Multi-objective Topology Research Articles

Multi-objective topology optimization of magnetic couplers for wireless power transfer

In this paper, the multi-objective topology optimizations of wireless power transfer (WPT) devices with two different coil geometries are proposed for obtaining the designs with good balance between transfer efficiency and safety. For this purpose, the proposed method adopts the normalized Gaussian network (NGnet) and Non-dominated Sorting Genetic Algorithm II (NSGA-II). In addition, the optimization under the different constraint on ferrite volume is carried out to verify its influence on optimization results. It has been shown that the proposed method successfully provides the Pareto solution to the design problem of the WPT device.

Multi-objective topology optimisation design of lattice structures with negative Poisson's ratio considering energy absorption and load-bearing characteristics

To make lattice structures have both load-bearing and energy absorption characteristics to protect the safety of personnel and equipment in the collision, this paper proposes a multi-objective topology optimisation method for the design of lattice structures with negative Poisson's ratio. The energy absorption and load-bearing characteristics of the lattice structure are characterised by negative Poisson's ratio and stiffness, respectively. A topology optimisation model is established to maximise the stiffness and negative Poisson's ratio of the lattice structure. The design optimisation of microscopic material is conducted by the energy homogenisation method. A modified optimality criteria method is employed to update design variables. The energy absorption and load-bearing characteristics of the optimised structure are tested and analysed by finite element simulation and compression experiment, respectively. The results show that the optimised lattice structure has both energy absorption and load-bearing characteristics. In general, the proposed method can provide a feasible reference for the topology optimisation design of anti-collision structures.

Multi-objective topology optimization of deep drawing dissimilar tailor laser welded blanks; experimental and finite element investigation

Laser welded blanks (LWBs) are semi-finished components typically manufacture by dissimilar materials, thicknesses, shapes, coatings, etc. After butt welding of the primary sheets, the product sheets are subjected to the sheet metal forming process. Formation of the heat-affected zones (HAZ) is typical in LWBs, which possess quite different mechanical properties than the base materials. Recently, laser beam technologies have been widely employed to weld different types of vehicles panels. In this study applying Nd:YAG laser welding, experimental and numerical investigations are carried out to evaluate the effects of process input factors on deep drawing process of LWBs. Laser beam power, welding speed, blank holder force (BHF), material properties, and friction coefficient are considered as process key input parameters. In addition, the laser welding and deep drawing processes were numerically simulated using Simufact Welding and Abaqus/Explicit software, Used the Simorgh supercomputer for heavy modeling calculations. Moreover, drawing depth, weld line movement, and energy absorption are taken into account as process main outputs or objective functions. Besides, using an advanced MATLAB code, multi objective optimization based on genetic algorithm is applied to determine the optimal design input parameters. It is observed that the critical stresses were taken place outside the weld zone and rupture due to high heat input of laser and metallurgical changes of the base metal occur in the pre-softening zone. In addition, the weld line displacement occurs as a result of plastic strain change of the weld joint that causes failure-prone zone creation as well as the adverse wrinkling. By considering weld line displacement and absorbed energy as multi-objective function, the optimal points is 1.15 mm and 0.21 KJ for weld line displacement and absorbed energy, respectively. Good agreement between the simulated and the experimental results revealed that the model would be appropriate for deep drawing of LWB process numerical simulation.

Multi-objective topology optimization of two-dimensional multi-phase microstructure phononic crystals

The band gap (BGs) of a material can be manipulated by tailoring its periodic microstructure. The phononic crystals (PnCs), representative of a periodically arranged structural material, are conventionally manufactured from single-phase or two-phase materials. In this study, we investigate the multi-objective topology optimization (MOTO) of periodic three-solid-phase PnCs. With a method of two-stage multi-objective genetic algorithm, the microstructures of the three-solid-phase PnCs were designed to exhibit the desired novel properties. Three case studies were obtained as follows: (1) maximum relative band gap width (RBGW) with a minimum mass, (2) maximum absolute band gap width (ABGW) at two different specified frequencies, and (3) maximum ABGW at specified mid-frequency. All the cases were effective for the MOTO of PnCs, and the Pareto optimal solution set could give the balance of the different competed objectives. Further, the principal mechanisms responsible for the creation of BGs, whether Bragg scattering or local resonance, are discussed. Moreover, comparing with the normal 2-phase materials, suchlike a wider lower-frequency BGs, some important advantages unveiled with the appearance of the three-solid-phase material.

