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The purpose of the present work is to develop the combination of the radial point interpolation method (RPIM) with a bi-directional evolutionary structural optimization (BESO) algorithm and extend it to the analysis of benchmark examples and automotive industry applications.

A BESO algorithm capable of detecting variations in the stress level of the structure, and thus respond to those changes by reinforcing the solid material, is developed. A meshless method, the RPIM, is used to iteratively obtain the stress field. The obtained optimal topologies are then recreated and numerically analyzed to validate its proficiency.

The proposed algorithm is capable to achieve accurate benchmark material distributions. Implementation of the BESO algorithm combined with the RPIM allows developing innovative lightweight automotive structures with increased performance.

Computational cost of the topology optimization analysis is constrained by the nodal density discretizing the problem domain. Topology optimization solutions are usually complex, whereby they must be fabricated by additive manufacturing techniques and experimentally validated.

In automotive industry, fuel consumption, carbon emissions and vehicle performance is influenced by structure weight. Therefore, implementation of accurate topology optimization algorithms to design lightweight (cost-efficient) components will be an asset in industry.

Meshless methods applications in topology optimization are not as widespread as the finite element method (FEM). Therefore, this work enhances the state-of-the-art of meshless methods and demonstrates the suitability of the RPIM to solve topology optimization problems. Innovative lightweight automotive structures are developed using the proposed methodology.

The purpose of this paper is to propose a new scheme for obtaining acceptable solutions for problems of continuum topology optimization of structures, regarding the distribution and limitation of discretization errors by considering h-adaptivity.

The new scheme encompasses, simultaneously, the solution of the optimization problem considering a solid isotropic microstructure with penalization (SIMP) and the application of the h-adaptive finite element method. An analysis of discretization errors is carried out using an a posteriori error estimator based on both the recovery and the abrupt variation of material properties. The estimate of new element sizes is computed by a new h-adaptive technique named “Isotropic Error Density Recovery”, which is based on the construction of the strain energy error density function together with the analytical solution of an optimization problem at the element level.

Two-dimensional numerical examples, regarding minimization of the structure compliance and constraint over the material volume, demonstrate the capacity of the methodology in controlling and equidistributing discretization errors, as well as obtaining a great definition of the void–material interface, thanks to the h-adaptivity, when compared with results obtained by other methods based on microstructure.

This paper presents a new technique to design a mesh made with isotropic triangular finite elements. Furthermore, this technique is applied to continuum topology optimization problems using a new iterative scheme to obtain solutions with controlled discretization errors, measured in terms of the energy norm, and a great resolution of the material boundary. Regarding the computational cost in terms of degrees of freedom, the present scheme provides approximations with considerable less error if compared to the optimization process on fixed meshes.

Investigates the efficiency of hybrid solution methods when incorporated into large‐scale topology and shape optimization problems and to demonstrate their influence on the overall performance of the optimization algorithms. Implements three innovative solution methods based on the preconditioned conjugate gradient (PCG) and Lanczos algorithms. The first method is a PCG algorithm with a preconditioner resulted from a complete or an incomplete Cholesky factorization, the second is a PCG algorithm in which a truncated Neumann series expansion is used as preconditioner, and the third is a preconditioned Lanczos algorithm properly modified to treat multiple right‐hand sides. The numerical tests presented demonstrate the computational advantages of the proposed methods which become more pronounced in large‐scale and/or computationally intensive optimization problems.

Furniture plays a significant role in daily life. Advanced computational and manufacturing technologies provide new opportunities to create novel, high-performance and customized furniture. This paper aims to enhance furniture design and production by developing a new workflow in which computer graphics, topology optimization and advanced manufacturing are integrated to achieve innovative outcomes.

Workflow development is conducted by exploring state-of-the-art computational and manufacturing technologies to improve furniture design and production. Structural design and fabrication using the workflow are implemented.

