Topology optimization for femto suspension design

The ongoing increase of track density requirements of hard disk drives (HDDs) and decrease of flying height of sliders have brought along formidable challenges to suspension design. Conventional design processes are quite tedious and inefficient. This paper presents a HDD suspension design process by using topology optimization. An efficient structural topology optimization method, based on the second derivatives information, is proposed to generate structures which satisfy multiple design objectives including both compliance and eigenfrequencies. This topology optimization approach is successfully applied in the HDD suspension design. The design begins with a very simple initial draft, and the design objectives are defined to minimize the spring rate and maximize the resonant frequencies of first bending, first torsion and sway modes of a suspension. An optimal design concept can be generated from the topology optimization. Then the design is further tuned by using the shape optimization. Finally, an optimal suspension design for femto sliders with much better dynamic characteristics is presented.     

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.     

Topology optimization applied to the design of 2D swirl flow devices

The design of fluid devices, such as flow machines, mixers, separators, and valves, with the aim to improve performance is of high interest. One way to achieve it is by designing them through the topology optimization method. However, there is a specific large class of fluid flow problems called 2D swirl flow problems which presents an axisymmetric flow with (or without) flow rotation around the axisymmetric axis. Some devices which allow such simplification are hydrocyclones, some pumps and turbines, fluid separators, etc. Once solving a topology optimization problem for this class of problems using a 3D domain results in a quite high computational cost, the development and use of 2D swirl models is of high interest. Thus, the main objective of this work is to propose a topology optimization formulation for 2D swirl flow fluid problem to design these kinds of fluid devices. The objective is to minimize the relative energy dissipation considering the viscous and porous effects. The 2D swirl laminar fluid flow modelling is solved by using the finite element method. A traditional material model is adopted by considering nodal design variables. An interior point optimization (IPOPT) algorithm is applied to solve the optimization problem. Numerical examples are presented to illustrate the application of this model for various 2D swirl flow cases.     

Topology optimization for the seismic design of truss-like structures

A practical optimization method is applied to design nonlinear truss-like structures subjected to seismic excitation. To achieve minimum weight design, inefficient material is gradually shifted from strong parts to weak parts of a structure until a state of uniform deformation prevails. By considering different truss structures, effects of seismic excitation, target ductility and buckling of the compression members on optimum topology are investigated. It is shown that the proposed method could lead to 60% less structural weight compared to optimization methods based on elastic behavior and equivalent static loads, and is efficient at controlling performance parameters under a design earthquake.     

Topology optimization of channel flow problems

This paper describes a topology design method for simple two-dimensional flow problems. We consider steady, incompressible laminar viscous flows at low-to-moderate Reynolds numbers. This makes the flow problem nonlinear and hence a nontrivial extension of the work of Borrvall and Petersson (2003).Further, the inclusion of inertia effects significantly alters the physics, enabling solutions of new classes of optimization problems, such as velocity-driven switches, that are not addressed by the earlier method. Specifically, we determine optimal layouts of channel flows that extremize a cost function which measures either some local aspect of the velocity field or a global quantity, such as the rate of energy dissipation. We use the finite element method to model the flow, and we solve the optimization problem with a gradient-based math-programming algorithm that is driven by analytical sensitivities. Our target application is optimal layout design of channels in fluid network systems. Using concepts borrowed from topology optimization of compliant mechanisms in solid mechanics, we introduce a method for the synthesis of fluidic components, such as switches, diodes, etc.     

Topology optimization for microstructural design under stress constraints

This work aims at introducing stress responses within a topology optimization framework applied to the design of periodic microstructures. The emergence of novel additive manufacturing techniques fosters research towards new approaches to tailor materials properties. This paper derives a formulation to prevent the occurrence of high stress concentrations, often present in optimized microstructures. Applying macroscopic test strain fields to the material, microstructural layouts, reducing the stress level while exhibiting the best overall stiffness properties, are sought for. Equivalent stiffness properties of the designed material are predicted by numerical homogenization and considering a metallic base material for the microstructure, it is assumed that the classical Von Mises stress criterion remains valid to predict the material elastic allowable stress at the microscale. Stress constraints with arbitrary bounds are considered, assuming that a sizing optimization step could be applied to match the actual stress limits under realistic service loads. Density–based topology optimization, relying on the SIMP model, is used and the qp–approach is exploited to overcome the singularity phenomenon arising from the introduction of stress constraints with vanishing material. Optimization problems are solved using mathematical programming schemes, in particular MMA, so that a sensitivity analysis of stress responses at the microstructural level is required and performed considering the adjoint approach. Finally, the developed method is first validated with classical academic benchmarks and then illustrated with an original application: tailoring metamaterials for a museum anti–seismic stand.     

Topology optimization for minimum stress design with the homogenization method

This paper is devoted to minimum stress design in structural optimization. The homogenization method is extended to such a framework and yields an efficient numerical algorithm for topology optimization. The main idea is to use a partial relaxation of the problem obtained by introducing special microstructures which are sequential laminated composites. Indeed, the so-called corrector terms of such microgeometries are explicitly known, which allows us to compute the relaxed objective function. These correctors can be interpreted as stress amplification factors, caused by the underlying microstructure.     

Topology optimization of large scale stokes flow problems

This note considers topology optimization of large scale 2D and 3D Stokes flow problems using parallel computations. We solve problems with up to 1,125,000 elements in 2D and 128,000 elements in 3D on a shared memory computer consisting of Sun UltraSparc IV CPUs.     

