Topology Optimization Results Research Articles

Lightweight Design of a Rear Axle Connection Bracket for a Heavy Commercial Vehicle by Using Topology Optimisation: A Case Study

An important design challenge of modern vehicles is mass reduction. Hence in many cases, mechanical design of vehicle components covers different optimization processes. One important structural optimization technique which is highly utilised in weight reduction applications is the topology optimization. This paper contains a multi-stage optimization based on the topology and design optimizations. During this study, the mechanical design of a rear axle-chassis connection bracket is achieved. First of all, the design load of the bracket was determined through a multibody dynamics analysis. This load case was determined among various driving conditions and the most critical load case was indicated as the design load of the bracket. This process was executed by using Adams/Car™ software. Subsequently, a design volume for the bracket was decided, which specifies the domain of topology optimization that will be employed later on. The determination of the design domain was made by considering the structural position of the design component, the neighbor components of the rear axle and the chassis. In this manner, the basic shape and dimensions of the bracket were created. The unnecessary volume of the draft design, which is not properly loaded under the design conditions was determined and removed from the design by means of topology optimization. The topology optimization was run in topology optimization module of ANSYS® Workbench 18.2 finite element analysis (FEA) software package. In the light of the primary shape obtained from the topology optimization study, a producible initial design model was built. This model was then subjected to FE analysis under the same circumstances with the draft model, in order to perform strength and deformation assessments of the initial design. Correspondingly, the critical regions were determined where stress concentrations were observed. The model was updated in a way that the stress values were reduced in these regions through the response surface methodology (RSM). The comparisons between the result and the initial geometries reveal that the mass of the connection bracket was reduced by 63%. Besides, the total deformation which was dropped by the design optimization is 13% lower than the initial design that was generated with the influence of topology optimization result.

A critical evaluation of topology optimization results for strut‐and‐tie modeling of reinforced concrete

AbstractDefining a suitable truss model is one of the most important steps of applying the strut‐and‐tie modeling (STM) method to design D‐regions in reinforced concrete (RC) structures. The truss model is a discrete representation of the stress field developed within a region of a concrete element. Topology optimization (TO) methods have been investigated by researchers for about two decades to generate suitable models for the STM method. Several truss models and numerous continuum TO results that could serve as an inspiration for suitable truss models have been proposed. However, limited attention has been paid to the evaluation of various TO results in the perspective of the STM method. As a result, it is at present unclear to what extent TO results offer a benefit for STM modeling, and which method should be preferred. In order to address this gap, an automatic and objective evaluation procedure is proposed in this paper. First, a TO result extraction method is proposed to systematically convert optimized topologies to truss‐like structures. Next, based on the extracted structures, three evaluation measures are formulated to evaluate TO results. These measures indicate whether an analyzable truss model could be extracted, to which extent tensile stress regions are covered by tensile ties and how economical the design will be. The effectiveness of the proposed evaluation procedure is validated using known STM solutions. Subsequently, the evaluation procedure is applied to 23 TO results from the literature, covering three different design problems. Most TO results show a good performance in covering tensile regions and would result in economical designs, and some undesired topologies are also identified by the evaluation method. Nevertheless, the use of continuum TO is most hampered by difficulties in identifying a suitable truss from the TO results.

Considerations on Topology Optimization of Magnetic Shield Structure for Control of Magnetic Energy

In this paper, we present a topology optimization analysis of a magnetic shield in three dimensions. We employ the density method in topology optimization analysis, which design distribution of material using non-dimensional density. In the topology optimization, checkerboard pattern and gray scale make difficult to manufacture. With the density method, filtering is applied to the sensitivity to prevent the appearance of a checkerboard pattern. Penalty parameter is introduced as multiplier of non-dimensional density, it is possible to adjust gray scale. Although technical papers related to penalty parameter can be seen, it is difficult to find research papers that have considered the relation between penalty parameter and gray scale. Therefore, in this study, we investigate the influence of the penalty parameter for the result of topology optimization.

