Thermoelastic Structural Topology Optimization Based on Moving Morphable Components Framework

This study investigates structural topology optimization of thermoelastic structures considering two kinds of objectives ofminimumstructural compliance and elastic strain energy with a specified available volume constraint.To explicitly express the configuration evolution in the structural topology optimization under combination of mechanical and thermal load conditions,the moving morphable components(MMC)framework is adopted.Based on the characteristics of the MMC framework,the number of design variables can be reduced substantially.Corresponding optimization formulation in the MMC topology optimization framework and numerical solution procedures are developed for several numerical examples.Different optimization results are obtained with structural compliance and elastic strain energy as objectives,respectively,for thermoelastic problems.The effectiveness of the proposed optimization formulation is validated by the numerical examples.It is revealed that for the optimization design of the thermoelastic structural strength,the objective function with the minimum structural strain energy can achieve a better performance than that from structural compliance design.

Explicit Topology Optimization Design of Stiffened Plate Structures Based on the Moving Morphable Component(MMC)Method

This paper proposes an explicit method for topology optimization of stiffened plate structures.The present work is devoted to simultaneously optimizing stiffeners’shape,size and layout by seeking the optimal geometry parameters of a series of moving morphable components(MMC).The stiffeners with straight skeletons and the stiffeners with curved skeletons are considered to enhance the modeling and optimization capability of the current approach.All the stiffeners are represented under the Lagrangian-description framework in a fully explicit way,and the adaptive ground structure method,as well as dynamically updated plate/shell elements,is used to obtain optimized designs with more accurate analysis results.Compared with existing works,the proposed approach provides an explicit description of the structure.Thus,a stiffened plate structure with clear stiffener distribution and smooth geometric boundary can be obtained.Several numerical examples provided,including straight and curved stiffeners,hierarchical stiffeners,and a stiffened plate with a cutout,validate the effectiveness and applicability of the proposed approach.

Explicit Isogeometric Topology Optimization Method with Suitably Graded Truncated Hierarchical B-Spline

This work puts forward an explicit isogeometric topology optimization(ITO)method using moving morphable components(MMC),which takes the suitably graded truncated hierarchical B-Spline based isogeometric analysis as the solver of physical unknown(SGTHB-ITO-MMC).By applying properly basis graded constraints to the hierarchical mesh of truncated hierarchical B-splines(THB),the convergence and robustness of the SGTHB-ITOMMC are simultaneously improved and the tiny holes occurred in optimized structure are eliminated,due to the improved accuracy around the explicit structural boundaries.Moreover,an efficient computational method is developed for the topological description functions(TDF)ofMMC under the admissible hierarchicalmesh,which consists of reducing the dimensionality strategy for design space and the locally computing strategy for hierarchical mesh.We apply the above SGTHB-ITO-MMC with improved efficiency to a series of 2D and 3Dcompliance design problems.The numerical results show that the proposed SGTHB-ITO-MMC method outperforms the traditional THB-ITO-MMCmethod in terms of convergence rate and efficiency.Therefore,the proposed SGTHB-ITO-MMC is an effective way of solving topology optimization(TO)problems.

An Optimization Approach for Stiffener Layout of Composite Stiffened Panels Based on Moving Morphable Components(MMCs)

An explicit topology optimization method for the stiffener layout of composite stiffened panels is proposed based on moving morphable components(MMCs).The skin and stiffeners are considered as panels with different bending stiffnesses,with the use of equivalent stiffness method.Then the location and geometric properties of composite stiffeners are determined by several MMCs to perform topology optimization,which can greatly simplify the finite element model.With the objective of maximizing structural stiffness,several typical cases with various loading and boundary conditions are selected as numerical examples to demonstrate the proposed method.The numerical examples illustrate that the proposed method can provide clear stiffener layout and explicit geometry information,which is not limited within the framework of parameter and size optimization.The mechanical properties of composite stiffened panels can be fully enhanced.