An efficient transdisciplinary workflow is developed, in which computer graphics, topology optimization and advanced manufacturing are combined. The workflow consists of the initial design, the optimization of the initial design, the postprocessing of the optimized results and the manufacturing and surface treatment of the physical prototypes. Novel chairs and tables, including flat pack designs, are produced using this workflow. The design and fabrication processes are simple, efficient and low-cost. Both additive manufacturing and subtractive manufacturing are used.

The research outcomes are directly applicable to the creation of novel furniture, as well as many other structures and devices.

A new workflow is developed by taking advantage of the latest topology optimization methods and advanced manufacturing techniques for furniture design and fabrication. Several pieces of innovative furniture are designed and fabricated as examples of the presented workflow.

The purpose of this paper is to describe an element addition strategy for topology optimization of thermally actuated compliant mechanisms under uniform temperature fields.

The proposed procedure is based on the evolutionary structural optimization (ESO) method. In previous works, this group of authors has successfully applied the ESO method for compliant mechanism optimization under directly applied input loads. The present paper progresses on this work line developing an extension of this procedure, based on an additive version of the method, to approach the more complicated case of thermal actuators.

The adopted method has been tested in several numerical applications and benchmark examples to illustrate and validate the approach, and designs obtained with this method are compared favorably with the analytical solutions and results derived by other authors using different optimization methods, showing the viability of this technique for uniformly heated actuators optimization.

As a simple initial approach, this research considers only uniform heating of the system, while many thermal actuators are heated nonuniformly. Future works will be based on electrothermal actuation, and nonuniform Joule heating will be considered as well, which might lead to more elegant and efficient solutions.

Compliant micromechanisms that are responsible for movement play a crucial role in microelectromechanical systems (MEMS) design, which cannot be manufactured using typical assembly processes and may not make use of traditional hinges or bearings. The topology optimization method described in this paper enables the systematic design of these devices, which can result in reduced conception time and manufacturing cost.

The ESO method has been successfully applied to several optimum material distribution problems, but not for thermal compliant mechanisms. Even if most applications of this method have been oriented for maximum stiffness structure design, this paper shows that this computation method may be also useful in the design of thermal compliant mechanisms and provides engineers with a very simple and practical alternative design tool.

The purpose of this paper is to propose a novel non-probabilistic reliability-based topology optimization (NRBTO) method for continuum structural design under interval uncertainties of load and material parameters based on the technology of 3D printing or additive manufacturing.

First, the uncertainty quantification analysis is accomplished by interval Taylor extension to determine boundary rules of concerned displacement responses. Based on the interval interference theory, a novel reliability index, named as the optimization feature distance, is then introduced to construct non-probabilistic reliability constraints. To circumvent convergence difficulties in solving large-scale variable optimization problems, the gradient-based method of moving asymptotes is also used, in which the sensitivity expressions of the present reliability measurements with respect to design variables are deduced by combination of the adjoint vector scheme and interval mathematics.

The main findings of this paper should lie in that new non-probabilistic reliability index, i.e. the optimization feature distance which is defined and further incorporated in continuum topology optimization issues. Besides, a novel concurrent design strategy under consideration of macro-micro integration is presented by using the developed RBTO methodology.

Uncertainty propagation analysis based on the interval Taylor extension method is conducted. Novel reliability index of the optimization feature distance is defined. Expressions of the adjoint vectors between interval bounds of displacement responses and the relative density are deduced. New NRBTO method subjected to continuum structures is developed and further solved by MMA algorithms.

This work presents a topology optimization methodology for designing microarchitectures of phononic crystals. The objective is to get microstructures having, as a consequence of wave propagation phenomena in these media, bandgaps between two specified bands. An additional target is to enlarge the range of frequencies of these bandgaps.

The resulting optimization problem is solved employing an augmented Lagrangian technique based on the proximal point methods. The main primal variable of the Lagrangian function is the characteristic function determining the spatial geometrical arrangement of different phases within the unit cell of the phononic crystal. This characteristic function is defined in terms of a level-set function. Descent directions of the Lagrangian function are evaluated by using the topological derivatives of the eigenvalues obtained through the dispersion relation of the phononic crystal.

