remodels itself with less stiff inferior tissue to meet load demand. This was in line with the Wolff’s law of transformation of bone. Tissue growth and remodeling process was found to shape the sheep femur to a mechanically optimized structure and this was initiated by SED in macro-scale according to traditional principle of Wolff’s law.展开更多
The damping material optimal placement for the structure with damping layer is studied based on evolutionary structural optimization (ESO) to maximize modal loss factors. A mathematical model is constructed with the o...The damping material optimal placement for the structure with damping layer is studied based on evolutionary structural optimization (ESO) to maximize modal loss factors. A mathematical model is constructed with the objective function defined as the maximum of modal loss factors of the structure and design constraints function defined as volume fraction of damping material. The optimal placement is found. Several examples are presented for verification. The results demonstrate that the method based on ESO is effective in solving the topology optimization of the structure with unconstrained damping layer and constrained damping layer. This optimization method suits for free and constrained damping structures.展开更多
Multi-objective optimal evolutionary algorithms (MOEAs) are a kind of new effective algorithms to solve Multi-objective optimal problem (MOP). Because ranking, a method which is used by most MOEAs to solve MOP, has so...Multi-objective optimal evolutionary algorithms (MOEAs) are a kind of new effective algorithms to solve Multi-objective optimal problem (MOP). Because ranking, a method which is used by most MOEAs to solve MOP, has some shortcoming s, in this paper, we proposed a new method using tree structure to express the relationship of solutions. Experiments prove that the method can reach the Pare-to front, retain the diversity of the population, and use less time.展开更多
Search-based statistical structural testing(SBSST)is a promising technique that uses automated search to construct input distributions for statistical structural testing.It has been proved that a simple search algorit...Search-based statistical structural testing(SBSST)is a promising technique that uses automated search to construct input distributions for statistical structural testing.It has been proved that a simple search algorithm,for example,the hill-climber is able to optimize an input distribution.However,due to the noisy fitness estimation of the minimum triggering probability among all cover elements(Tri-Low-Bound),the existing approach does not show a satisfactory efficiency.Constructing input distributions to satisfy the Tri-Low-Bound criterion requires an extensive computation time.Tri-Low-Bound is considered a strong criterion,and it is demonstrated to sustain a high fault-detecting ability.This article tries to answer the following question:if we use a relaxed constraint that significantly reduces the time consumption on search,can the optimized input distribution still be effective in faultdetecting ability?In this article,we propose a type of criterion called fairnessenhanced-sum-of-triggering-probability(p-L1-Max).The criterion utilizes the sum of triggering probabilities as the fitness value and leverages a parameter p to adjust the uniformness of test data generation.We conducted extensive experiments to compare the computation time and the fault-detecting ability between the two criteria.The result shows that the 1.0-L1-Max criterion has the highest efficiency,and it is more practical to use than the Tri-Low-Bound criterion.To measure a criterion’s fault-detecting ability,we introduce a definition of expected faults found in the effective test set size region.To measure the effective test set size region,we present a theoretical analysis of the expected faults found with respect to various test set sizes and use the uniform distribution as a baseline to derive the effective test set size region’s definition.展开更多
Weight reduction has attracted much attention among ship designers and ship owners.In the present work,based on an improved bi-directional evolutionary structural optimization(BESO) method and surrogate model method,w...Weight reduction has attracted much attention among ship designers and ship owners.In the present work,based on an improved bi-directional evolutionary structural optimization(BESO) method and surrogate model method,we propose a hybrid optimization method for the structural design optimization of beam-plate structures,which covers three optimization levels:dimension optimization,topology optimization and section optimization.The objective of the proposed optimization method is to minimize the weight of design object under a group of constraints.The kernel optimization procedure(KOP) uses BESO to obtain the optimal topology from a ground structure.To deal with beam-plate structures,the traditional BESO method is improved by using cubic box as the unit cell instead of solid unit to construct periodic lattice structure.In the first optimization level,a series of ground structures are generated based on different dimensional parameter combinations,the KOP is performed to all the ground structures,the response surface model of optimal objective values and dimension parameters is created,and then the optimal dimension parameters can be obtained.In the second optimization level,the optimal topology is obtained by using the KOP according to the optimal dimension parameters.In the third optimization level,response surface method(RSM) is used to determine the section parameters.The proposed method is applied to a hatch cover structure design.The locations and shapes of all the structural members are determined from an oversized ground structure.The results show that the proposed method leads to a greater weight saving,compared with the original design and genetic algorithm(GA) based optimization results.展开更多