Topology-optimized insulating facebrick with aerogel filling

This research presents the design of a new clay brick filled with aerogel. The design has been performed using multi-objective topology optimization that considers both stiffness and thermal conductivity. The current research uses the free-form design method of topology optimization with set boundary conditions for the evaluation of the stiffness and thermal conductivity. The internal structure of a standard-sized brick filled with aerogel is designed in this work. The article also offers numerical evaluations that compare the performance of the new optimized design to a standard full brick. A topology optimized-brick design is presented and shown to significantly improve the thermal insulation. Suggestions for future research include performing experimentally validations.

Characterization of fracture in topology-optimized bioinspired networks.

Designing strong and robust bioinspired structures requires an understanding of how function arises from the architecture and geometry of materials found in nature. We draw from trabecular bone, a lightweight bone tissue that exhibits a complex, anisotropic microarchitecture, to generate networked structures using multiobjective topology optimization. Starting from an identical volume, we generate multiple different models by varying the objective weights for compliance, surface area, and stability. We examine the relative effects of these objectives on how resultant models respond to simulated mechanical loading and element failure. We adapt a network-based method developed initially in the context of modeling trabecular bone to describe the topology-optimized structures with a graph-theoretical framework, and we use community detection to characterize locations of fracture. This complementary combination of computational methods can provide valuable insights into the strength of bioinspired structures and mechanisms of fracture.

Optimal design and thermal modelling for liquid-cooled heat sink based on multi-objective topology optimization: An experimental and numerical study

This work suggests a design method of liquid-cooled heat sink based on topology optimization. First, a multi-objective optimization problem is developed in order to manage the tradeoff between the minimization of fluid power dissipation and the maximization of heat exchange. The novel cooling channels with clear topology information are generated under both single-uniform and the multiple-non uniform heat source conditions. The effects of initial guess, weighting factor, and Reynolds number on the Pareto optimal solutions are discussed. Next, a full scale 3D conjugate heat transfer numerical model is built to test the flow and thermal performances of the heat sinks. The results show that the optimized cooling channel can achieve a lower thermal resistance and a higher Nusselts number in comparison to the conventional parallel channel, which means the optimal channel can remove more heat energy while the pumping power supply is minimum. Finally, both traditional parallel and topology optimized channel are manufactured by CNC machine and the high performance of the optimally designed heat sink is validated by conducting experimental tests.

Topology optimization and 3D printing of multimaterial magnetic actuators and displays.

Upcoming actuation systems will be required to perform multiple tightly coupled functions analogous to their natural counterparts; e.g., the ability to control displacements and high-resolution appearance simultaneously is necessary for mimicking the camouflage seen in cuttlefish. Creating integrated actuation systems is challenging owing to the combined complexity of generating high-dimensional designs and developing multifunctional materials and their associated fabrication processes. Here, we present a complete toolkit consisting of multiobjective topology optimization (for design synthesis) and multimaterial drop-on-demand three-dimensional printing for fabricating complex actuators (>106 design dimensions). The actuators consist of soft and rigid polymers and a magnetic nanoparticle/polymer composite that responds to a magnetic field. The topology optimizer assigns materials for individual voxels (volume elements) while simultaneously optimizing for physical deflection and high-resolution appearance. Unifying a topology optimization-based design strategy with a multimaterial fabrication process enables the creation of complex actuators and provides a promising route toward automated, goal-driven fabrication.

Structural Optimization design of marine hydraulic Tube clamp

The layout design and structure design of rubber elastic tube clamp have a direct impact on the vibration and noise characteristics of pipeline system, as well as the fatigue life of tube clamp itself and related parts in pipeline system. It is a typical multi-objective optimization design problem. How to design an elastic tube clamp that meets the requirements of stiffness, strength and fatigue life at the same time is an important issue in the design of marine pipeline system. In this paper, the structural optimization of rubber elastic tube clamps is studied by using the non-linear multi-objective topology optimization method.

