Design of multiple materials structure based on an explicit and implicit hybrid topology optimization method

Topological optimization is an innovative method to realize the lightweight design. This paper proposes a hybrid topology optimization method that combines the SIMP (solid isotropic material with penalization) method and genetic algorithm (GA), called the SIMP-GA method. In the method, SIMP is used to update the chromosomes, which can accelerate convergence. The filtering scheme in the SIMP method can filter unconnected elements to ensure the connectivity of the structure. We studied the influence of varying the filtering radius on the optimized structure. Simultaneously, in the SIMP-GA method, each element is regarded as a gene, which controls the population number to a certain extent, reduces the amount of calculation, and improves the calculation efficiency. The calculation of some typical examples proves that the SIMP-GA method can obtain a better solution than the gradient-based method. Compared with the conventional genetic algorithm and GA-BESO (Bi-directional Evolutionary Structural Optimization) method, the calculation efficiency of the proposed method is higher and similar results are obtained. The innovative topology optimization method could be an effective way for structural lightweight design.

This work puts forward an explicit isogeometric topology optimization (ITO) method using moving morphable components (MMC), which takes the suitably graded truncated hierarchical B-Spline based isogeometric analysis as the solver of physical unknown (SGTHB-ITO-MMC). By applying properly basis graded constraints to the hierarchical mesh of truncated hierarchical B-splines (THB), the convergence and robustness of the SGTHB-ITOMMC are simultaneously improved and the tiny holes occurred in optimized structure are eliminated, due to the improved accuracy around the explicit structural boundaries. Moreover, an efficient computational method is developed for the topological description functions (TDF) of MMC under the admissible hierarchical mesh, which consists of reducing the dimensionality strategy for design space and the locally computing strategy for hierarchical mesh. We apply the above SGTHB-ITO-MMC with improved efficiency to a series of 2D and 3D compliance design problems. The numerical results show that the proposed SGTHB-ITO-MMC method outperforms the traditional THB-ITO-MMC method in terms of convergence rate and efficiency. Therefore, the proposed SGTHB-ITO-MMC is an effective way of solving topology optimization (TO) problems.

Topology optimization of damping material for reducing resonance response based on complex dynamic compliance

An integrated method of topological optimization and path design for 3D concrete printing

This article presents the application of the TOSS (topology optimization for stiffness and strength) algorithm, a hybrid optimization strategy for topology optimization, used for the design of a strip foundation as a basic geotechnical structure. One of the challenges of this field is to improve structural performance by using less material than conventional structures. Therefore, the SIMP (solid isotropic material with penalization) is applied to optimize the foundation concerning its deformational behavior. The downstream SKO (soft kill option) then solves for optimality concerning the foundation's stress distribution. Numerical experiments with the TOSS algorithm reveal great potential for material savings. The coupled solution presents the benefit of reducing emissions due to material savings of more than 20% in comparison to the individual SIMP and SKO algorithms. A positive by‐product of the method is that stress peaks under the foundation are reduced due to the homogenization of stresses as a result of SKO optimization, thus creating the conditions for better durability of the foundation.

In this work, an acoustic topology optimization method for structural surface design covered by porous materials is proposed. The analysis of acoustic problems is performed using the isogeometric boundary element method. Taking the element density of porous materials as the design variable, the volume of porous materials as the constraint, and the minimum sound pressure or maximum scattered sound power as the design goal, the topology optimization is carried out by solid isotropic material with penalization (SIMP) method. To get a limpid 0–1 distribution, a smoothing Heaviside-like function is proposed. To obtain the gradient value of the objective function, a sensitivity analysis method based on the adjoint variable method (AVM) is proposed. To find the optimal solution, the optimization problems are solved by the method of moving asymptotes (MMA) based on gradient information. Numerical examples verify the effectiveness of the proposed topology optimization method in the optimization process of two-dimensional acoustic problems. Furthermore, the optimal distribution of sound-absorbing materials is highly frequency-dependent and usually needs to be performed within a frequency band.

Recently, the necessity of reducing the probability of spread of viruses has fostered the creativity of engineers to develop tools that would allow actions of every-day life to be executed differently. Moreover, the maturity of the Fused Filament Fabrication (FFF) technology and the associated low costs has allowed creative solutions to be produced and used in real-life applications. A distinctive example is represented by the common action of opening a door. Since hands are a typical vector of contamination for viruses such as Coronavirus, hands-free devices aim at making use of the existing structure and kinematic to complete the same action in a different fashion. Typically, the mechanical and manufacturing requirements of these devices include a suitable stiffness-to-mass ratio, a reduced printing time as well as the minimization of supports which need to be removed in a post-printing phase. To tackle all these requirements a dedicated topology optimization (TO) method can be used since the preliminary design phase. Several design requirements of different nature can be included in the problem formulation: mechanical ones, like mass and stiffness, and manufacturing ones, like drawing direction or minimum member size. In this paper, a feasibility study on a hands-free 3D printed door opener has been carried out by means of the Solid Isotropic Material with Penalization (SIMP) method for TO and its CAD-compatible variant, i.e., the SIMP approach reformulated in the framework of non-uniform rational basis spline hyper-surfaces. The aim of the study is to identify optimal solutions to be adapted to a real-case scenario wherein different loading cases and manufacturing constraints are evaluated. Different optimal solutions are obtained, reconstructed to be compatible with CAD environment and the optimized geometry numerically assessed. Finally, the optimal solutions are also evaluated with respect to indicators such as printing time, total filament mass and mass of the supports required by the printing process.