The continuum structural-acoustic topology optimization with external loading is investigated herein. Finite element method （FEM） is used to obtain the structural frequency response and boundary element method （BEM...The continuum structural-acoustic topology optimization with external loading is investigated herein. Finite element method （FEM） is used to obtain the structural frequency response and boundary element method （BEM） is adopted to perform exterior acoustic radiation analysis. The evolutionary structural optimization （ESO） is served as an optimization method in structural-acoustic radiation topology analysis. The acoustic radiation optimization of a plate under harmonic excitation is given for example. The numerical results show that using ESO solution to analyze structural-acoustic topology optimization is feasible and effective.展开更多
基金Chinese National Natural Science Foundation(No.51890881)Science and Technology Project of Hebei Education Department(Nos.ZD2020156,QN2018228).
文摘Because of descriptive nonlinearity and computational inefficiency,topology optimization with fatigue life under aperiodic loads has developed slowly.A fatigue constraint topology optimization method based on bidirectional evolutionary structural optimization(BESO)under an aperiodic load is proposed in this paper.In viewof the severe nonlinearity of fatigue damagewith respect to design variables,effective stress cycles are extracted through transient dynamic analysis.Based on the Miner cumulative damage theory and life requirements,a fatigue constraint is first quantified and then transformed into a stress problem.Then,a normalized termination criterion is proposed by approximatemaximum stress measured by global stress using a P-normaggregation function.Finally,optimization examples show that the proposed algorithm can not only meet the requirements of fatigue life but also obtain a reasonable configuration.
基金supported by National Natural Science Foundation of China[Grant No.51575399]the National Key Research and Development Program of China[Grant No.2016YFB0101602].
文摘Stress-based topology optimization is one of the most concerns of structural optimization and receives much attention in a wide range of engineering designs.To solve the inherent issues of stress-based topology optimization,many schemes are added to the conventional bi-directional evolutionary structural optimization(BESO)method in the previous studies.However,these schemes degrade the generality of BESO and increase the computational cost.This study proposes an improved topology optimization method for the continuum structures considering stress minimization in the framework of the conventional BESO method.A global stress measure constructed by p-norm function is treated as the objective function.To stabilize the optimization process,both qp-relaxation and sensitivity weight scheme are introduced.Design variables are updated by the conventional BESO method.Several 2D and 3D examples are used to demonstrate the validity of the proposed method.The results show that the optimization process can be stabilized by qp-relaxation.The value of q and p are crucial to reasonable solutions.The proposed sensitivity weight scheme further stabilizes the optimization process and evenly distributes the stress field.The computational efficiency of the proposed method is higher than the previous methods because it keeps the generality of BESO and does not need additional schemes.
文摘In this paper,a new algorithm combining the features of bi-direction evolutionary structural optimization(BESO)and reinforcement learning(RL)is proposed for continuum structural topology optimization(STO).In contrast to conventional approaches which only generate a certain quasi-optimal solution,the goal of the combined method is to provide more quasi-optimal solutions for designers such as the idea of generative design.Two key components were adopted.First,besides sensitivity,value function updated by Monte-Carlo reinforcement learning was utilized to measure the importance of each element,which made the solving process convergent and closer to the optimum.Second,ε-greedy policy added a random perturbation to the main search direction so as to extend the search ability.Finally,the quality and diversity of solutions could be guaranteed by controlling the value of compliance as well as Intersection-over-Union(IoU).Results of several 2D and 3D compliance minimization problems,including a geometrically nonlinear case,show that the combined method is capable of generating a group of good and different solutions that satisfy various possible requirements in engineering design within acceptable computation cost.