A general multi-objective topology optimization methodology developed for customized design of pelvic prostheses

In this study, a multi-objective topology optimization method has been formulated and carried out for various resection types, with minimization of a weighted sum of the compliance (maximized stiffness) under six routine activities of daily life as the objective function and volume reduction as a constraint. Unique prosthetic geometries with low weight and remarkable strength closely matching the pelvic bone shape were obtained. The strength of the optimized implants was investigated through finite element analysis and it has been found that the initial geometries of the optimized implants could withstand the static loading conditions of various routine activities having less stress concentration areas. A 3D printed patient-specific topology optimized hemi-pelvic prosthesis has been designed based on the proposed method and implanted successfully in a patient with pelvic sarcoma. Therefore, pelvic prostheses can be designed and then manufactured via additive manufacturing technologies with the minimum material in less time and having robust mechanical fixation responses. Conclusively, the topology optimization method used for the design of pelvic prostheses improves the biomechanical performance of the implants with reduced weight and higher stiffness than the traditional implants. Including the topology optimization procedure in the phase of designing patient-specific pelvic implants is therefore, highly recommended.

A multi-objective optimization problem in mixed and natural convection for a vertical channel asymmetrically heated

This paper deals with a multi-objective topology optimization problem in an asymmetrically heated channel, based on both pressure drop minimization and heat transfer maximization. The problem is modeled by assuming steady-state laminar natural convection f low. The incompressible Navier-Stokes equations coupled with the convection-diffusion equation, under the Boussinesq approximation, are employed and are solved with the finite volume method. In this paper, we discuss some limits of classical pressure drop cost function for buoyancy driven flow and, we then propose two new expressions of objective functions: the first one takes into account work of pressure forces and contributes to the loss of mechanical power while the second one is related to thermal power and is linked to the maximization of heat exchanges. We use the adjoint method to compute the gradient of the cost functions. The topology optimization problem is first solved for a Richardson (Ri) number and Reynolds number (Re) set respectively to Ri ∈ {100,200,400} and Re = 400. All these configuration are investigated next in order to demonstrate the efficiency of the new expressions of cost functions. We compare two types of interpolation functions for both the design variable field and the effective diffusivity. Both interpolation techniques have pros and cons and give slightly the same results. We notice that we obtain less isolated solid elements with the sigmoid type interpolation functions.Then, we choose to work with the sigmoid and solve the topology optimization problem in case of pure natural convection, by setting Rayleigh number to {3×103,4×104,5×105}. In all considered cases, our algorithm succeeds to enhance one of the phenomenon modeled by the proposed cost functions without deteriorating the other one. The optimized design obtained suppresses any reversal flow at the exit of the channel. We also show that the thermal exchanges are improved by computing the Nusselt numbers and bulk temperature. We conclude that the new expressions of objective functions are well suited to deal with natural convection optimization problem in a vertical channel.

Multi-Objective Topology Optimization of a Magnetic Actuator Using an Adaptive Weight and Tunneling Method

This paper proposes a multi-objective optimization method using an adaptive weight determination scheme and tunneling method. To find the optimum designs that are evenly distributed on the Pareto front, the weights of different objective functions are adaptively determined by using the concept of a hyperplane so that new solutions can be gradually found in the objective space. In addition, to avoid locally optimized solutions that are dominated by other Pareto optimum designs, a tunneling method is employed in the optimization process. To confirm the effectiveness of the proposed method, topology optimization of the magnetic actuator is performed. The magnetic force and volume of the actuator are considered as two conflicting objective functions in the optimization problem, and Pareto optimum solutions that are evenly distributed in the objective space could be obtained.