Topology optimization of flow domains using the lattice Boltzmann method

We consider the optimal design of two- (2D) and three-dimensional (3D) flow domains using the lattice Boltzmann method (LBM) as an approximation of Navier-Stokes (NS) flows. The problem is solved by a topology optimization approach varying the effective porosity of a fictitious material. The boundaries of the flow domain are represented by potentially discontinuous material distributions. NS flows are traditionally approximated by finite element and finite volume methods. These schemes, while well established as high-fidelity simulation tools using body-fitted meshes, are effected in their accuracy and robustness when regular meshes with zero-velocity constraints along the surface and in the interior of obstacles are used, as is common in topology optimization. Therefore, we study the potential of the LBM for approximating low Mach number incompressible viscous flows for topology optimization. In the LBM the geometry of flow domains is defined in a discontinuous manner, similar to the approach used in material-based topology optimization. In addition, this non-traditional discretization method features parallel scalability and allows for high-resolution, regular fluid meshes. In this paper, we show how the variation of the porosity can be used in conjunction with the LBM for the optimal design of fluid domains, making the LBM an interesting alternative to NS solvers for topology optimization problems. The potential of our topology optimization approach will be illustrated by 2D and 3D numerical examples.     

Topology optimization design of crushed 2D-frames for desired energy absorption history

The present work deals with topology optimization for obtaining a desired energy absorption history of a crushed structure. The optimized energy absorbing structures are used to improve the crashworthiness of transportation vehicles. The ground structure consists of rectangular 2D-beam elements with plastic hinges. The elements can undergo large rotations, so the analysis accommodates geometric nonlinearities. A quasi-static nonlinear finite element solution is obtained with an implicit backward Euler algorithm, and the analytical sensitivities are computed by the direct differentiation method.     

Topology optimization of steady Navier-Stokes flow via a piecewise constant level set method

This paper presents a piecewise constant level set method for the topology optimization of steady Navier-Stokes flow. Combining piecewise constant level set functions and artificial friction force, the optimization problem is formulated and analyzed based on a design variable. The topology sensitivities are computed by the adjoint method based on Lagrangian multipliers. In the optimization procedure, the piecewise constant level set function is updated by a new descent method, without the needing to solve the Hamilton-Jacobi equation. To achieve optimization, the piecewise constant level set method does not track the boundaries between the different materials but instead through the regional division, which can easily create small holes without topological derivatives. Furthermore, we make some attempts to avoid updating the Lagrangian multipliers and to deal with the constraints easily. The algorithm is very simple to implement, and it is possible to obtain the optimal solution by iterating a few steps. Several numerical examples for both two- and three-dimensional problems are provided, to demonstrate the validity and efficiency of the proposed method.     

Topology optimization of fluid flow channel in cold plate for active phased array antenna

This article presents a topology optimization method for the design of the fluid flow channel of cold plate, aiming to solve the problem of heat dissipation for power devices in active phased array antenna (APAA). The density-based topology optimization method is used in the topology optimization design of flow path, in which the conjugate heat transfer analysis is performed. In the numerical experiment, we use the central plane of the cold plate to make a two-dimensional topology optimization, and then the result of two-dimensional topology optimization was used to build the three-dimensional flow channel of cold plate. The results of simulation show that the optimized flow channel has a better ability of heat dissipation compared with the traditional S style flow channel, which provides important reference for engineering application.     

Topology optimization of fluid channels with flow rate equality constraints

This note presents topology optimization of fluid channels with flow rate equality constraints. The equality constraints on the specified boundaries are implemented using the lumped Lagrange multiplier method. The quadratic penalty term and cut-off sensitivity are used to maintain the stability of optimization.     

高速列车车体端部防撞装置拓扑优化设计

针对高速列车的被动安全性,基于大变形碰撞仿真理论,用PAM CRASH进行碰撞仿真,用OptiStruct对车体端部防撞装置进行拓扑优化,从而完成防撞装置的轻量化设计.结果表明：在保证防撞装置结构稳定性的同时,最大撞击力减小23%,质量减轻33.6%,达到提高车辆被动安全性的目的.     

基于Inspire的一体式复合支架拓扑优化设计

针对发动机悬架与发电机支架集成的一体式复合支架轻量化设计问题,采用solidThinking软件中的Inspire模块,基于变密度理论,以支架刚度和模型体积为优化目标,以设计空间的单元相对密度为设计变量,以模型振动频率和厚度为约束条件,对复合支架进行拓扑优化设计。在保证支架结构强度可靠性的前提下,优化后复合支架的质量减小、1阶模态频率提高。     

最小位移类桁架连续体拓扑设计优化

为将拓扑优化中的柔度最小化问题拓展到一般位移最小化问题,用有限元划分设计域,采用类桁架连续体材料模型,并假设杆件在设计域内连续分布.将杆件在节点位置的密度和方向作为设计变量,将指定位置和方向的位移作为目标函数,采用基于目标函数梯度的优化准则法,通过优化杆件的连续分布场形成拓扑优化的类桁架连续体.该方法可结合结构力学的基本概念,选择部分杆件形成拓扑优化刚架.     

Topology optimization in OpenMDAO

Recently, topology optimization has drawn interest from both industry and academia as the ideal design method for additive manufacturing. Topology optimization, however, has a high entry barrier as it requires substantial expertise and development effort. The typical numerical methods for topology optimization are tightly coupled with the corresponding computational mechanics method such as a finite element method and the algorithms are intrusive, requiring an extensive understanding. This paper presents a modular paradigm for topology optimization using OpenMDAO, an open-source computational framework for multidisciplinary design optimization. This provides more accessible topology optimization algorithms that can be non-intrusively modified and easily understood, making them suitable as educational and research tools. This also opens up further opportunities to explore topology optimization for multidisciplinary design problems. Two widely used topology optimization methods—the density-based and level-set methods—are formulated in this modular paradigm. It is demonstrated that the modular paradigm enhances the flexibility of the architecture, which is essential for extensibility.