基金funded by the National Natural Science Foundation of China(Grant No.51505096)the Natural Science Foundation of Heilongjiang Province(Grant No.LH2020E064).
文摘Natural frequency and dynamic stiffness under transient loading are two key performances for structural design related to automotive,aviation and construction industries.This article aims to tackle the multi-objective topological optimization problem considering dynamic stiffness and natural frequency using modified version of bi-directional evolutionary structural optimization(BESO).The conventional BESO is provided with constant evolutionary volume ratio(EVR),whereas low EVR greatly retards the optimization process and high EVR improperly removes the efficient elements.To address the issue,the modified BESO with variable EVR is introduced.To compromise the natural frequency and the dynamic stiffness,a weighting scheme of sensitivity numbers is employed to form the Pareto solution space.Several numerical examples demonstrate that the optimal solutions obtained from the modified BESO method have good agreement with those from the classic BESO method.Most importantly,the dynamic removal strategy with the variable EVR sharply springs up the optimization process.Therefore,it is concluded that the modified BESO method with variable EVR can solve structural design problems using multi-objective optimization.
基金supported by the National Natural Science Foundation of China (Grant No.51505096)the Natural Science Foundation of Heilongjiang Province (Grant No.LH2020E064).
文摘A smooth bidirectional evolutionary structural optimization(SBESO),as a bidirectional version of SESO is proposed to solve the topological optimization of vibrating continuum structures for natural frequencies and dynamic compliance under the transient load.A weighted function is introduced to regulate the mass and stiffness matrix of an element,which has the inefficient element gradually removed from the design domain as if it were undergoing damage.Aiming at maximizing the natural frequency of a structure,the frequency optimization formulation is proposed using the SBESO technique.The effects of various weight functions including constant,linear and sine functions on structural optimization are compared.With the equivalent static load(ESL)method,the dynamic stiffness optimization of a structure is formulated by the SBESO technique.Numerical examples show that compared with the classic BESO method,the SBESO method can efficiently suppress the excessive element deletion by adjusting the element deletion rate and weight function.It is also found that the proposed SBESO technique can obtain an efficient configuration and smooth boundary and demonstrate the advantages over the classic BESO technique.
文摘Live bone inherently responds to applied mechanical stimulus by altering its internal tissue composition and ultimately biomechanical properties, structure and function. The final formation may structurally appear inferior by design but complete by function. To understand the loading response, this paper numerically investigated structural remodeling of mature sheep femur using evolutionary structural optimization method (ESO). Femur images from Computed Tomography scanner were used to determine the elastic modulus variation and subsequently construct finite element model of the femur with stiffest elasticity measured. Major muscle forces on dominant phases of healthy sheep gait were imposed on the femur under static mode. ESO was applied to progressively alter the remodeling of numerically simulated femur from its initial to final design by iteratively removing elements with low strain energy density (SED). The computations were repeated with two different mesh sizes to test the convergence. The elements within the medullary canal had low SEDs and therefore were removed during the optimization. The SEDs in the remaining elements varied with angle around the circumference of the shaft. Those elements with low SED were inefficient in supporting the load and thus fundamentally explained how bone remodels itself with less stiff inferior tissue to meet load demand. This was in line with the Wolff’s law of transformation of bone. Tissue growth and remodeling process was found to shape the sheep femur to a mechanically optimized structure and this was initiated by SED in macro-scale according to traditional principle of Wolff’s law.
基金Science and Technology Foundation of China Academy of Engineering Physics (20060321)
文摘The damping material optimal placement for the structure with damping layer is studied based on evolutionary structural optimization (ESO) to maximize modal loss factors. A mathematical model is constructed with the objective function defined as the maximum of modal loss factors of the structure and design constraints function defined as volume fraction of damping material. The optimal placement is found. Several examples are presented for verification. The results demonstrate that the method based on ESO is effective in solving the topology optimization of the structure with unconstrained damping layer and constrained damping layer. This optimization method suits for free and constrained damping structures.