The description of the optimization algorithm is emphasized, and its intrinsic properties to attain adequate phononic crystal topologies are discussed. Particular attention is addressed to validate the analytical expressions of the topological derivative. Application examples for several cases are presented, and the numerical performance of the optimization algorithm for attaining the corresponding solutions is discussed.

The original contribution results in the description and numerical assessment of a topology optimization algorithm using the joint concepts of the level-set function and topological derivative to design phononic crystals.

This is an attempt to better bridge the gap between the mathematical and the engineering/physical aspects of the topic. The authors trace the different sources of non-convexification in the context of topology optimization problems starting from domain discretization, passing through penalization for discreteness and effects of filtering methods, and end with a note on continuation methods.

Starting from the global optimum of the compliance minimization problem, the authors employ analytical tools to investigate how intermediate density penalization affects the convexity of the problem, the potential penalization-like effects of various filtering techniques, how continuation methods can be used to approach the global optimum and how the initial guess has some weight in determining the final optimum.

The non-convexification effects of the penalization of intermediate density elements simply overshadows any other type of non-convexification introduced into the problem, mainly due to its severity and locality. Continuation methods are strongly recommended to overcome the problem of local minima, albeit its step and convergence criteria are left to the user depending on the type of application.

In this article, the authors present a comprehensive treatment of the sources of non-convexity in density-based topology optimization problems, with a focus on linear elastic compliance minimization. The authors put special emphasis on the potential penalization-like effects of various filtering techniques through a detailed mathematical treatment.

Topology optimization is a state-of-the-art technique for the innovative design of electromagnetic devices. The ON/OFF method is a typical approach for this purpose. However, the drawbacks of long iteration time and poor ability to express curved surfaces make the industry not shown their due interest so far in the ON/OFF method. The purpose of this paper is to study a novel ON/OFF method for topology optimization, which can bring feasible optimized shapes that are more friendly for industrial realization in a shorter time.

The proposed improved ON/OFF method uses structured triangular elements for finite element modeling because the triangular elements can more freely express shape features. Every four triangular elements are pieced together to form a square cell, each quadrilateral cell is associated with a binary value indicating the material state of the four triangular elements. The binary metaheuristic algorithms are used to optimize the material distribution. After the material filling for the elements based on the output of the metaheuristic algorithm, a two-step surface smoother will be performed as the postprocess to make the shapes more friendly for manufacturing.

The comparative numerical results on a benchmark topology optimization problem show that the proposed method can bring feasible optimized shapes that are more friendly for industrial realization in a shorter time. In addition, the speed and robustness of convergence, especially in the case of multiobjective topology optimization problem, are significantly improved.

A novel ON/OFF method for topology optimization is proposed. Compared with the traditional ON/OFF method, the proposed method is better in terms of searching efficiency and robustness. Moreover, the proposed method can provide feasible optimized shapes that are more friendly for industrial realization.

This study highlights the demand for low-cost and high accuracy products through the design and development of new 3D printing technologies. Besides, significant progress has been made in this field. A comparative study helps to understand the latest development in materials and future prospect of this technology.

Nevertheless, a large amount of progress still remains to be made. While some of the works have focused on the performances of the materials, the rest have focused on the development of new methods and techniques in additive manufacturing.

This paper critically evaluates the current 3D printing technologies, including the development and optimizations made to the printing methods, as well as the printed objects. Meanwhile, previous developments in this area and contributions to the modern trend in manufacturing technology are summarized briefly.

The paper can be summarized in three sections. Firstly, the existing printing methods along with the frequently used printing materials, as well as the processing parameters, and the factors which influence the quality and mechanical performances of the printed objects are discussed. Secondly, the optimization techniques, such as topology, shape, structure and mechanical property, are described. Thirdly, the latest development and applications of additive manufacturing are depicted, and the scope of future research in the relevant area is put forward.