Multidiscipline topology optimization

Topology optimization is used for determining the best layout of structural components to achieve predetermined performance goals. The density method which uses material density of each finite element as the design variable, is employed. Unlike the most common approach which uses the optimality criteria methods, the topology design problem is formulated as a general optimization problem and is solved by the mathematical programming method. One of the major advantages of this approach is its generality; thus it can solve various problems, e.g. multi-objective and multi-constraint problems. In this study, the structural weight is chosen as the objective function and structural responses such as the compliances, displacements and the natural frequencies, are treated as the constraints. The MSC/NASTRAN finite element code is employed for response analyses. One example with four different optimization formulations was used to demonstrate this approach.     

PolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes

We present an efficient Matlab code for structural topology optimization that includes a general finite element routine based on isoparametric polygonal elements which can be viewed as the extension of linear triangles and bilinear quads. The code also features a modular structure in which the analysis routine and the optimization algorithm are separated from the specific choice of topology optimization formulation. Within this framework, the finite element and sensitivity analysis routines contain no information related to the formulation and thus can be extended, developed and modified independently. We address issues pertaining to the use of unstructured meshes and arbitrary design domains in topology optimization that have received little attention in the literature. Also, as part of our examination of the topology optimization problem, we review the various steps taken in casting the optimal shape problem as a sizing optimization problem. This endeavor allows us to isolate the finite element and geometric analysis parameters and how they are related to the design variables of the discrete optimization problem. The Matlab code is explained in detail and numerical examples are presented to illustrate the capabilities of the code.     

A three-dimensional shape optimization system—shop3D

A modular approach for shape optimization of three-dimensional solid structures is described. A major consideration in the development of this capability is the desire to use a commercially available finite element program, such as NASTRAN, for analysis. Since NASTRAN cannot be called as a subroutine, a system architecture was developed of independently executable modules in which sequential execution is controlled by job control language. Also, shape sensitivities are not commonly available in commercial programs. A hybrid approach which is based on the material derivative concept is developed to obtain shape sensitivities by post processing finite element results stored on files. A quick generation of a good optimization model combined with an efficient optimization system will result in a drastic design time saving. In this paper, different modeling approaches for shape optimization are discussed. Emphasis will be placed upon a special modeling technique which overlays the design model onto an already existing finite element model. Several automotive related examples are used to evaluate the program's effectiveness.     

Shape design sensitivity analysis and optimization of spatially rotating objects

Shape design sensitivity analysis (DSA) and optimization of spatially rotating objects is presented in this paper. Design sensitivity expressions are derived using a continuum DSA method for spatial objects rotating with angular velocity and angular acceleration, based on three definitions of the finite element mass matrix: consistent, lumped, and diagonalized. The design sensitivity expression derived using a diagonalized element mass matrix, which is consistent with the finite element analysis (FEA) method used in ANSYS, is implemented, although the method can work with other FEA codes, such as MSC/NASTRAN or ABAQUS. Since the continuum DSA method is used, sensitivity information can be computed outside the FEA codes by postprocessing finite element data. Rotating block and turbine blade examples are presented to validate the proposed DSA method. The turbine blade example is optimized using an integrated optimization module of the Design Sensitivity Analysis and Optimization (DSO) tool developed at the University of Iowa. The integrated module consists of ANSYS, MSC/NASTRAN, or ABAQUS for FEA; Design Optimization Tool (DOT) for nonlinear programming; and DSA and design model update programs developed in DSO.     

PLASHTRAN: An expert consultant on two-dimensional finite element modeling techniques

An expert consultant and teaching aid has been developed to aid users of the MSC/NASTRAN (MacNeal-Schwendler Corp, Los Angeles, CA, USA) finite element code in the modeling process with two-dimensional elements. Written in LISP and LOOPS, an object-oriented programming language, the system, known as PLASHTRAN, allows engineers to work in a natural environment to obtain modeling recommendations. The program performs efficiently, especially when iterations in design require changes in the finite element model. The easily expandable modeling framework allows the knowledge base to incorporate new information.     