Multi-Objective Topology Optimization of Rotating Machines Using Deep Learning

This paper presents the fast topology optimization methods for rotating machines based on deep learning. The cross-sectional image of electric motors and their performances obtained during a multi-objective topology optimization based on the finite-element method and genetic algorithm (GA) is used for training of the convolutional neural network (CNN). Two different approaches are proposed: 1) CNN trained by preliminary optimization with a small population for GA is used for the main optimization with a large population and 2) CNN is used for screening of torque performances in the optimization with respect to the motor efficiency.

Topology optimization of truncated cone insulator with graded permittivity using variable density method

Dielectrics with functionally graded material (d-FGM), which have spatially nonuniform dielectric properties, is effective to improve the insulation performance without complicating the structure. In the application of d-FGM, searching the optimal distribution of dielectric properties (permittivity or conductivity) is the most important goal, which however is difficult for conventional insulation design approaches. In this paper, the topology optimization technique is introduced to design a truncated cone insulator with permittivity FGM, which is to relieve local electric field (E-field) enhancement at the triple junctions. Firstly, a multi-objective topology optimization model is proposed using the variable density method. Secondly, the optimal values of several model parameters are determined based on the analysis of E-field uniformity. Finally, finite elements calculation demonstrates that the E-field uniformity is significantly improved for the topology-optimized permittivity FGM, and the E-field enhancement at triple junctions is strongly inhibited. It is thus expected that by applying the topology-optimized permittivity FGM insulator, the breakdown strength in gas or vacuum would be effectively improved.

A multiobjective topology optimization approach for cost and time minimization in additive manufacturing

SummaryThe ever‐present drive for increasingly high‐performance designs realized on shorter timelines has fostered the need for computational design generation tools such as topology optimization. However, topology optimization has always posed the challenge of generating difficult, if not impossible to manufacture designs. The recent proliferation of additive manufacturing technologies provides a solution to this challenge. The integration of these technologies undoubtedly has the potential for significant impact in the world of mechanical design and engineering. This work presents a new methodology which mathematically considers additive manufacturing cost and build time alongside the structural performance of a component during the topology optimization procedure. Two geometric factors, namely, the surface area and support volume required for the design, are found to correlate to cost and build time and are controlled through the topology optimization procedure. A novel methodology to consider each of these factors dynamically during the topology optimization procedure is presented. The methodology, based largely on the use of the spatial gradient of the density field, is developed in such a way that it does not leverage the finite element discretization scheme. This work investigates a problem that has not yet been explored in the literature: direct minimization of support material volume in density‐based topology optimization. The entire methodology is formulated in a smooth and differentiable manner, and the sensitivity expressions required by gradient based optimization solvers are presented. A series of example problems are provided to demonstrate the efficacy of the proposed methodology.

Multi-objective topology and geometry optimizationof statically determinate beams

The paper concerns topology and geometry optimization of statically determinate beams with arbitrary number of supports. The optimization problem is treated as a bi-criteria one, with the objectives of minimizing the absolute maximum bending moment and the maximum deflection for a uniform gravity load. The problem is formulated and solved using the Pareto optimality concept and the lexicographic ordering of the objectives. The non-dominated sorting genetic algorithm NSGA-II and the local search method are used for the optimization in the Pareto sense, whereas the genetic algorithm and the exhaustive search method for the lexicographic optimization. Trade-offs between objectives are examined and sets of Pareto-optimal solutions are provided for different topologies. Lexicographically optimal beams are found assuming that the maximum moment is a more important criterion. Exact formulas for locations and values of the maximum deflection are given for all lexicographically optimal beams of any topology and any number of supports. Topologies with lexicographically optimal geometries are classified into equivalence classes, and specific features of these classes are discussed. A qualitative principle of the division of topologies equivalent in terms of the maximum moment into topologies better and worse in terms of the maximum deflection is found.

