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How to realize the switching between various topology optimization approaches such as SIMP and moving morphable component (MMC) method, is a crucial challenge in the field of structural design. In this article, a robust conversion framework is proposed to convert a pixel‐type topology optimization result to MMC representation. Based on the sparse optimization approach, the framework enables the determination of the minimum number of components with a specified shape error. This method provides an efficient bridge for these two types of geometric descriptions, and promotes the free switching between the topology optimization frameworks with pixel‐based and MMC‐based design domains. The proposed procedure contains a pre‐processing of resolution improvement, symmetry axis extraction with sparse optimization, and variational shape approximation. Two practical applications are demonstrated using the proposed framework. First, it can be applied to the intermediate results of SIMP, to achieve faster optimization convergence. Furthermore, a stress‐based shape optimization approach can be applied to the obtained MMCs, and novel progressive continuity constraints are also introduced to maintain boundary continuity. Several examples demonstrate advantages of the proposed framework. [ABSTRACT FROM AUTHOR]

An explicit topology optimization-based design paradigm is proposed for the design of photonic topological crystalline insulators (TCIs). To strictly guarantee the topological property, rational engineering of symmetry-indicators is carried out by mathematical programming, which simultaneously maximizes the width of nontrivial topological band gaps and achieves the desired quantized bulk polarization. Our approach is successfully applied to design photonic TCIs with time-reversal symmetry in two-dimensional point groups, higher-order magnetic TCIs, and higher-order photonic TCIs. This methodology paves the way for inverse design of optimized photonic/phononic, multiphysics, and multifunctional three-dimensional TCIs. [ABSTRACT FROM AUTHOR]

This article presents an explicit topology optimization approach using boundary element method based moving morphable void (MMV). Structural analysis in the conventional MMV approach is performed on a fixed mesh over the entire design domain. However, in the proposed method structural boundaries are described using B‐splines and discretized with boundary elements making explicit representation of the boundaries possible. In this regard, the proposed approach has following merits: a) the use of weak material, which is often adopted to mimic voids can be completely avoided; b) exact and explicit description of voids in MMV allows the capture of tiny structural features in a robust and effective way; c) numerical instabilities stemming from the use of fixed meshes can be naturally avoided. Several numerical examples are provided to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Summary: This article proposes an efficient approach for solving three‐dimensional (3D) topology optimization problem. In this approach, the number of design variables in optimization as well as the number of degrees of freedom in structural response analysis can be reduced significantly. This is accomplished through the use of scaled boundary finite element method (SBFEM) for structural analysis under the moving morphable component (MMC)‐based topology optimization framework. In the proposed method, accurate response analysis in the boundary region dictates the accuracy of the entire analysis. In this regard, an adaptive refinement scheme is developed where the refined mesh is only used in the boundary region while relating coarse mesh is used away from the boundary. Numerical examples demonstrate that the computational efficiency of 3D topology optimization can be improved effectively by the proposed approach. [ABSTRACT FROM AUTHOR]

One of the challenging issues in additive manufacturing (AM) oriented topology optimization is how to design structures that are self-supportive in a manufacture process without introducing additional supporting materials. In the present contribution, it is intended to resolve this problem under an explicit topology optimization framework where optimal structural topology can be found by optimizing a set of explicit geometry parameters. Two solution approaches established based on the Moving Morphable Components (MMC) and Moving Morphable Voids (MMV) frameworks, respectively, are proposed and some theoretical issues associated with AM oriented topology optimization are also analyzed. Numerical examples provided demonstrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In the present paper, an explicit topology optimization approach based on moving morphable components (MMC) with curved skeletons (central lines) is proposed. This is achieved by constructing the topology description function (TDF) which describes the geometry of a structural component with curved skeleton explicitly in an elegant way. The proposed method has very flexible geometry modeling capability and represents a substantial improvement of the geometry modeling capability of existing MMC based approaches. Numerical examples demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract: The present paper aims to address a long-standing and challenging problem in structural topology optimization: explicit feature control of the optimal topology. The basic idea is to resort to the level set solution framework and impose constraints on the extreme values of the signed distance level set function used for describing the topology of the structure. Numerical examples are also presented and discussed to illustrate the effectiveness of the proposed approach. [Copyright &y& Elsevier]