空间相机支撑杆峰值应力分析与试验验证

考核某空间相机主镜组件支撑杆在宽带随机激励下的强度,直接获得支撑杆的峰值应力响应在工程上存在一定困难。为了提高支撑强度,加强星上载荷的安全性,采用有限元软件MSC.PATRAN/NASTRAN进行有限元建模,对主镜组件进行单位加速度载荷下的频率响应仿真,分析获得了正弦振动下结构的峰值应力。利用随机振动和正弦振动之间的峰值等效原理,获得了共振频率点处的随机振动的峰值应力。对支撑杆进行了随机激励下的应力测试试验。比较仿真分析与试验的峰值应力结果,误差在7%以内,说明工程分析方法和技术路线是合理可行的,为进一步展开力学分析和结构优化设计奠定了基础。     

A 99 line topology optimization code written in Matlab

The paper presents a compact Matlab implementation of a topology optimization code for compliance minimization of statically loaded structures. The total number of Matlab input lines is 99 including optimizer and Finite Element subroutine. The 99 lines are divided into 36 lines for the main program, 12 lines for the Optimality Criteria based optimizer, 16 lines for a mesh-independency filter and 35 lines for the finite element code. In fact, excluding comment lines and lines associated with output and finite element analysis, it is shown that only 49 Matlab input lines are required for solving a well-posed topology optimization problem. By adding three additional lines, the program can solve problems with multiple load cases. The code is intended for educational purposes. The complete Matlab code is given in the Appendix and can be down-loaded from the web-site http://www.topopt.dtu.dk. Received October 22, 1999     

On the influence of model reduction techniques in topology optimization of flexible multibody systems using the floating frame of reference approach

Employing the floating frame of reference formulation in the topology optimization of dynamically loaded components of flexible multibody systems seems to be a natural choice. In this formulation the deformation of flexible bodies is approximated by global shape functions, which are commonly obtained from finite element models using model reduction techniques. For topology optimization these finite element models can be parameterized using the solid isotropic material with penalization (SIMP) approach. However, little is known about the interplay of model reduction and SIMP parameterization. Also securing the model reduction quality despite major changes of the design during the optimization has not been addressed yet. Thus, using the examples of a flexible frame and a slider-crank mechanism this work discusses the proper choice of the model reduction technique in the topology optimization of flexible multibody systems.     

On the usefulness of non-gradient approaches in topology optimization

Topology optimization is a highly developed tool for structural design and is by now being extensively used in mechanical, automotive and aerospace industries throughout the world. Gradient-based topology optimization algorithms may efficiently solve fine-resolution problems with thousands and up to millions of design variables using a few hundred (finite element) function evaluations (and even less than 50 in some commercial codes). Nevertheless, non-gradient topology optimization approaches that require orders of magnitude more function evaluations for extremely low resolution examples keep appearing in the literature. This forum article discusses the practical and scientific relevance of publishing papers that use immense computational resources for solving simple problems for which there already exist efficient solution techniques.     

A discrete level-set topology optimization code written in Matlab

This paper presents a compact Matlab implementation of the level-set method for topology optimization. The code can be used to minimize the compliance of a statically loaded structure. Simple code modifications to extend the code for different and multiple load cases are given. The code is inspired by a Matlab implementation of the solid isotropic material with penalization (SIMP) method for topology optimization (Sigmund, Struct Multidiscipl Optim 21:120–127, 2001). Including the finite element solver and comments, the code is 129 lines long. The code is intended for educational purposes, and in particular it could be used alongside the Matlab implementation of the SIMP method for topology optimization to demonstrate the similarities and differences between the two approaches.     