Multi-objective BESO topology optimization for stiffness and frequency of continuum structures

Topology optimization of structures seeking the best distribution of mass in a design space to improve the structural performance and reduce the weight of a structure is one of the most comprehensive issues in the field of structural optimization. In addition to structures stiffness as the most common objective function, frequency optimization is of great importance in variety of applications too. In this paper, an efficient multi-objective Bi-directional Evolutionary Structural Optimization (BESO) method is developed for topology optimization of frequency and stiffness in continuum structures simultaneously. A software package including a Matlab code and Abaqus FE solver has been created for the numerical implementation of multi-objective BESO utilizing the weighted function method. At the same time, by considering the weaknesses of the optimized structure in single-objective optimizations for stiffness or frequency problems, slight modifications have been done on the numerical algorithm of developed multi-objective BESO in order to overcome challenges due to artificial localized modes, checker boarding and geometrical symmetry constraint during the progressive iterations of optimization. Numerical results show that the proposed Multiobjective BESO method is efficient and optimal solutions can be obtained for continuum structures based on an existent finite element model of the structures.

Research on Multiobjective Topology Optimization of Diesel Engine Cylinder Block Based on Analytic Hierarchy Process

There are alternating impact loads for the diesel engine cylinder block. The topology optimization of the extreme single‐working condition cannot guarantee its overall mechanical performance, and the traditional multiworking condition optimization has the problem that the weight coefficients are difficult to determine. Thus, a multiobjective topology optimization method based on analytic hierarchy process is proposed. Firstly, the static, dynamic characteristics and structure efficiency are calculated by the finite element analysis which indicates the direction of topology optimization for the cylinder block. The hierarchical structure model of topology optimization, including 12 weighting coefficients, is constructed considering static multiworking condition stiffness and dynamic multiorder natural frequency. The comprehensive evaluation function for the cylinder block is established by the compromise programming method and the weight coefficients are determined based on analytic hierarchy process. The optimization mathematical model is established and the multiobjective topology optimization of the cylinder block is carried out. The optimization results show that the proposed method can take into account structural multiworking condition performance, which has obvious advantages over the single objective topology optimization. The simulation results show that the static and dynamic characteristics are improved to some extent and the overall mechanical performance of the new model is more uniform with a 5.22% reduction in weight. It shows that the topology structure of the cylinder block is more reasonable.

Lightweight Design of Multi-Objective Topology for a Large-Aperture Space Mirror

For a large-aperture space telescope, one of the key techniques is the method for designing the lightweight primary mirror assembly (PMA). In order to minimize the mirror surface error under axial gravity, lateral gravity, and polishing pressure at the same time, a method for topology optimization with multi-objective function combined with parametric optimization is introduced in this paper. The weighted compliance minimum is selected as the objective function to maximum the mirror structural stiffness. Then sensitivity analysis method and size optimization are used to determine the mirror structure parameters. Compared with two types of commonly used lightweight configurations, the new configuration design shows obvious superiority. In addition, the surface figure root mean square (RMS) of the mirror mounted by given bipod flexure (BF) under 1 g lateral gravity is minimized only with a value of 3.58 nm, which proves the effectiveness of the design method proposed in this paper.

Data mining based on clustering and association rule analysis for knowledge discovery in multiobjective topology optimization

Optimum design problems, including structural optimization problems, often include multiple objectives. A multiobjective optimization problem usually provides a number of optimal solutions, called non-dominated solutions or Pareto-optimal solutions. In multiobjective topology optimization scenarios, decision makers face the challenging task of choosing the most effective solution that meets their needs; serial comparisons among a set of Pareto-optimal solution are cumbersome, as are trial-and-error attempts to find an appropriate solution among a host of alternatives. On the other hand, the recent integration of data mining techniques in multiobjective optimization methods can provide decision makers with important, highly pertinent, and useful knowledge.In this paper, we propose a data mining technique for knowledge discovery in multiobjective topology optimization. The proposed method sequentially applies clustering and association rule analysis to a Pareto-optimal solution set. First, clustering is applied in the design space and the result is then visualized in the objective space. After clustering, detailed features in each cluster are analyzed based on the concept of association rule analysis, so that characteristic substructures can be extracted from each cluster of solutions. In four numerical examples, we demonstrate that the proposed method provides pertinent knowledge that aids comprehension of the key substructures responsible for one or more desired performances, thereby giving decision makers a useful tool for discovery of particularly effective design solutions.