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A key requirement for product design is the ability to capture the physical features of structures quickly and efficiently. One way to achieve this purpose is to use machine learning to support topology optimization. However, due to the diversity of application requirements in product updates, the machine learning-based optimization model needs to be frequently rebuilt by collecting large amounts of data. In this work, Moving Morphable Component approach is combined with Deep Neural Network to achieve the quick topology optimization design of acoustic devices. A deep transfer learning approach to the predictive model is also developed for the model to be adapted to different design conditions. Thus, using the proposed approach, not only the originally designed acoustic structure can be quickly optimized, but also the serialized structures evolved from the source model can be easily obtained. Numerical examples illustrate the effectiveness and advantages of the proposed method. [ABSTRACT FROM AUTHOR]

MMC is one of the topology optimization methods that provides explicit boundary description of the optimized topology. However, due to the inherent nature of MMC, the obtained geometry could exhibit distinct local singularities. To cope with this issue, a non-parametric geometry patching technique for MMC is developed. A moving node patching technique for both 2D and 3D cases is developed in conjunction with MMC to obtain structures with smooth boundaries. Numerical examples in 2D and 3D are presented to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

For spatially varying multiscale configurations (SVMSCs) that increasingly gain engineering perspective, a design scheme enabling the direct tuning of their microstructural layouts is still desired. Challenges lie behind the fact that an arbitrary setting on the (field) distributions about the microstructural geometric features is likely to violate the underlying conditions of total differential, and the article is aimed to resolve the issue systematically. This is done by representing (two-dimensional) SVMSCs from the viewpoint of quasi-conformal mapping, where the microstructural profile can be summarised by a (complete) family consisting of four geometric feature fields. By modifying the so-called Beltrami equations that automatically satisfy the total differential condition, the relationships among these four geometric feature fields can be explicitly derived, and their degrees of freedom are reduced to two. Different choices for which two field quantities as the free design variables result in various geometric-feature-based modes, which almost cover all scenarios of SVMSC design by means of directly tuning their microstructural profiles. Furthermore, we can now directly manipulate the stretch ratio, one of the four field variables, to avoid ill microstructural distortion, which has been a challenging issue for SVMSCs representation. Fueled by an asymptotic homogenisation scheme (Zhu et al. in J Mech Phys Solids 124:612–633, 2019, ), the present method is then employed for geometric-feature-based compliance design of SVMSC. [ABSTRACT FROM AUTHOR]

Developing appropriate analytic-function-based constitutive models for new materials with nonlinear mechanical behavior is demanding. For such kinds of materials, it is more challenging to realize the integrated design from the collection of the material experiment under the classical topology optimization framework based on constitutive models. The present work proposes a mechanistic-based data-driven topology optimization (DDTO) framework for three-dimensional continuum structures under finite deformation. In the DDTO framework, with the help of neural networks and explicit topology optimization method, the optimal design of the three-dimensional continuum structures under finite deformation is implemented only using the uniaxial and equi-biaxial experimental data. Numerical examples illustrate the effectiveness of the data-driven topology optimization approach, which paves the way for the optimal design of continuum structures composed of novel materials without available constitutive relations. [ABSTRACT FROM AUTHOR]

Explicit topology optimization methods have received ever-increasing interest in recent years. In particular, a 188-line Matlab code of the two-dimensional (2D) Moving Morphable Component (MMC)-based topology optimization method was released by Zhang et al. (Struct Multidiscip Optim 53(6):1243-1260, 2016). The present work aims to propose an efficient and easy-to-extend 256-line Matlab code of the MMC method for three-dimensional (3D) topology optimization implementing some new numerical techniques. To be specific, by virtue of the function aggregation technique, accurate sensitivity analysis, which is also easy-to-extend to other problems, is achieved. Besides, based on an efficient identification algorithm for load transmission path, the degrees of freedoms (DOFs) not belonging to the load transmission path are removed in finite element analysis (FEA), which significantly accelerates the optimization process. As a result, compared to the corresponding 188-line 2D code, the performance of the optimization results, the computational efficiency of FEA, and the convergence rate and the robustness of optimization process are greatly improved. For the sake of completeness, a refined 218-line Matlab code implementing the 2D-MMC method is also provided. [ABSTRACT FROM AUTHOR]