基金Supported by the National Natural Science Foundation of China(60073043,70071042,60133010)
文摘Multi-objective optimal evolutionary algorithms (MOEAs) are a kind of new effective algorithms to solve Multi-objective optimal problem (MOP). Because ranking, a method which is used by most MOEAs to solve MOP, has some shortcoming s, in this paper, we proposed a new method using tree structure to express the relationship of solutions. Experiments prove that the method can reach the Pare-to front, retain the diversity of the population, and use less time.
基金Publication of this article in an open access journal was funded by the Portland State University Library’s Open Access Fund.
文摘Search-based statistical structural testing(SBSST)is a promising technique that uses automated search to construct input distributions for statistical structural testing.It has been proved that a simple search algorithm,for example,the hill-climber is able to optimize an input distribution.However,due to the noisy fitness estimation of the minimum triggering probability among all cover elements(Tri-Low-Bound),the existing approach does not show a satisfactory efficiency.Constructing input distributions to satisfy the Tri-Low-Bound criterion requires an extensive computation time.Tri-Low-Bound is considered a strong criterion,and it is demonstrated to sustain a high fault-detecting ability.This article tries to answer the following question:if we use a relaxed constraint that significantly reduces the time consumption on search,can the optimized input distribution still be effective in faultdetecting ability?In this article,we propose a type of criterion called fairnessenhanced-sum-of-triggering-probability(p-L1-Max).The criterion utilizes the sum of triggering probabilities as the fitness value and leverages a parameter p to adjust the uniformness of test data generation.We conducted extensive experiments to compare the computation time and the fault-detecting ability between the two criteria.The result shows that the 1.0-L1-Max criterion has the highest efficiency,and it is more practical to use than the Tri-Low-Bound criterion.To measure a criterion’s fault-detecting ability,we introduce a definition of expected faults found in the effective test set size region.To measure the effective test set size region,we present a theoretical analysis of the expected faults found with respect to various test set sizes and use the uniform distribution as a baseline to derive the effective test set size region’s definition.
基金the National Natural Science Foundation of China(No.51509033)
文摘Weight reduction has attracted much attention among ship designers and ship owners.In the present work,based on an improved bi-directional evolutionary structural optimization(BESO) method and surrogate model method,we propose a hybrid optimization method for the structural design optimization of beam-plate structures,which covers three optimization levels:dimension optimization,topology optimization and section optimization.The objective of the proposed optimization method is to minimize the weight of design object under a group of constraints.The kernel optimization procedure(KOP) uses BESO to obtain the optimal topology from a ground structure.To deal with beam-plate structures,the traditional BESO method is improved by using cubic box as the unit cell instead of solid unit to construct periodic lattice structure.In the first optimization level,a series of ground structures are generated based on different dimensional parameter combinations,the KOP is performed to all the ground structures,the response surface model of optimal objective values and dimension parameters is created,and then the optimal dimension parameters can be obtained.In the second optimization level,the optimal topology is obtained by using the KOP according to the optimal dimension parameters.In the third optimization level,response surface method(RSM) is used to determine the section parameters.The proposed method is applied to a hatch cover structure design.The locations and shapes of all the structural members are determined from an oversized ground structure.The results show that the proposed method leads to a greater weight saving,compared with the original design and genetic algorithm(GA) based optimization results.
文摘The continuum structural-acoustic topology optimization with external loading is investigated herein. Finite element method （FEM） is used to obtain the structural frequency response and boundary element method （BEM） is adopted to perform exterior acoustic radiation analysis. The evolutionary structural optimization （ESO） is served as an optimization method in structural-acoustic radiation topology analysis. The acoustic radiation optimization of a plate under harmonic excitation is given for example. The numerical results show that using ESO solution to analyze structural-acoustic topology optimization is feasible and effective.