Abstract: Considering stress constraints in structural topology optimization is very important from both theoretical and application perspectives. Most of the corresponding studies in literature, however, are only focused on the problems involving single phase homogenous materials. In the present paper, stress-constrained topology optimization of continuum structures involving multi-phase heterogeneous materials is investigated. A level-set based variational consistent solution framework is developed. Numerical examples are also presented and discussed to illustrate the effectiveness of the proposed approach. [Copyright &y& Elsevier]

SUMMARY Although the phenomenon of stress concentration is of paramount importance to engineers when they are designing load-carrying structures, stiffness is often used as the solely concerned objective or constraint functional in the studies of optimal topology design of continuum structures. Sometimes this will lead to optimal designs with severe stress concentrations that may be highly responsible for the fracture, creep, and fatigue of structures. The aim of the present work is to develop some effective numerical techniques for designing stiff structures with less stress concentrations. This is achieved by introducing some specific stress measures, which are sensitive to the existence of high local stresses, in the problem formulation and resolving the corresponding optimization problem numerically in a level set framework. Our study indicates that with use of the proposed numerical schemes, some intrinsic difficulties in stress-related topology optimization of continuum structures can be overcome in a natural way. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: In classical deterministic topology optimization, the effect of the possible boundary variations on the performance of the structure is not taken into account, which may lead to designs that are very sensitive to manufacturing errors. As a consequence, the performance of the real structure may be far from optimal and even not meet the design requirements. In the present paper, structural topology optimization considering the uncertainty of boundary variations is considered via level set approach. In order to make the optimal designs less sensitive to the possible boundary variations, we choose the compliance and fundamental frequency of structure enduring the worst case perturbation as the objective function for ensuring the robustness of the optimal solution. With use of the Schwarz inequality, the original Bi-level optimization problem is transformed to a single-level optimization problem, which can be solved efficiently. Numerical examples demonstrate the effectiveness of the proposed approach. [Copyright &y& Elsevier]

Abstract: Considering stress-related objective or constraint functions in structural topology optimization problems is very important from both theoretical and application perspectives. It has been known, however, that stress-related topology optimization problem is challenging since several difficulties must be overcome in order to solve it effectively. Traditionally, SIMP (Solid Isotropic Material with Penalization) method was often employed to tackle it. Although some remarkable achievements have been made with this computational framework, there are still some issues requiring further explorations. In the present work, stress-related topology optimization problems are investigated via a level set-based approach, which is a different topology optimization framework from SIMP. Numerical examples show that under appropriate problem formulations, level set approach is a promising tool for stress-related topology optimization problems. [Copyright &y& Elsevier]

The present paper introduces a hybrid explicit–implicit topology optimization method for shell-infill composite structure design. The proposed approach effectively combines the advantages of the explicit Moving Morphable Component (MMC) method, which describes structural topology only using a set of geometric parameters, and the implicit Solid Isotropic Material with Penalization (SIMP) method, which offers greater design freedom for characterizing the structural features. Compared to the existing methods for shell-infill structure design, the proposed approach can obtain optimized shell-infill structures with complex infill topology without resorting to complex filtering/projection operations. Numerical examples demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

• Simultaneous shape and topology optimization of shell is achieved under the explicit framework. • Both structural geometry and topology of the shell can be described in an explicit way. • The obtained results can be seamlessly linked with CAD systems. In the present work, an investigation on the simultaneous shape and topology optimization of shell structures based upon the Moving Morphable Component (MMC) approach is performed. Unlike the problem that is often solved under the traditional implicit optimization methods, the proposed method is developed in a pure explicit way, which is helpful for the optimization and design of shell structures with complicated geometry. To achieve purpose, the geometric shape and topological form of general shell structure are respectively modeled by Non-Uniform Rational B-Splines (NURBS) in physical space and a series of components in parametric space. Resorting to the pure explicit description, the topology and shape of the shell can be optimized simultaneously with fewer design variables and the obtained results can also be seamlessly linked with CAD systems. Some numerical examples are provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, two novel methods are proposed for optimizing the layout of structural systems with embedding components considering the minimum/maximum distance constraints between the components. The key ideas are using level set functions to describe the shapes of arbitrary irregular embedding components and resorting to the concept of structural skeleton to formulate the distance control constraints explicitly. Numerical examples presented demonstrate that the proposed approaches can give a complete control of the layout of embedding components in an explicit and local way. [ABSTRACT FROM AUTHOR]