Multi-objective optimization of crashworthiness of vehicle front longitudinal beam

Front longitudinal beam (FLB) is an important structure for the analysis of force transmission and energy absorption path in different crashing scenarios. In the present paper, the finite element (FE) model of a full-scale vehicle yun-100 Zotye is employed to explore the energy absorption of FLB, and aiming at its poor energy absorption problem, circular beam was used as the original topology optimization space of FLB. The advantages of both static and dynamic topology optimization methods are fully considered, and a variable density method is combined with a hybrid cellular automaton (HCA) method. The substructure dissipated energy and force for frontal crash in a full-scale vehicle are obtained at a speed of 13.8 m/s. The maximum stiffness in axial is obtained through the static topology optimization method and the maximum energy-absorbing structure of FLB which is satisfied with axial strength obtained through the dynamic topology optimization method. According to the results of topology optimization, a multi-cell thin-walled structure is interpreted as the novel FLB. A parametric study on geometric parameters is also performed to explore their effects on crashing characteristics of novel FLB, and it is found that they significantly influenced the crashworthiness of multi-cell thin-walled structure (especially the absorption of energy). Furthermore, in order to maximize the characteristics of novel FLB, a multi-objective optimization process is carried out using non-dominated sorting genetic algorithm (NSGA-II). The optimized FLB after multi-objective optimization is applied to Zotye of 100% vehicle frontal crash. The results showed that the peak value of acceleration decreased by 10.3% and the mass of the optimized FLB reduced to 0.59 kg. It indicated that the optimized FLB manifested excellent crashworthiness and better protective characteristics.

Topology optimization of fins for energy storage tank with phase change material

Six models based on different fin configuration of the energy storage tank with phase change material were established. The fin structure of model 3 is designed by topology optimization method. The thermal storage and release process of the six models were calculated by numerical simulation method. The results show that according to the thermal storage and release process of model 2, fin of model 3 is designed by topology optimization method. Thermal storage and release process of model 3 are both satisfactory agreement with the topology optimization results. Uniformity of temperature and liquid fraction is also significantly improved. Moreover, the model 3 can reduce the thermal storage time by 70% compared to model 2 and reduce the thermal release time by 81%. Furthermore, by comparison with all the 6 models, model 3 with the fin design based on the topology optimization method is found to have the significant advantages of less fins, metal saving, and low weight.

The parameterized level set method for structural topology optimization with shape sensitivity constraint factor

In recent years, the parameterized level set method (PLSM) has attracted widespread attention for its good stability, high efficiency and the smooth result of topology optimization compared with the conventional level set method. In the PLSM, the radial basis functions (RBFs) are often used to perform interpolation fitting for the conventional level set equation, thereby transforming the iteratively updating partial differential equation (PDE) into ordinary differential equations (ODEs). Hence, the RBFs play a key role in improving efficiency, accuracy and stability of the numerical computation in the PLSM for structural topology optimization, which can describe the structural topology and its change in the optimization process. In particular, the compactly supported radial basis function (CS-RBF) has been widely used in the PLSM for structural topology optimization because it enjoys considerable advantages. In this work, based on the CS-RBF, we propose a PLSM for structural topology optimization by adding the shape sensitivity constraint factor to control the step length in the iterations while updating the design variables with the method of moving asymptote (MMA). With the shape sensitivity constraint factor, the updating step length is changeable and controllable in the iterative process of MMA algorithm so as to increase the optimization speed. Therefore, the efficiency and stability of structural topology optimization can be improved by this method. The feasibility and effectiveness of this method are demonstrated by several typical numerical examples involving topology optimization of single-material and multi-material structures.

Research on Lightweight Design and Indirect Hot Stamping Process of the New Ultra-High Strength Steel Seat Bracket

Aiming at the need for lightweight requirements of the electric bus components, combined with the performance advantages of the hot stamping ultra-high strength steel, a new type of seat bracket structure is proposed. The new structure was analyzed by finite element method and the variable density topology optimization results. Subsequently, the new seat bracket was manufactured by the indirect hot stamping process. The results showed that the new type of seat bracket can reduce the weight by 17.04% after topology optimization, which achieved the goal of lightweight design of the structure. After indirect hot stamping, the bottom of the seat bracket microstructures were mainly martensite and the ultimate tensile strength was about 1560 MPa, the microhardness was equally distributed at about 513.5 HV. Finally, according to the stiffness check test, the seat bracket satisfied the user requirements.