Structural Optimization of Fiber-Reinforced Material Based on Moving Morphable Components (MMCs)

Fiber-reinforced composite materials have excellent specific stiffness,specific strength,and other properties,and have been increasingly widely used in the field of advanced structures.However,the design space dimensions of fiber-reinforced composite materials will expand explosively,bringing challenges to the efficient analysis and optimal design of structures.In this paper,the authors propose an explicit topology optimization method based on the moving morphable components for designing the fiber-reinforced material.We constrain the intersection area between components to guarantee the independence of each component and avoid the situation that one component is cut by other components.Adding the fiber orientation angle as a design variable,the method can optimize the structural layout and the fiber orientation angle concurrently under the given number of fiber layers and layer thickness.We use two classical examples to verify the feasibility and accuracy of the proposed method.The optimized results are in good agreement with the designs obtained by the 99-line code.The authors also popularize the proposed method to engineering structure.The results manifest that the proposed method has great value in engineering application.

Geographical classification of Nanfeng mandarin by near infrared spectroscopy coupled with chemometrics methods

Near infrared spectroscopy(NIRS),coupled with principal component analysis and wavelength selection techniques,has been sed to develop a robust and reliable reduced-spectrum classifi-cation model for determining the geographical origins of Nanfeng mandarins.The application of the changeable size moving window principal component analysis(CSMWPCA)provided a notably improved lassification model,with correct classification rates of 92.00%,100.00%,90.00%,100.00%,100.00%,100.00%and 100.00%for Fujian,Guangxi,Hunan,Baishe,Baofeng,Qiawan,Sanxi samples,respectively,as well as,a total dassification rate of 97.52%in the wavelength range from 1007 to 1296 nm.To test and apply the proposed method,the procedure was applied to the analysis of 59 samples in an independent test set.Good identification results(correct rate of 96.61%)were also received.The improvement achieved by the application of CSMWPCA method was particularly remarkable when taking the low complexities of the final model(290 variables)into account.The results of the study showed the great potential of NIRS as a fast,nondestructive and environmentally acceptable method for the rapid and reliable determination for geographical classifcation of Nanfeng mandarins.

Self-consistent Clustering Analysis-Based Moving Morphable Component(SMMC)Method for Multiscale Topology Optimization

Current multiscale topology optimization restricts the solution space by enforcing the use of a few repetitive microstructures that are predetermined,and thus lack the ability for structural concerns like buckling strength,robustness,and multi-functionality.Therefore,in this paper,a new multiscale concurrent topology optimization design,referred to as the self-consistent analysis-based moving morphable component(SMMC)method,is proposed.Compared with the conventional moving morphable component method,the proposed method seeks to optimize both material and structure simultaneously by explicitly designing both macrostructure and representative volume element(RVE)-level microstructures.Numerical examples with transducer design requirements are provided to demonstrate the superiority of the SMMC method in comparison to traditional methods.The proposed method has broad impact in areas of integrated industrial manufacturing design:to solve for the optimized macro and microstructures under the objective function and constraints,to calculate the structural response efficiently using a reduced-order model:self-consistent analysis,and to link the SMMC method to manufacturing(industrial manufacturing or additive manufacturing)based on the design requirements and application areas.

Topology optimization of plate structures using plate element-based moving morphable component(MMC)approach

A topology optimization approach for designing the layout of plate structures is proposed in this article.In this approach,structural mechanical behavior is analyzed under the framework of Kirchhoff plate theory,and structural topology is described explicitly by a set of moving morphable components.Compared to the existing treatments where structural topology is generally described in an implicit manner,the adopted explicit geometry/layout description has demonstrated its advantages on several aspects.Firstly,the number of design variables is reduced substantially.Secondly,the obtained optimized designs are pure black-and-white and contain no gray regions.Besides,numerical experiments show that the use of Kirchhoff plate element helps save 95-99%computational time,compared with traditional treatments where solid elements are used for finite element analysis.Moreover the accuracy of the proposed method is also validated through a comparison with the corresponding theoretical solutions.Several numerical examples are also provided to demonstrate the effectiveness of the proposed approach.