The present paper aims to present a new approach for controlling both maximum and minimum length scales of structural members in the Solid Isotropic Material with Penalization (SIMP)-based topology optimization framework. In the proposed approach, length scale control is achieved with help of structural skeleton, which is a key concept in mathematical morphology and a powerful tool for describing structural topologies. Numerical examples show that the proposed approach does have the capability to give a complete control of the length scales of an optimal structure in an explicit and local way. [ABSTRACT FROM AUTHOR]

• A sketch-guided topology optimization approach based on machine learning is proposed. • The approach can express design intent and convey a priori knowledge in topology optimization. • Computer-digitized/hand-drawn sketches are explicit constraint functions. Structural topology optimization is an important design tool in the conceptual design phase of a product. However, the current topology optimization design is mostly driven strictly based on mathematical and mechanical models. Although the innovative design can be automated, it mostly lacks effective manual experience guidance. To improve the efficiency of computer-aided structural design models, this work proposes a sketch-guided topology optimization approach based on machine learning. Using neural network-based style transfer techniques, computer-digitized/hand-drawn sketches are explicitly incorporated into topology optimization in the form of constraint functions. The obtained optimization results not only satisfy the requirements of optimal mechanical properties, but also fully demonstrate the design intention and requirements of designers. Numerical examples show that the proposed approach can effectively compensate for the lack of manual experience guidance for topology optimization. [Display omitted] [ABSTRACT FROM AUTHOR]

In this article, a novel explicit approach for designing complex thin-walled structures based on the Moving Morphable Component (MMC) method is proposed, which provides a unified framework to systematically address various design issues, including topology optimization, reinforced-rib layout optimization, and sandwich structure design problems. The complexity of thin-walled structures mainly comes from flexible geometries and the variation of thickness. On the one hand, the geometric complexity of thin-walled structures leads to the difficulty in automatically describing material distribution (e.g., reinforced ribs). On the other hand, thin-walled structures with different thicknesses require various hypotheses (e.g., Kirchhoff–Love shell theory and Reissner–Mindlin shell theory) to ensure the precision of structural responses. Whereas for cases that do not fit the shell hypothesis, the precision loss of response solutions is non-negligible in the optimization process since the accumulation of errors will cause entirely different designs. Hence, the current article proposes a novel embedded solid component to tackle these challenges. The geometric constraints that make the components fit to the curved thin-walled structure are whereby satisfied. Compared with traditional strategies, the proposed method is free from the limit of shell assumptions of structural analysis and can achieve optimized designs with clear load transmission paths at the cost of few design variables and degrees of freedom for finite element analysis (FEA). Finally, we apply the proposed method to several representative examples to demonstrate its effectiveness, efficiency, versatility, and potential to handle complex industrial structures. [ABSTRACT FROM AUTHOR]