Topology optimization of thermal structure for isotropic and anisotropic materials using the element-free Galerkin method

ABSTRACTA numerical model of topology optimization for isotropic and anisotropic thermal structures was established by combining the element-free Galerkin (EFG) method and the rational approximation of material properties model. The relative density of EFG nodes was defined as the design variable, and the moving least-squares shape function was used to construct the relative density of calculation points. The EFG topology optimization model of anisotropic thermal structure was verified by benchmark examples based on the finite element method (FEM). The effects of the orthotropic factor and off-angle on EFG topology optimization results were studied. The results show that EFG optimal structures have better heat dissipation performance, and the boundary profiles are clearer than with FEM even without filtering techniques, enabling manufacture using 3D printing technology. The proper topology thermal structure can be obtained by adjusting the orthotropic factor and off-angle, thus improving the heat dissipation performance of the thermal structure.

A Contrastive Study of Two Heaviside-based Morphological Filters

Morphological filters can be used to eliminate the numerical instabilities in topology optimization results, including the checkerboard patterns, mesh-dependence and intermediate densities. In this paper, two morphological filters, namely Type 1 and Type 2 filters are constructed according to the morphology-based restriction schemes. Type 1 filters are constructed using the Heaviside filter and the improved Heaviside filter proposed by Sigmund and, Type 2 filters are constructed using the Heaviside filter and the improved Heaviside filter proposed by Guest. The optimization effects of the two kinds of morphological filters are investigated, including the convergence, the ability to obtain discrete designs, iteration times and compliances. Test results show that open and close filters exhibit better performances than the advanced filters, and the advanced filters are inclined to produce instabilities during the optimization process.

Study on Topology Optimization of Constrained Damping of Commercial Vehicle Floor

The constrained damping is often used to improve the vibration characteristics of the floor of commercial vehicles. In order to obtain a reasonable layout of the constrained damping of the floor, the topological optimization design of the constrained damping on floor was conducted using the ESO (evolutionary structural optimization) method. Targeting the maximization of the modal loss factor and the amount of material as constraint condition, the joint simulation analysis is carried out with MATLAB and NASTRAN. In order to analyze the influence of sensitivity filter radius parameters on topology optimization results, the finite element model of rectangular plate was established and different filter radius parameters were set up for simulation analysis. The results show that the modal loss factor of the structure increases first and then decreases with the number of iterations. When the sensitivity filtering radius is increased, the modal loss factor of the structure is also increased first and then decreased. A clear damping boundary and a structural modal loss factor can be obtained when the sensitivity filtering radius is greater than 10 times the element size. The results based on rectangular plate are applied to the cab floor, and the first and third orders are optimized. The first order modal loss factor increases 3.7% and the third order is improved by 9.2% when the material content is 50% of the total laying. The effect of optimization is obvious.

Crash Model Order Reduction for Efficient Topology Optimization Using the ESLs Method

This paper presents an efficient structural topology optimization strategy for crashworthiness. The proposed method combines the equivalent static loads (ESLs) method with the crash model order reduction method. The ESLs method transforms crashworthiness topology optimization problems into a series of linear static topology problems. The crash model order reduction scheme is applicable to speed up the crash simulation. Therefore, the crashworthiness topology optimization is performed in a reduction manner and the efficiency is improved. The topology optimization results are filtered into a black-white design for the crash simulation to avoid the element distortion problem. The process is repeated until the convergence criteria is satisfied. The effectiveness of proposed method is demonstrated by investing a numerical example. The results show that, the proposed method can efficiently solve structural topology optimization problems for crashworthiness.

An approach for topology optimization of damping layer under harmonic excitations based on piecewise constant level set method

The topology optimization of a thin plate structure with bounded damping layer patches under external harmonic excitations to suppress the vibrations of specified points in the plate is investigated. The piecewise constant level set (PCLS) method is applied to represent the region with damping material and the region only with base material. Applying Melosh-Zienkiewicz-Cheung (MZC) element, the stiffness matrix, the mass matrix and the damping matrix are expressed in detail, where the global non-proportional damping matrix is considered. The functional derivative of the objective function (the squared vibration amplitudes of specified points in a plate) with respect to the PCLS function is deduced, by introducing the adjoint problems and applying matrix sensitivity analysis. The quadratic penalty method and the total variation regularization are utilized to fulfill the volume constraint and to avoid checkerboard patterns, respectively. A penalty gradient algorithm is proposed. In numerical experiments, three rectangular plates with different boundary conditions and locations of the external excitations are investigated. Effects of the excitation frequency as well as the damping coefficients on topology optimization results are also discussed.