Explicit Topology Optimization with Moving Morphable Component(MMC)Introduction Mechanism

In this article,an explicit topology optimization approach with components-growing ability is proposed under the moving morphable component(MMC)framework.In this approach,the shape and topology layout of structures are explicitly optimized by growth evolution of moving morphable components.To this end,a competition criterion is developed to optimize the structural layout from two options:adding several new components or changing the current layout.In addition,some numerical technqiues are also developed to preserve the stability of the iterative process.The present topology optimization approach allows rational generation of new components and does not require a specific distribution of components in the initial design,which is compulsory for the conventional MMC method.Three numerical examples are provided to illustrate the effectiveness of the proposed method.The optimization results indicate that the proposed method does have the potential to improve the existing MMC-based explicit topology optimization framework by eliminating the initial design dependency of optimal solutions.

A meshless moving morphable component-based method for structural topology optimization without weak material

Traditional topology optimization methods often introduce weak artificial material to mimic voids to avoid the singularity of the global stiffness matrix and carry out topology optimization with a fixed finite element(FE)mesh.This treatment,however,may not only increase the computational cost for structural analysis but also lead to unfavorable numerical instabilities,especially when large deformations and dynamic/buckling behaviors are involved.In the present work,a new meshless moving morphable component-based method(ML-MMC),which structural analysis is carried out only on the solid region occupied by components,is proposed.In this approach,the coupling of discrete components is achieved through the adaptively constructed influence domain of the meshless shape function.Therefore,the singularity problem of the stiffness matrix can be naturally avoided without introducing weak artificial material.Compared with traditional methods,the number of degrees of freedoms(DOFs)can be reduced substantially under this treatment.The effectiveness of the proposed approach is also illustrated by some representative examples.

Topology Optimization Considering Steady-State Structural Dynamic Responses via Moving Morphable Component(MMC)Approach

This work presents a moving morphable component(MMC)-based framework for solving topology optimization problems considering both single-frequency and band-frequency steady-state structural dynamic responses.In this work,a set of morphable components are introduced as the basic building blocks for topology optimization,and the optimized structural layout can be found by optimizing the parameters characterizing the locations and geometries of the components explicitly.The degree of freedom(DOF)elimination technique is also employed to delete unnecessary DOFs at each iteration.Since the proposed approach solves the corresponding optimization problems in an explicit way,some challenging issues(e.g.,the large computational burden related to finite element analysis and sensitivity analysis,the localized eigenmodes in low material density regions,and the impact of excitation frequency on the optimization process)associated with the traditional approaches can be circumvented naturally.Numerical results show that the proposed approach is effective for solving topology optimization problems involving structural dynamic behaviors,especially when high-frequency responses are considered.

Topology Optimization of Acoustic-Mechanical Structures for Enhancing Sound Quality

Sound quality is one of the essential criteria for measuring the acoustic performance of acoustic devices.In contrast to the optimization of sound characteristics,both the quantitative description of sound quality and the numerical instability that may occur during optimization need to be investigated.In the present work,an explicit topology optimization approach is proposed to enhance the sound quality of acoustic-mechanical structures,where the sound quality is described,resorting to frequency response within a specified frequency band.To this end,the moving morphable component(MMC)-based approach is adopted to achieve the explicit topology design,and the mixed finite element method is introduced to evaluate the sound quality.With the use of the explicit description of MMC,the acoustic-structure boundary can be captured accurately,which is important for acoustic response analysis.Moreover,a regularization topology optimization formulation is also developed to avoid the numerical issues produced in some special frequency bands.Numerical examples demonstrate the effectiveness of the proposed approach in improving sound quality performance.

Hybrid algorithms for handling the numerical noise in topology optimization

This paper presents new hybrid methods for the identification of optimal topologies by combining the teaching-learning based optimization(TLBO)and the method of moving asymptotes(MMA).The topology optimization problem is parameterizing with a low dimensional explicit method called moving morphable components(MMC),to make the use of evolutionary algorithms more efficient.Gradient-based solvers have good performance in solving large-scale topology optimization problems.However,in unconventional cases same as crashworthiness design in which there is numerical noise in the gradient information,the uses of these algorithms are unsuitable.The standard evolutionary algorithms can solve such problems since they don’t need gradient information.However,they have a high computational cost.This paper is based upon the idea of combining metaheuristics with mathematical programming to handle the probable noises and have faster convergence speed.Due to the ease of computations,the compliance minimization problem is considered as the case study and the artificial noise is added in gradient information.