• A rib-reinforced thin-walled structure design method considering wire arc additive manufacturing constraint was presented. • The topological optimization and design of a core bearing structure of a satellite storage tank supporting structure were conducted. • This method was used to design a core load-bearing structure of a large satellite, i.e., the 3.5-meter tank supporting structure, which was fabricated by the WAAM process for the first time in the spacecraft field. • The structure passed the mechanical test and eventually achieved a weight reduction of 31.6%. The thin-walled reinforced structure is important for achieving structural lightweight in spacecraft. With the rapid development of additive manufacturing technology, large-size, thin-walled, stiffened structures with complex structural forms can be manufactured. However, topology optimization considering manufacturing constraints has always been difficult in this field. This paper proposes a design method for reinforced structures that enables control over structural connectivity based on the Moving Morphable Components (MMC) method, which uses reinforced components with explicit geometrical parameters as primitives for topology optimization. The proposed method solves the challenges of rapidly designing complex geometric reinforcements, forming clear force transfer paths, and effectively reduces the structural topology optimization challenges caused by process constraints associated with the arc start/quench process of wire arc additive manufacturing (WAAM). This method was used to design a core load-bearing structure of a large satellite, i.e., the 3.5-meter tank supporting structure, which was fabricated by the WAAM process for the first time in the spacecraft field. The structure passed the mechanical test and eventually achieved a weight reduction of 31.6%. [ABSTRACT FROM AUTHOR]

Energy in lower dimensions, such as edges or corners, can be robustly confined by the higher-order topological insulators (HOTIs) against defects. Being promising for wave manipulation, the unique property of HOTIs is protected by the associated topological invariant and bulk band. Nevertheless, it is still challenging to fast design topologically nontrivial continuum unit cells with highly localized edge/corner modes in photonic and phononic systems. In the present work, with the help of a multitask learning model simultaneously predicting the discrete-valued topological invariant and continuum-valued bandgap range, a fast design framework is developed using an explicit topology optimization method for mechanical HOTIs. In the solution process, the machine learning model and backpropagation algorithm are integrated into a MultiStart solver to accelerate the design efficiency by 3–4 orders than the traditional topology optimization method. Furthermore, a novel programmable mechanical imaging device illustrates the applications of the optimized HOTI with highly localized corner states. This AI-enhanced design paradigm can be easily extended for the fast design of optimized topological materials among various physical systems. [Display omitted] • A ML-enhanced topology optimization method is proposed to fast design phononic HOTIs. • Multitask learning model simultaneously predicts topological property and band structure. • HOTIs with highly localized corner states are designed within 45 s on a desktop computer. • A novel programmable mechanical imaging device is constructed with the optimal HOTIs. [ABSTRACT FROM AUTHOR]

A machine-learning assisted topology optimization approach is proposed for architectural design with artistic flavor. This work establishes a novel framework to systematically integrate structural topology optimization with subjective human design preferences. To embed artistic flavor into the design, neural style transfer technique is adopted for measuring and generating the prior knowledge from a reference image with concerned artistic flavor. With the use of different convolutional layers in the VGG-19 (Visual Geometry Group) model-based CNN (Convolutional Neural Network), both style and content of the artistic flavor from low to high levels of abstraction can be constructed. Then, the measured knowledge can be integrated into pixel-based topology optimization as a formal similarity constraint. Both 2D and 3D problems are solved to illustrate the effectiveness of the proposed approach where inheritance of artistic heritage can be achieved in a systematic manner. [Display omitted] • Structural topology optimization is integrated with human design preferences. [ABSTRACT FROM AUTHOR]

Topology optimization considering stress constraints has received ever-increasing attention in recent years for both of its academic challenges and great potential in real-world engineering applications. Traditionally, stress-constrained topology optimization problems are solved with approaches where structural geometry/topology is represented in an implicit way. This treatment, however, would lead to problems such as the existence of singular optima, the risk of low accuracy of stress computation, and the lack of direct link between optimized results and computer-aided design/engineering (CAD/CAE) systems. With the aim of resolving the aforementioned issues straightforwardly, a Moving Morphable Void (MMV)-based approach is proposed in the present study. Compared with existing approaches, the distinctive advantage of the proposed approach is that the structural geometry/topology is described in a completely explicit way. This feature provides the possibility of obtaining optimized designs with crisp and explicitly parameterized boundaries using much fewer numbers of degrees of freedom for finite element analysis and design variables for optimization, respectively. Several numerical examples provided demonstrate the effectiveness and advantages of the proposed approach. [ABSTRACT FROM AUTHOR]