Gradient porous structured materials possess significant potential of being applied in many engineering fields. To accelerate the design process of infill graded microstructures of uniform local density, a novel asymptotic homogenisation topology optimisation method was proposed by Zhu et al. (J Mech Phys Solids 124:612–633, 2019), aiming for (1) significantly enriching the pool of representable graded microstructures; and (2) deriving an homogenised formulation for stress analysis in consistency with fine-scale results. But the work is severely confined from being widely applied, mainly due to the following two reasons. Firstly, to circumvent macroscopically pointwise computation for solving various microscopic cell problems, linearisation had to be adopted for its numerical implementation, and this significantly reduces the design freedom. Secondly, lacking of sensitive analysis, genetic algorithm was chosen for optimisation, inevitably decreasing the computational efficiency. To address these bottleneck challenging issues, a zoning scheme empowered by computational parallelism is introduced, and the sensitivity analysis associated with the new asymptotic framework is conducted. Through comparisons with fine-scale simulation results, the proposed algorithm is shown to be an effective tool for evaluating the mechanical behaviour of graded microstructures. As an optimisation tool, the mapping function takes a concise and explicit form. But its parameterisation still needs further investigation, so as to improve the solution optimality of the present approach, especially in comparison with another recently proposed method (Groen and Sigmund, Internat J Numer Methods Engrg 113(8):1148–1163, 2018). Optimisation results for three-dimensional graded microstructures are also shown, which are not frequently discussed in literature, possibly because of the high computational cost generated. [ABSTRACT FROM AUTHOR]

In the present work, a highly efficient moving morphable component (MMC)-based approach for multi-resolution topology optimization is proposed. In this approach, high-resolution optimization results can be obtained with a smaller number of design variables and a relatively low degree of freedoms (DOFs). This is achieved by taking the advantage that the topology optimization model and the finite element analysis model are totally decoupled in the MMC-based problem formulation. A coarse mesh is used for structural response analysis and a design domain partitioning strategy is introduced to preserve the topological complexity of the optimized structures. Numerical examples are then provided so as to demonstrate that with the use of the proposed approach, computational efforts can be saved substantially for large-scale topology optimization problems. [ABSTRACT FROM AUTHOR]

In the present paper, an explicit method for controlling the structural complexity of continuum structures in topology optimization is proposed. This method is devised under the Moving Morphable Component (MMC) based framework where the geometries of the basic building blocks for topology optimization are described explicitly. Compared to the existing structural complexity control approaches which are generally developed in an implicit geometry/topology description framework, the proposed method allows an explicit definition of structural complexity, which facilitates the construction of the controlling schemes significantly. The effectiveness of the proposed method is demonstrated by numerical examples shown at the end of the paper. [ABSTRACT FROM AUTHOR]

This paper presents a new topology optimization approach based on the so-called Moving Morphable Components (MMC) solution framework. The proposed method improves several weaknesses of the previous approach (e.g., Guo et al. in J Appl Mech 81:081009, 2014a) in the sense that it can not only allow for components with variable thicknesses but also enhance the numerical solution efficiency substantially. This is achieved by constructing the topological description functions of the components appropriately, and utilizing the ersatz material model through projecting the topological description functions of the components. Numerical examples demonstrate the effectiveness of the proposed approach. In order to help readers understand the essential features of this approach, a 188 line Matlab implementation of this approach is also provided. [ABSTRACT FROM AUTHOR]

In the present work, some symmetry theorems for structural optimization problems involving reliability measure and bi-modulus materials are established. In the first part of this paper, two types of symmetric reliability-based structural optimization problems are discussed. It is proved that, for the first type symmetric RBDO problems, the existence of symmetric global optimal solutions can be guaranteed even through the probability density function (PDF) is non-symmetric. While for the second type symmetric RBDO problems, more severe conditions on PDF are required to ensure the existence of symmetric global optimal solutions. In the second part of the paper, the convexity of the compliance of truss structures involving bi-modulus materials is confirmed firstly. Based on this result, it is found that for both deterministic and robust symmetric compliance minimization of truss structures involving bi-modulus materials, symmetric global optima always exist. The theoretical results are also demonstrated through some academic examples. [ABSTRACT FROM AUTHOR]

The present paper studies the integrated size and topology optimization of skeletal structures under natural frequency constraints. It is found that, unlike the conventional compliance-oriented topology optimization problems, the considered problem may be strongly singular in the sense that the corresponding feasible domain may be disconnected and the global optimal solutions are often located at the tips of some separated low dimensional sub-domains when the cross-sectional areas of the structural components are used as design variables. As in the case of stress-constrained topology optimization, this unpleasant behavior may prevent the gradient-based numerical optimization algorithms from finding the true optimal topologies. To overcome the difficulties posed by the strongly singular optima, some particular forms of area/moment of inertia-density interpolation schemes, which can restore the connectedness of the feasible domain, are proposed. Based on the proposed optimization model, the probability of finding the strongly singular optimum with gradient-based algorithms can be increased. Numerical examples demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In the present paper, some extensions of the previous theoretical results about the symmetry properties of structural optimization problems are reported. It is found that generally the condition of convexity can be relaxed to quasi-convexity in order to guarantee the existence of symmetry global optima. Furthermore, some new results about the symmetry properties of robust and discrete structural optimization problems are also presented. Numerous concrete examples illustrate the claims made in the present work explicitly. [ABSTRACT FROM AUTHOR]

In this note, a conjecture on the existence of symmetric optimal solution under multiple loads made in Rozvany (Struct Multidisc Optim 43:297-317, 2011, Conjecture 4) has been confirmed. [ABSTRACT FROM AUTHOR]