An Efficient Topology Optimization Strategy for Structural Crashworthiness Using Model and ESLs Reduction Method

This paper presents an efficient structural topology optimization strategy for crashworthiness. Although equivalent static loads (ESLs) provides a relatively effective way to solve nonlinear dynamic response topology optimization problems, efficiency is still required to improve. To overcome above disadvantage, the proposed method combines the ESLs with model reduction (MR) method. The ESLs method transforms crashworthiness topology optimization problems into a series of linear static topology problems. The model reduction scheme is applicable to reduce the linear matrix equation and ESLs to interface degrees of freedom (DOFs), by selecting interface DOFs between design and non-design space as master DOFs. Therefore, the linear static topology optimization is performed in a reduction manner and the efficiency is improved. The topology optimization results are filtered into a black-white design for the crash simulation to avoid the element distortion problem. The process is repeated until the convergence criteria is satisfied. A numerical example is used to verify the reliability of the proposed method. The results are compared with the dynamic response optimization method using ESLs (ESLSO). The results show that, the proposed method can efficiently solve structural topology optimization problems for crashworthiness.

Optimizing Weight of Housing Elements of Two-stage Reducer by Using the Topology Management Optimization Capabilities Integrated in SOLIDWORKS: A Case Study

This paper presents the results of a conducted topology management optimization study based on the finite element analysis on a two-stage spur gear reducer housing body and cover using the SOLIDWORKS Simulation module. The main goal of the study is to optimize the overall weight of the reducer by thinning specific areas of the casted gearbox housing elements according to the calculated minimal strain energy. The topology optimization algorithm that is used in current research gives an optimal structural shape of the housing elements of the reducer with the largest stiffness, considering the given amount of mass that will be removed from the initial design space. The complete sequence of steps for conducting the topology management optimization study is shown, taking into account the constraints arising from the construction features and the method of manufacturing the housing elements of the gear reducer. Conclusions on the use of the topology optimization results are given and potential directions for further development of the approach are also identified.

Messing with boundaries - quantifying the potential loss by pre-set parameters in topology optimization

Additive manufacturing can increase the flexibility in the design phase of product development and that, in its turn, has changed the designer’s way of thinking. The design problem has reformulated; from designs that were not possible to be constructed, due to lack of equipment and technology, to constructions that the designer could not think to design. Topology optimization and generative design are useful tools in the hands of designer that can help him/her in the pursuit of the global optimum of a construction and in the choice of an alternative design solution respectively. However, topology optimization results are always depended on the given boundary conditions and restrictions. In other words, the designer’s decisions can affect the results of topology optimization and can easily lead to a local and not a global solution. In this paper, an identification and categorization of the most important parameters, that can affect the topology optimization results, were conducted. The main focus of the implemented research was on the pre-processing of topology optimization and especially on the designer’s decisions. The applied topology optimization approach here was a simple compliance optimization based on the SIMP interpolation methodology (Solid Isotropic Material with Penalization) and it was executed with the use of the commercial software Tosca (Abaqus). Different alternative designs of a wall bracket were used as a case study to test the sensitivity of the optimization algorithm and quantify the potential loss.

РАЗРАБОТКА АЛГОРИТМА ОТОБРАЖЕНИЯ РЕЗУЛЬТАТОВ ТОПОЛОГИЧЕСКОЙ ОПТИМИЗАЦИИ ПРИ РЕШЕНИИ ДВУМЕРНЫХ ЗАДАЧ СТАЦИОНАРНОЙ ТЕПЛОПРОВОДНОСТИ

РАЗРАБОТКА АЛГОРИТМА ОТОБРАЖЕНИЯ РЕЗУЛЬТАТОВ ТОПОЛОГИЧЕСКОЙ ОПТИМИЗАЦИИ ПРИ РЕШЕНИИ ДВУМЕРНЫХ ЗАДАЧ СТАЦИОНАРНОЙ ТЕПЛОПРОВОДНОСТИ

Topology optimisation design of mechanical tee backsheet

A finite element model of ASTM 114.3 mechanical tee backsheet is established by using the finite element software ANSYS. The stress distribution of backsheet under pretension force load is obtained through the strength analysis, and based on it, a topology optimisation calculations of backsheet is analysed. According to the topology optimisation results, the backsheet structure is redesigned and the finite element analysis to it shows that reducing the volume of the model of the backsheet while improving its stress distribution, the maximum equivalent stress is reduced and the enhanced chip reliability.