基于单元生死功能的转向架构架拓扑优化设计

为了更好地实现转向架构架的轻量化设计,根据设计经验,采用渐进结构优化法(ESO)的基本思想,通过对ANSYS单元生死功能的二次开发,应用APDL(ANSYS Parametric Design Language)编制拓扑优化程序,以直观的有限元模型代替复杂的拓扑优化的数学模型,提出了一种构架拓扑优化设计的工程方法。通过方法优化,使某高速动力车转向架构架在疲劳强度符合要求的前提下,结构应力趋于均匀分布,质量减少了143.92kg。结果表明,提出的方法是有效的和可行的,具有一定的工程实用价值,为设计提供依据。     

Application of topology optimization to design an electric bicycle main frame

Electric bicycle main frame is the most principal structure, connecting and supporting other various components, while bearing a variety of forces and moments. In this paper the topology optimization technology is applied to generate robust electric bicycle main frame by optimizing the material distribution subject to the constraints and dynamic loads. Geometric, mechanical and finite element models, as well as a flexible coupling dynamic model are constructed. Validity and accuracy of these models are investigated through real-life testing. By applying typical road excitation, dynamic loads of all key points are extracted. A set of forces data is extracted every 0.5?s during the whole simulation, including peak values of these forces. In order to obtain appropriate topology optimization results, the values of two crucial parameters, volume fraction and minimum member size, are discussed respectively. Then the topology optimization of multi-load case is implemented with the objective of minimizing the set of weighted compliances resulting from individual load cases. Results illustrate that element density distribution of the model is optimized with manufacturing constraints of minimum member size control and extrusion constraint. Consequently, the better frame form design of the electric bicycle is obtained. Modal analysis for the original and refined models is performed respectively to evaluate the structure stiffness. The results indicate that this optimization program is effective enough to develop a new electric bicycle frame as a reference for manufacturers.     

Topology optimization of switched reluctance motors for the desired torque profile

This paper presents the design optimization of switched reluctance motors (SRMs). The design goals are high average torque, low torque ripple and low mass under the constrained phase current of SRMs. To achieve these goals, we design not only the geometries of SRMs using topology optimization, but also voltage on–off angles. The performance analysis of SRMs is carried out to predict the torque profile. Fourier series expansion is used to obtain the explicit expression of inductance curves, which allows us to perform the analytical design sensitivity analysis of the torque profile. The optimization problem is solved using the sequential linear programming (SLP) method. In the optimized geometry, the arc lengths of poles are increased with the notched shape near airgap, and the holes inside the rotor are created. In addition, the mechanical characteristics of the optimized SRM are investigated using the modal and thermal analysis by MSC/NASTRAN.     

Optimisation and experimental verification of a dust-removal beater for the electrodes of electrostatic precipitators

The results of research into changes in vibrations of collecting electrodes are presented in the paper. The changes come from the optimisation of geometric and dynamic parameters of the shaking down system inelectrostatic precipitators (ESP). The computational verification was carried out using the finite element method on the MSC NASTRAN package. Vibrations and accelerations of the collecting electrodes were measured. The results were used in the comparative analysis and the analysis of spectral density of acceleration power. The paper shows how calculating methods completed by measurements allow us to solve important and sophisticated practical problem.     

Shape preserving design of vibrating structures using topology optimization

In several engineering components, the shape of some functional surfaces needs to be preserved in order to avoid losing performance or even its functionality when subjected to loads. This is particularly important when tight tolerances are required for operational conditions in some regions. If the deformation significantly affects product functionality, it is interesting to use a shape preserving design technique. This will often reduce deformation in a local region. To achieve that, we deal with topology optimization of elastic, continuum structures with Rayleigh damping, subjected to time-harmonic, design-independent external dynamic loading with prescribed excitation frequency, amplitude and spatial distribution. In topology optimization for vibrating structures, the obtained design should often have its resonance frequencies driven far away from the given excitation frequency in order to avoid resonance and to reduce vibration levels. In this work, we explore harmonic vibration problems with the excitation frequency lower than the first resonance frequency of the initial structure. Dynamic compliance minimization is used to improve dynamic response of the structure. An additional local dynamic compliance constraint is used to define the shape preserving problem, thus, reducing deformation in specific regions of a part named shape preserving region (SPR). A commercial FE code (ANSYS^?) is used to solve the finite element problem. The optimization Method of Moving Asymptotes (MMA) is used with the modified Solid Isotropic Material with Penalization (SIMP) material interpolation scheme. The effectiveness of this technique is presented using 2D plane structures. Coherent results were achieved using the proposed optimization formulation. It is possible to observe significant decrease on local deformation, at expense of little increase on global dynamic compliance.     