A several cycles of design-verification-modification are needed during traditional design, which is very time-consuming. Topology optimization is rapidly expanding in the recent years in the field of structural mechanics. Currently it is widely applied to structural design. The combination of topology optimization and sizing and/or shape optimization has been adopted for flight vehicle structural design, which results possible better designs. In the paper, continuum structural topology optimizations as well as size optimization are combined for a folding wing structural design. A structure optimization problem is established using Solid Isotropic Material with Penalization (SIMP) method, it consists of the thickness variable of the skin and the relative element density variables of the tip part of the folding wing. The design objective is to minimize the compliance of the whole structure, and the constraints are structural mass constraints and stress constraints. The problem was solved based on commercial software package HyperWorks™. The resulting design shows that a new tip structure which satisfies the requirements of stiffness and strength was reconstructed.

This paper discusses a geometrical optimization method for thermoelectric generators. Our method provides the optimized geometry in accord with various arbitrary conditions such as types of materials, volume of materials, temperatures of installation position, and shape of installation position. It has the potential to contribute to improving thermoelectric devices in supporting design stages. By establishing the coupled equations of state for the thermoelectric problem, an analytical model subject to these equations is introduced that mimics the closed circuit composed of the thermoelectric materials, electrodes and a resistor. The total electric power lost through the resistor is formulated as an objective function for optimization. The proposed optimization method for thermoelectric generators is implemented as a geometrical optimization method using the solid isotropic material with penalization (SIMP) method used in topology optimizations. Simple relations are formulated between the density function of SIMP method and physical properties of thermoelectric material. Sensitivity analysis for the objective function is formulated with respect to the density function and the adjoint equations required for calculating it. Depending on the sensitivity, the density function is updated using the method of moving asymptotes, which has numerous benefits in various optimization problems by virtue of its combination with topology optimization. Finally, the numerical examples are provided to demonstrate the validity of our method.

Design of component structure in assemblies for simultaneously regulating contact pressure distribution and natural frequencies

The high-temperature superconducting magnet (HTS) is one of the core technologies of a superconducting maglev. The effects of multiphysics fields including electromagnetic, mechanical, and thermal should be taken into consideration in design. Traditional design methods rely on the initial configuration and the engineer's experience and only consider the design for the heat conduction performance or the structure strength, which often significantly increases the weight. To solve the above problems, based on COMSOL Multiphysics software, the mathematical model of topology optimization of the main support was established with electromagnetic force and thermal stress as the input loads. The objective functions were assigned to total strain energy and heat leakage, combined with stress value and volume fraction constraint conditions. The solid isotropic material with penalization (SIMP) method was used to carry out the topological analysis of multiphysics. Finally, the innovative structure of main support is obtained. Through finite element analysis of multiphysics fields, the heat leakage, the max Von-Mises stress, and weight were taken as evaluation indexes to compare the optimal structure performance. The results show that the method adopted in this paper can reduce the heat leakage by 61.7% while reducing the weight of the main support by 85%, and the max Von-Mises stress does not exceed the yield limit of the material. The work of this paper provides a theoretical foundation for the engineering design of the heat conduction structure of a HTS magnet.

This work proposes an improved topology optimization model for optimizing continuum structures with self-weight loading conditions. A modified Solid Isotropic Material with Penalization (SIMP) model is proposed to avoid the parasitic effect. At the same time, the penalty factor of the SIMP model is increased to maintain the activeness of the prescribed volume constraint and to drive the design domain to binary distribution. The optimization objectives include minimizing the total strain energy of the design domain and minimizing the total displacement of the fixed domain. The shape optimization procedure is used to furtherly enhance structural performance. The whole optimization procedure is implemented with a two-dimensional model under the loading conditions of self-weight and external force. The classic MBB beam and self-weight arch are utilized to verify the proposed method, and conceptual layout designs of the steel structure bridge are conducted. It is proved that the proposed model is effective for topology optimization of continuum structures including self-weight. And it is found that the optimal structural topology is affected by the ratio of the external force to self-weight.

Topology optimization can devise structures with superior performance, while the results produced by topology optimization are often very complex and difficult to be manufactured directly. The additive manufacturing is a free-form manufacturing technique in which the component is built in a layer-by-layer manner. The integration of topology optimization and additive manufacturing technologies has the potential to bring significant synergy benefits. However, typical topology optimization algorithms have not considered the unique manufacturing limitations of additive manufacturing. This article focuses on the topology optimization for additive manufacturing considering self-supporting constraint based on the Solid Isotropic Material with Penalization (SIMP) framework. An explicit self-supporting constraint model is constructed, and the proposed method realizes self-supported by gradual evolution of supporting structures. The corresponding sensitivity analysis is investigated, which requires less computational cost and can be solved in parallel. Besides, a directional sensitivity filter is specifically proposed to promote the evolution of supporting structures. The performance and functionality of the proposed method is illustrated with three compliance minimization problems. All cases achieve self-supported successfully, and the solutions own good manufacturability.

Novel thermal management of electronic devices by nano enhanced phase change materials: A numerical study

Experimental evaluation of topologically optimized manipulator-link using PLC and HMI based control system