In topology optimization design, specific requirements over the complexity of component geometry often need to be satisfied for practical purposes. In this paper, with the introduction of a novel complexity control measure built on the structural skeletons of solid and void regions, an explicit structural complexity control approach for the topology optimization of continuum structures is proposed under the framework of level-set representation. The use of skeletons enables us to control the minimum sizes of structural holes so as to meet the manufacturing demands. Through numerical comparison with the cases that have been investigated implicitly, we show that the proposed approach is an effective tool to control the structural complexity in an explicit way. [ABSTRACT FROM AUTHOR]

Three dimensional (3D) topology optimization problems always involve huge numbers of Degrees of Freedom (DOFs) in finite element analysis (FEA) and design variables in numerical optimization, respectively. This will inevitably lead to large computational efforts in the solution process. In the present paper, an efficient and explicit topology optimization approach which can reduce not only the number of design variables but also the number of degrees of freedom in FEA is proposed based on the Moving Morphable Voids (MMVs) solution framework. This is achieved by introducing a set of geometry parameters (e.g., control points of B-spline surfaces) to describe the boundary of a structure explicitly and removing the unnecessary DOFs from the FE model at every step of numerical optimization. Numerical examples demonstrate that the proposed approach does can overcome the bottleneck problems associated with a 3D topology optimization problem in a straightforward way and enhance the solution efficiency significantly. [ABSTRACT FROM AUTHOR]

The present paper aims to propose a novel approach for damage identification of continuum structures based on their dynamic performances. The main idea is resorting to the level set model, which is used to describe the shape and topology of the damage regions implicitly. The original natural frequency-based inverse problem is thus transferred into a generalized shape optimization problem which can be tackled by solving an evolution type Hamilton–Jacobi equation. Compared to traditional approaches, the distinctive advantage of the proposed approach is that it can deal with damage regions of complex shapes in a convenient way. Numerical examples demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

A novel approach, which can control the minimum length scale in topology optimization in a straightforward and explicit way, is proposed in the present paper. This approach is constructed under the so-called Moving Morphable Components (MMC) based solution framework where optimized structural topology can be found by changing the shapes and layout of a set of trapezoid-shaped structural components on a fixed finite element mesh. The eXtended Finite Element Method (XFEM) is employed for structural response analysis and shape sensitivity information is obtained by carrying out numerical integration along the structural boundary. A precision definition of the minimum length scale of a structure is also suggested based on the proposed solution framework. Compared with existing approaches, the proposed approach can achieve minimum length scale control by simply setting lower bounds on a set of geometric design variables. Only a small number of purely geometric constraints imposed on the sizes of intersection regions should be considered explicitly in order to get a complete minimum length scale control. Numerical examples demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Many engineering and biological materials have been found to have tension–compression asymmetry properties. An extension of the linear thermoelastic behavior called a bi-modulus constitutive model is proposed to study the impact of thermo-mechanical coupling in such materials and structures. The well-posedness of the corresponding bi-modulus thermoelasticity problems is confirmed via a variational approach. An efficient numerical analysis method is developed for such nontrivial material behavior and is further employed for structural topology optimization. The importance of the proposed analysis and design framework is demonstrated by the significant impact of the tension–compression asymmetry and thermal effect on structural responses and optimum structural configurations. • A thermo-mechanical constitutive model considering TCA is constructed. • The well-posedness of the bi-modulus thermoelasticity theory is demonstrated. • An efficient analysis algorithm of thermoelastic structures with TCA is proposed. • MMC-based design optimization of thermoelastic structures with TCA is developed. [ABSTRACT FROM AUTHOR]

