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This paper aims to present a deep learning–based surrogate model for fast multi-material topology optimization of an interior permanent magnet (IPM) motor. The multi-material topology optimization based on genetic algorithm needs large computational burden because of execution of finite element (FE) analysis for many times. To overcome this difficulty, a convolutional neural network (CNN) is adopted to predict the motor performance from the cross-sectional motor image and reduce the number of FE analysis.

To predict the average torque of an IPM motor, CNN is used as a surrogate model. From the input cross-sectional motor image, CNN infers dq-inductance and magnet flux to compute the average torque. It is shown that the average torque for any current phase angle can be predicted by this approach, which allows the maximization of the average torque by changing the current phase angle. The individuals in the multi-material topology optimization are evaluated by the trained CNN, and the limited individuals with higher potentials are evaluated by finite element method.

It is shown that the proposed method doubles the computing speed of the multi-material topology optimization without loss of search ability. In addition, the optimized motor obtained by the proposed method followed by simplification for manufacturing is shown to have higher average torque than a reference model.

This paper proposes a novel method based on deep learning for fast multi-material topology optimization considering the current phase angle.

The optimal material microstructures in pure material design are no longer efficient or optimal when accounting macroscopic structure performance with specific boundary conditions. Therefore, it is important to provide a novel multiscale topology optimization framework to tailor the topology of structure and the material to achieve specific applications. In comparison with porous materials, composites consisting of two or more phase materials are more attractive and advantageous from the perspective of engineering application. This paper aims to provide a novel concurrent topological design of structures and microscopic materials for thermal conductivity involving multi-material topology optimization (material distribution) at the lower scale.

In this work, the effective thermal conductivity properties of microscopic three or more phase materials are obtained via homogenization theory, which serves as a bridge of the macrostructure and the periodic material microstructures. The optimization problem, including the topological design of macrostructures and inverse homogenization of microscopic materials, are solved by bi-directional evolutionary structure optimization method.

As a result, the presented framework shows high stability during the optimization process and requires little iterations for convergence. A number of interesting and valid macrostructures and material microstructures are obtained in terms of optimal thermal conductive path, which verify the effectiveness of the proposed mutliscale topology optimization method. Numerical examples adequately consider effects of initial guesses of the representative unit cell and of the volume constraints of adopted base materials at the microscopic scale on the final design. The resultant structures at both the scales with clear and distinctive boundary between different phases, making the manufacturing straightforward.

This paper presents a novel multiscale concurrent topology optimization method for structures and the underlying multi-phase materials for thermal conductivity. The authors have carried out the concurrent multi-phase topology optimization for both 2D and 3D cases, which makes this work distinguished from existing references. In addition, some interesting and efficient multi-phase material microstructures and macrostructures have been obtained in terms of optimal thermal conductive path.

The purpose of this paper is to get the topology shape and material distribution of composite rotor beam under the requirement of cross-sectional characteristics.

A new multi-material topology optimization method is given. Designated shear center (SC) position and stiffness terms are combined as the objective function. Multi-material model including isotropic and anisotropic materials are employed. Sensitivity analysis is given based on gradient-based algorithm, and density filtering scheme is adopted to avoid checkerboard problem.

The topology design method of composite rotor beam provides innovative cross-sectional shape and material distribution method. The final topology shape like “ > ” is given for different material types and cross-sectional shape under SC position requirement. The coefficient of stiffness components has great influence on the cross-sectional final topology shape.

The proposed method is just to give cross-sectional topology shape. To obtain final actual composite rotor beam structure, shape and size optimization should be conducted if the topology shape is given.

This method is suitable for the preliminary design of helicopter rotor beam to get designated SC position and stiffness terms.

The proposed method provides a new gradient-based algorithm for multi-material topology optimization design of composite rotor beam.

The purpose of this paper is to develop a multi-material topology optimization method for permanent magnet-assisted synchronous reluctance motors.

In the proposed method, the optimization procedure consists of two steps. In the first step, the entire rotor area was selected for the design region and the distribution of the core and air materials was optimized. In the second step, the design region was limited to the air region of the former solution and the distribution of magnets and cores or magnets and air was optimized.

Because of the two-step process of the proposed method, the design parameters can be reduced compared to the conventional method. As a result, this study can prevent the solution space from becoming more complex and superior solutions can be founded effectively.