Numerical investigating the effect of machining parameters on residual stresses in orthogonal cutting

The aim of the present study is to develop a finite element analysis based on the nonlinear finite element code MSC.Superform for investigating the effect of cutting speed and feed rate on surface and subsurface residual stresses induced after orthogonal cutting. Basically, the present analysis is a coupled thermo-mechanical dynamic-transient problem. The results from the model are compared to experimental measurements available in the literature, concerning orthogonal cutting of steel AISI 1045 and are in good agreement with experimental data.     

Topology optimization in crashworthiness design

Topology optimization has developed rapidly, primarily with application on linear elastic structures subjected to static loadcases. In its basic form, an approximated optimization problem is formulated using analytical or semi-analytical methods to perform the sensitivity analysis. When an explicit finite element method is used to solve contact–impact problems, the sensitivities cannot easily be found. Hence, the engineer is forced to use numerical derivatives or other approaches. Since each finite element simulation of an impact problem may take days of computing time, the sensitivity-based methods are not a useful approach. Therefore, two alternative formulations for topology optimization are investigated in this work. The fundamental approach is to remove elements or, alternatively, change the element thicknesses based on the internal energy density distribution in the model. There is no automatic shift between the two methods within the existing algorithm. Within this formulation, it is possible to treat nonlinear effects, e.g., contact–impact and plasticity. Since no sensitivities are used, the updated design might be a step in the wrong direction for some finite elements. The load paths within the model will change if elements are removed or the element thicknesses are altered. Therefore, care should be taken with this procedure so that small steps are used, i.e., the change of the model should not be too large between two successive iterations and, therefore, the design parameters should not be altered too much. It is shown in this paper that the proposed method for topology optimization of a nonlinear problem gives similar result as a standard topology optimization procedures for the linear elastic case. Furthermore, the proposed procedures allow for topology optimization of nonlinear problems. The major restriction of the method is that responses in the optimization formulation must be coupled to the thickness updating procedure, e.g., constraint on a nodal displacement, acceleration level that is allowed.     

CAE技术在汽车座椅骨架开发中的应用

为提高汽车座椅骨架的开发质量,在某型汽车座椅骨架开发中应用CAE技术进行骨架静强度和疲劳等模拟.采用壳单元与梁单元相结合建立座椅骨架有限元模型;根据座椅骨架台架耐久试验要求和试验条件,对座椅安装孔进行全约束处理,并在试验加载位置施加相应的载荷;采用Abaqus/Standard分析座椅骨架强度;在静强度分析基础上应用F...     

Multi-physics bi-directional evolutionary topology optimization on GPU-architecture

Topology optimization has proven to be viable for use in the preliminary phases of real world design problems. Ultimately, the restricting factor is the computational expense since a multitude of designs need to be considered. This is especially imperative in such fields as aerospace, automotive and biomedical, where the problems involve multiple physical models, typically fluids and structures, requiring excessive computational calculations. One possible solution to this is to implement codes on massively parallel computer architectures, such as graphics processing units (GPUs). The present work investigates the feasibility of a GPU-implemented lattice Boltzmann method for multi-physics topology optimization for the first time. Noticeable differences between the GPU implementation and a central processing unit (CPU) version of the code are observed and the challenges associated with finding feasible solutions in a computational efficient manner are discussed and solved here, for the first time on a multi-physics topology optimization problem. The main goal of this paper is to speed up the topology optimization process for multi-physics problems without restricting the design domain, or sacrificing considerable performance in the objectives. Examples are compared with both standard CPU and various levels of numerical precision GPU codes to better illustrate the advantages and disadvantages of this implementation. A structural and fluid objective topology optimization problem is solved to vary the dependence of the algorithm on the GPU, extending on the previous literature that has only considered structural objectives of non-design dependent load problems. The results of this work indicate some discrepancies between GPU and CPU implementations that have not been seen before in the literature and are imperative to the speed-up of multi-physics topology optimization algorithms using GPUs.