Flexoelectricity is the coupling between polarization and strain gradient. As the large strain gradient leads to a strong flexoelectric effect, the design of flexoelectric nano-structure via topology optimization has seen growing attentions. In the present work, an explicit topology optimization framework is proposed for flexoelectric structures design. To achieve this purpose, the Moving Morphable Void (MMV)-based approach is employed in the context of Isogeometric Analysis (IGA) combined with the Trimming Surface Analysis (TSA). Energy conversion factor and effective electric polarizability are respectively optimized to improve the flexoelectric performance of the nanostructure. Performing design under the explicit framework coupled with IGA can bring several advantages. Due to the use of NURBS basis functions of IGA, the required continuity in the approximation of the PDEs of flexoelectricity can be satisfied straightforwardly. Furthermore, with the use of the TSA technique, the occurrence of weak/gray material, which may cause numerical instability in flexoelectricity design, can be avoided. Also due to the explicit geometry description in MMV, the optimized result can be imported to the CAD system directly, which is significant for nanoscale structure from manufacturing perspective. Several representative numerical examples for topology optimization of flexoelectric structures are presented to demonstrate the effectiveness and advantages of the proposed approach. [ABSTRACT FROM AUTHOR]

• A topology optimization approach of stiffened plate structure with various cross-sectional properties of stiffener is proposed. • The geometric characteristics of stiffeners can be conveniently controlled using Moving Morphable Components description. • Based on EFG method, the dynamic connection between the plate and the beam node can be realized directly. • Compared with the purely solid optimization model, the proposed method can realize the topology optimization of the stiffened plate structure in an efficient and accurate way. In the present work, a Moving Morphable Components (MMC)-based approach is proposed for topological design of stiffened plate structures, where the stiffeners are used as the building blocks of optimization. Unlike traditional approaches where three-dimensional solid model is often adopted for numerical analysis, in the proposed approach, beam model and plate model are adopted for the modeling of the stiffeners and base plate, respectively, in the context of Element-Free Galerkin (EFG) method. This treatment can not only reduce the computational cost associated with structural analysis substantially but also capture the concerned structural responses more accurately. Several numerical examples are provided to demonstrate the effectiveness and efficiency of the proposed approach. [Display omitted] [ABSTRACT FROM AUTHOR]

In the present work, a hybrid MMC-MMV approach is developed for designing additive manufacturing-oriented shell-graded-infill structures. The key idea is to describe the geometry of a shell-graded-infill structure explicitly using some geometry parameters. To this end, a set of morphable voids is adopted to describe the boundary of the coating shell, while a set of morphable components combing with a coordinate perturbation technique are introduced to represent the graded infill distribution. Under such treatment, both the crisp boundary of the coating shell and the graded infill can be optimized simultaneously, with a small number of design variables. Numerical examples demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

There have been quite a few research works on the topology optimization under stress constraints. However, most of them only treated two dimensional (2D) cases. In the present work, a new approach for topology optimization of three dimensional (3D) shell structures under stress constraints is presented. This approach is constructed by combining the Moving Morphable Void (MMV) approach with trimming technique-based Isogeometric analysis (IGA), where the shell geometry is described using Non-Uniform Rational B-Spline (NURBS) and a set of trimming curves. The proposed approach not only shares the same advantages of MMV approach for topology optimization (e.g., involving small number of design variables, linking with CAD system seamlessly, etc.), but also has the capability of providing high accuracy stress analysis results using much smaller number of degree of freedoms with the help of trimming surface analysis (TSA) technique. Several numerical examples are also presented to demonstrate the effectiveness and advantages of the proposed approach. • An approach is presented for stress topology optimization of shell structures. • The adopted explicit framework can link the optimized results with CAD systems. • The proposed trimming technique provides high accuracy stress analysis results. [ABSTRACT FROM AUTHOR]

In the present work, a new IGA-based MMV (moving morphable void) approach for structural topology optimization is developed. In this approach, the MMV-based topology optimization framework is seamlessly integrated into IGA by using TSA (trimming surface analysis) technique. Compared with existing works where TSA is also employed for topology optimization, the proposed approach provides a robust and flexible control of structural geometry/topology, and has the capability of preventing the occurrence of self-intersection and jagged boundaries in a straightforward manner. The newly developed method is also applied to topology optimization of shell structures, which are widely used in engineering applications. It is found that by using only a relatively small number of IGA-based elements, the present MMV and IGA-based method can obtain optimized shell structures with smooth boundaries with the same ease as for 2-D planar problems. Numerical examples are also provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]