Since limited case study is denoted in this paper, much more case studies, for example, three-dimensional optimization problems, are needed to be discussed.

The optimal solutions obtained by the proposed method have a smaller magnet volume and higher average torque than that of the conventional method.

In the proposed methods, optimization methodology, which consists of two-steps process, is differed from the conventional method.

The purpose of this paper is to propose an effective and efficient numerical method that can consider natural frequency in multi-material topology optimization (MMTO) and which is scalable for complex three-dimensional (3D) problems.

The optimization algorithm is developed by combining custom FORTRAN code for MMTO with the open-source software Mystran, which is used as a finite element analysis (FEA) solver. The proposed algorithm allows the designer to shift the fundamental frequency of the design beyond a defined frequency spectrum from the initial designing phase. The methodology is formulated in a smooth and differentiable manner, with the sensitivity expressions, required by gradient-based optimization solvers, presented.

Natural frequency constraint has been successfully implemented into MMTO. The use of open-source software Mystran as an FEA solver in the algorithm provides ability to solve complex problems. Mystran offers powerful built-in functions for eigenvalue extraction using methods like Givens, modified Givens, inverse power and the Lanczos method, which provide the ability to solve complex models. The algorithm is successfully able to solve both two- and three-material MMTO jobs for two-dimensional and 3D geometries.

Natural frequency constraint consideration into topology optimization is very challenging due to three common issues: localized eigenmodes, mode switching and high computational cost. The proposed algorithm addresses these inherent issues, implements natural frequency constraint to MMTO and solves for complex models, which is hardly possible using conventional methods.

The purpose of this paper is to develop a topology optimization algorithm considering natural frequencies.

To incorporate natural frequency as design criteria of shell-infill structures, two types of design models are formulated: (1) type I model: frequency objective with mass constraint; (2) type II model: mass objective with frequency constraint. The interpolation functions are constructed by the two-step density filtering approach to describe the fundamental topology of shell-infill structure. Sensitivities of natural frequencies and mass with respect to the original element densities are derived, which will be used for both type I model and type II model. The method of moving asymptotes is used to solve both models in combination with derived sensitivities.

Mode switching is one of the challenges faced in eigenfrequency optimization problems, which can be overcome by the modal-assurance-criterion-based mode-tracking strategy. Furthermore, a shifting-frequency-constraint strategy is recommended for type II model to deal with the unsatisfactory topology obtained under direct frequency constraint. Numerical examples are systematically investigated to demonstrate the effectiveness of the proposed method.

In this paper, a topology optimization method considering natural frequencies is proposed by the author, which is useful for the design of shell-infill structures to avoid the occurrence of resonance in dynamic conditions.

Negative Poisson’s ratio (NPR) material has huge potential applications in various industrial fields. However, lower Young’s modulus due to the porous form limits its further applications. Based on the topology optimization technique, this paper aims to optimize the structure consisting two isotropic porous materials with positive Poisson’s ratio (PPR) and NPR and void.

Under prescribed dual-volume fraction constraints, the structural compliance is taken as the objective. Young’s modulus and Poisson’s ratio are, respectively, interpolated and expressed with Lamé’s parameters for easier programming. Accordingly, the sensitivities can be derived through the chain rule. Several two- and three-dimensional illustrative examples are presented to demonstrate the capability and effectiveness of the proposed approach. The influences of Poisson’s ratios, volume fractions and Young’s moduli on the optimized results are investigated.

For NPR materials having unique load responses, the resulting topologies of PPR and NPR materials have distinct material distributions in comparison of the results from two PPR materials. Furthermore, it is observed that higher structural stiffness can be achieved from the hybrid of PPR and NPR materials than that obtained from the structures made of individual constituent materials.

A topology optimization methodology is proposed to design structures composed of PPR and NPR materials.

There are many investigations in design methodologies, but there are also divergences and convergences as there are so many points of view. This study aims to evaluate to corroborate and deepen other researchers’ findings, dissipate divergences and provide directing to future work on the subject from a methodological and convergent perspective.

This study analyzes the previous reviews (about 15 reviews) and based on the consensus and the classifications provided by these authors, a significant sample of research is analyzed in the design for additive manufacturing (DFAM) theme (approximately 80 articles until June of 2017 and approximately 280–300 articles until February of 2019) through descriptive statistics, to corroborate and deepen the findings of other researchers.