Topological design of compliant orthogonal displacement amplification mechanism under the unidirectional input force

The orthogonal displacement amplification mechanism is used to output and amplify the displacement perpendicular to the direction of the input force, and its configuration often uses a typical bridge-type. However, the bridge-type amplifier to achieve orthogonal shift conversion must enter the bidirectional symmetric input forces, otherwise the output will produce parasitic displacement. In view of this problem, the topology optimization method is used to find the new configuration of the displacement amplification mechanism, so that it can still realize the orthogonal displacement transformation under the unidirectional input force condition. Based on the solid isotropic material with penalization (SIMP) topological description method, the ratio of output and input displacements is maximized as the objective function, the ratio of parasitic displacement and output displacement as one of constraint functions, and the topological optimization mathematical model of the compliant orthogonal displacement amplifier is established under the unidirectional input force. The sensitivity information of the objective and constraint functions is deduced by the adjoint matrix method, and the optimization problem is solved by the method of moving asymptotes (MMA). The topology optimization results of orthogonal displacement amplifier are given through numerical examples, and the effect of spring stiffness on the topology optimization result is also discussed. Finally, the parasitic motions of the displacement amplification mechanism obtained from topology optimization and the bridge-type amplification mechanism are compared through the finite element analysis and experiment. Finite element simulation and experiment confirm the correctness and validity of the proposed method.

Topology optimization in ROPS-safe design process of operator cabin for forestry, agricultural and construction machinery

ROPS (roll over protective structure) and FOPS (falling objects protective structure) today are mandatory elements of every modern operator cabin for forestry, agricultural, construction and other machinery. This passive safety structures, integrated into cabin, can save life of the operator during rollover and heavy objects falling accident. Usually this structures consists of a supporting frame, capable of withstanding all the loads, which are occurring in machine accident. These elements, besides their main purpose, should satisfy additional requirements: not to cut operator visibility range, allow wide doorway for working and emergency doors and so on. Also initial design style solution restricts possible arrangement for load-bearing elements of the ROPS. Last decades in ROPS design process engineers extensively use explicit finite element technique to predict behavior and fitness of the ROPS structure by numerical simulation of rollover loads. This greatly reduce the costs of experiments, allowing to exclude dozens and hundreds of poor solutions at early stage of design without building expensive prototypes. However, uneven search of construction solution, even with support of numerical simulations, can be very time consuming. This work describes two-stage optimization technique, including topology and parametric optimization, which significantly reduce amount of structure variants, analyzed in ROPS design process. Therefore, optimization is an alternative to convenient way of inheritable and intuitive way of design. Topology optimization method with specially built finite element model of the forestry machine cabin used to find the most beneficial loadpaths for ROPS load bearing. Then, simplified shell-beam finite element model built, using results of topology optimization, and a parametric optimization technique used to find optimal cross-sections dimensions for main load-bearing elements of the protection structure. Finally, detailed shell model of the whole cabin elaborated and verified using standard explicit finite element simulations of all ROPS loadcases. Final simulations proved the strength of the designed ROPS structure and give confidence in successful experiment tests. The main advantages of the described two-stage optimization technique are significant reduction of considered variants due to exclude of inappropriate solution in advance, initial design style solution is not changed.

Lightweight design of turnover frame of bridge detection vehicle using topology and thickness optimization

Turnover frame is one of the core connection parts of the bridge detection vehicle. Its performances, including stiffness, manufacturability and durability, are essential for the bridge detection vehicle. Lightweight of turnover frame can decrease the total vehicle weight, which is well conformed to the Chinese national standard GB 1589–2016 (Limits of dimensions, axle load and masses for motor vehicles, trailers and combination vehicles). In this paper, the methods of topology and thickness optimization are utilized to design a new turnover frame. Firstly, the finite element (FE) models of original turnover frame and up mechanism are created, and then the von Mises stress and deformation are obtained. The FE results are validated by the stress experiment of the turnover frame, the maximum error is 7.8% relative to experiment results. Secondly, a novel layout of turnover frame is obtained using solid isotropic microstructure with penalization (SIMP) method under multi-conditions. The thickness optimization is carried out based on topology optimization results. The manufacturability and functionality are considered for optimized results. Finally, stress and durability experiment validations of optimal design are carried out. The stress results are consistent with the simulation, and the structure is in excellent conditions after 600,000 cycles of repeated loads under harsh working conditions in proving ground. By comparing the FE results between the original and optimal turnover frame, it shows that the optimal scheme has 21.5% reduction in total mass while maintaining better stiffness and durability.