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Usually, an optimal topology is obtained by optimizing the material distribution within a prescribed domain; for example, a rectangular domain with a specified length and width for a plane problem. However, the dimensions (i.e. aspect ratio) of a rectangular design domain have significant influence on the resultant optimal topology. In this paper, a minimum Averaged Compliance Density (ACD) based method for topology optimization of structures is proposed. Unlike the conventional topology optimization method, the ACD is taken as the objective function, and the topology and domain dimensions of the structure are optimized simultaneously. As an example, the topology of a cantilever beam with large aspect ratio will be optimized, which is often difficult for traditional topology optimization algorithms. Through optimizing the topology and the dimensions of the design domain, a base structure is obtained, which is repeated to yield the whole, assembled beam. The influence of the relative values of shear force and moment is analyzed numerically. Results show that as the value of the bending moment increases relative to the shear force, the optimal topology changes from a truss‐like structure to a vertically stiffened box‐like structure.

This paper aims to present a new topology method in designing the lightweight and complex structures for 3D printing.

Computer-aided design (CAD) and topology design are the two main approaches for 3D truss lattices designing in 3D printing. Though these two ways have their own advantages and have been used by the researchers in different engineering situations, these two methods seem to be incompatible. A novel topology method is presented in this paper which can combine the merits of both CAD and topology design. It is generally based on adding materials to insufficient parts in a given structure so the resulting topology evolves toward an optimum.

By using the topology method, an optimized-Kagome structure is designed and both 3D original-Kagome structure and 3D optimized-Kagome structure are manufactured by fused deposition modeling (FDM) 3D printer with ABS and the compression tests results show that the 3D optimized-Kagome has a higher specific stiffness and strength than the original one.

The presented topology method is the first work that using the original structure-based topology algorithm other than a boundary condition-based topology algorithm for 3D printing lattice and it can be considered as general way to optimize a commonly used light-weight lattice structure in strength and stiffness.

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 structural design problem can be viewed as an iterative design loop with each iteration involving two stages for topology and shape designs with genetic algorithm (GA) as the optimization tool for both.

The topology optimization problem, which is ill posed, is regularized using a constraint on perimeter and solved using GA. The problem is formulated as one of compliance minimization subject to volume constraint for the single loading case. A dual formulation of this has been used for the multiple loading cases resulting in as many behavioral constraints as there are loading cases. The tentative topology given by the topology optimization module is taken and the domain boundary is approximated using straight lines, B‐splines and cubic spline curves and design variables are selected among the boundary defining points. Optimum boundary shape of the problem has been obtained using GA in two different ways: without stress constraints; and with stress constraints.

The proposed two stage strategy has been tested on benchmark structural optimization problems and its performance is found to be extremely good.

The strategy appears to be eminently suitable for implementation in a general purpose FE software as an add‐on module for structural design optimization.

It has been observed that the integrated topology and shape design method is robust and easy to implement in comparison with other techniques. The computing time requirements for the GA does not appear daunting in the present scenario of high performance parallel computing and improved GA techniques.

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.

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.

This paper aims to obtain a symmetrical step-down topology with lower equivalent capacity and wider step-down range under the condition of the same output. Three new symmetrical step-down topologies of zigzag autotransformer are proposed in this paper. Taking the equivalent capacity as the main parameter, the obtained topologies are modeled and analyzed in detail.

This paper adopts the research methods of design, modeling, analysis and simulation verification. First, the zigzag autotransformer is redesigned according to the design objective of symmetrical step-down topology. Second, the mathematical model of the designed topology is established, and the detailed theoretical analysis is carried out. Finally, the theoretical results are verified by simulation.

Three symmetrical zigzag autotransformer step-down topologies are designed, the winding configurations of the corresponding topology are presented, the step-down ranges of these three topologies are calculated and the influence of step-down ratio on equivalent capacity of autotransformer is analyzed. Through analysis, the target step-down topologies are obtained when the step-down ratio is [0.969, 1.414] and [1.414, 8].

Because the selected research object is only zigzag autotransformer, the research results may lack generality. Therefore, researchers are encouraged to further study topologies of other autotransformers.

This paper includes the implications of step-down ratio on the equivalent capacity of autotransformer and the configuration of transformer windings.

The topologies designed in this paper enable zigzag autotransformer to be applied in step-down circumstances.

Robust design is very important for manufacturers to ensure the quality of the finished product. Therefore, a robustness measure is needed for the topological design of electromagnetic problems which may be sensitive to parameter variations. The purpose of this paper is to propose a robust objective function for topological design problems.

In this paper, a robust objective function for topology optimization is defined on an uncertainty set using the worst case analysis. The robustness of a topological design is defined as the worst response due to the variations of the location of the topology change. The approach is based on the definition of a topological gradient.

The robust topology optimization (RTO) was applied to eddy current crack reconstruction problems. The numerical applications showed that this method can provide more reliable results for the reconstruction in the presence of significant noise in the measured signal.

The RTO may be applied to some more complicated design problems; however large computational costs may result.

This paper has defined a robustness metric for topology design and a robust design model is proposed for topology optimization problems.

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.

Topology optimization is a method used for developing optimized geometric designs by distributing material pixels in a given design space that maximizes a chosen quantity of interest (QoI) subject to constraints. The purpose of this study is to develop a problem-agnostic automatic differentiation (AD) framework to compute sensitivities of the QoI required for density distribution-based topology optimization in an unstructured co-located cell-centered finite volume framework. Using this AD framework, the authors develop and demonstrate the topology optimization procedure for multi-dimensional steady-state heat conduction problems.

Topology optimization is performed using the well-established solid isotropic material with penalization approach. The method of moving asymptotes, a gradient-based optimization algorithm, is used to perform the optimization. The sensitivities of the QoI with respect to design variables, required for optimization algorithm, are computed using a discrete adjoint method with a novel AD library named residual automatic partial differentiator (Rapid).

Topologies that maximize or minimize relevant quantities of interest in heat conduction applications are presented. The efficacy of the technique is demonstrated using a variety of realistic heat transfer applications in both two and three dimensions, in conjugate heat transfer problems with finite conductivity ratios and in non-rectangular/non-cuboidal domains.

In contrast to most published work which has either used finite element methods or Cartesian finite volume methods for transport applications, the topology optimization procedure is developed in a general unstructured finite volume framework. This permits topology optimization for flow and heat transfer applications in complex design domains such as those encountered in industry. In addition, the Rapid library is designed to provide a problem-agnostic pathway to automatically compute all required derivatives to machine accuracy. This obviates the necessity to write new code for finding sensitivities when new physics are added or new cost functions are considered and permits general-purpose implementations of topology optimization for complex industrial applications.