Throughout this work, this paper found statistics indicating that the main areas studied are: multiple objective optimizations, execution of the design, general DFAM and DFAM for functional performance. Among the main conclusions: there is a lack of innovation in the products developed with the methodologies, there is a lack of exhaustivity in the methodologies, there are few efforts to include environmental aspects in the methodologies, many of the methods include economic and cost evaluation, but are not very explicit and broad (sustainability evaluation), it is necessary to consider a greater variety of functions, among other conclusions

The novelty in this study is the methodology. It is very objective, comprehensive and quantitative. The starting point is not the case studies nor the qualitative criteria, but the figures and quantities of methodologies. The main contribution of this review article is to guide future work on the subject from a methodological and convergent perspective and this article provides a broad database with articles containing information on many issues to make decisions: design methodology; optimization; processes, selection of parts and materials; cost and product management; mechanical, electrical and thermal properties; health and environmental impact, etc.

This research presents a design method for designing greenhouse structures based on topology optimization. Moreover, the structural design of a gothic greenhouse is proposed in which its structural strength has been improved by using this proposed method. In this method, the design of the structure is done mathematically; therefore, in the design process, more attention can be focused on the constraint space and boundary conditions. It was also shown how the static reliability and fatigue coefficients will change as a result of the design of the greenhouse structure with this method. Another purpose of this study is to find the weakest part of the greenhouse structure against lateral winds and other general loads on the greenhouse structure.

In the proposed method, the outer surface and the allowable volume as a constraint domain were considered. The desired loads can be located on the constraint domain. The topology optimization was used to minimize the mass and structural compliance as the objective function. The obtained volume was modified for simplifying the construction. The changes in the shape of the greenhouse structure were investigated by choosing three different penalty numbers for the topology optimization algorithm. The final design of the proposed structure was performed based on the total simultaneous critical loads on the structure. The results of the proposed method were compared in the order of different volume fractions. This showed that the volume fraction approach can significantly reduce the weight of the structure while maintaining its strength and stability.

Topology optimization results showed different strut and chords composition because of the changes in maximum mass limit and volume fraction. The results showed that the fatigue was more hazardous, and it decreased the strength of structure nearly three times more than a static analysis. Further, it was noticed that how the penalty numbers can affect topology optimization results. An optimal design based on topology optimization results was presented to improve the proposed greenhouse design against destruction and demolition. Furthermore, this study shows the most sensitive part of the greenhouse against the standard loads of wind, snow, and crop.

The obtained designs were compared with a conventional arch greenhouse, and then the structural performances were shown based on standard loads. The results showed that in designing the proposed structure, the optimized changes increased the structure strength against the standard loads compared to a simple arch greenhouse. Moreover, the stress safety factor and fatigue safety factor because of different designs of this structure were also compared with each other.

Topology optimization of structures under self-weight loading is a challenging problem which has received increasing attention in the past years. The use of standard formulations based on compliance minimization under volume constraint suffers from numerous difficulties for self-weight dominant scenarios, such as non-monotonic behaviour of the compliance, possible unconstrained character of the optimum and parasitic effects for low densities in density-based approaches. This paper aims to propose an alternative approach for dealing with topology design optimization of structures into three spatial dimensions subject to self-weight loading.

In order to overcome the above first two issues, a regularized formulation of the classical compliance minimization problem under volume constraint is adopted, which enjoys two important features: (a) it allows for imposing any feasible volume constraint and (b) the standard (original) formulation is recovered once the regularizing parameter vanishes. The resulting topology optimization problem is solved with the help of the topological derivative method, which naturally overcomes the above last issue since no intermediate densities (grey-scale) approach is necessary.

A novel and simple approach for dealing with topology design optimization of structures into three spatial dimensions subject to self-weight loading is proposed. A set of benchmark examples is presented, showing not only the effectiveness of the proposed approach but also highlighting the role of the self-weight loading in the final design, which are: (1) a bridge structure is subject to pure self-weight loading; (2) a truss-like structure is submitted to an external horizontal force (free of self-weight loading) and also to the combination of self-weight and the external horizontal loading; and (3) a tower structure is under dominant self-weight loading.

An alternative regularized formulation of the compliance minimization problem that naturally overcomes the difficulties of dealing with self-weight dominant scenarios; a rigorous derivation of the associated topological derivative; computational aspects of a simple FreeFEM implementation; and three-dimensional numerical benchmarks of bridge, truss-like and tower structures.