Geometry Optimization of Branched Sheet Metal Products

Geometry Optimization plays an important role concerning to design tasks in mechanical engineering. For those we are studying sheet metal products like cable conduits. We formulate a nonlinear, continuous optimization problem to find an optimal geometry for such a sheet metal product. The goal is to find from a given topology the optimal geometry parameters concerning to the minimal bending of a cable conduit, spanning a huge distance. Hereby a lot of constraints, like given sizes of cross-section areas of the chambers, given quantity of sheet metal, and so on have to be fullfilled. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mixed-integer models for topology optimization in sheet metal design

Topology optimization lies at the heart of many design tasks in mechanical engineering. For those sheet metal products that consist of a bundle of separate channels (such as conduits) we formulate the design task as a linear mixed-integer optimization problem. The design goal is to find a topology where each channel has a given cross section area, using a minimum amount of sheet met al. In addition to a light-weight design, stiffness should also be taken into account. The entire approach is demonstrated in the design of a conduit with five separate channels. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal control of hydroforming processes

We consider an optimal control problem for sheet metal hydroforming. As a first step derivative free optimization algorithms are used to control the time dependent blank holder force and the fluid pressure, which are typical control variables. Our goal is to obtain a desired final configuration. We present numerical examples for 2D and 3D ABAQUS simulations for the hydroforming process of complexly curved sheet metals with bifurcated cross-sections. Since a single ABAQUS simulation takes a long time, optimization algorithms based on reduced models are under investigation. The reduced order model is based on a Galerkin solver for the elastoplasticity problem. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于LiToSim平台的海上风机过渡段优化软件开发

针对海上风机过渡段结构,考虑风机多尺度优化模型和所受环境荷载采取极端情况下,引入双向渐进结构拓扑优化方法,以全局应力最小化为目标、体积为约束,对风机过渡段进行优化设计;并在自主研发的LiToSim平台基础上,嵌入风机优化数值计算程序,最终形成一款关于海上风机过渡段拓扑优化的定制化软件TUR/TOPT.借助定制化软件TUR/TOPT平台,对比过渡段传统柔度优化与应力优化结果,突显出应力优化在减材设计过程中结构应力明显降低且能有效避免应力集中等方面的优势;TUR/TOPT软件的生成在风机建设选型过程中具有重要指导价值.     

Optimization of topology and shape by combining phase field modeling and discrete stochastic algorithms

We propose a concept for the comprehensive optimization of load bearing structures. The main idea is to decompose the optimization task. First, we use a phase field model to evolve the topology as basic design. The parameters of this process are the filling level of the design domain and the tendency to nucleate more or less holes. Second, we use an interface to set up a subsequent structural model, where cross-sections and positions of nodes are simultaneous optimization parameters of a metaheuristic optimization method. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An efficient optimization method for mechanical shells considering cut-outs

In this contribution an optimization method for shell structures is presented. This method was developed in order to perform a simultaneous optimization of the shape and position of the mid surface and a topology optimization to introduce cut-outs. A topology optimization method for continuum structures is combined with a manufacturing constraint for deep drawable sheet metals. It is shown, how more than a million design variables can be handled efficiently using a mathematical optimization algorithm for the design update and the finite element method for the structural simulation. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Topology and Geometry Optimization of Branched Sheet Metal Products

In order to optimize branched sheet metal profiles consisting of several chambers, decisions concerning topology and geometry have to be made. This leads to a problem entailing discrete and nonlinear features. We describe an integrated approach combining both aspects. The underlying idea is to use a branch-and-bound algorithm. In each node of the branch-and-bound tree, a nonlinear optimization problem has to be solved. We describe how the branch-and-bound tree is constructed, i.e., how the topology decision can be classified in a meaningful way. Moreover, we explain how to approach the nonlinear optimization problem arising in the nodes of the tree. We conclude by presenting a numerical example. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Geometry Optimization of Branched Sheet Metal Products

We consider the geometry optimization of branched sheet metal products, which can be produced continuously and in integral style using the new technologies of linear flow splitting and linear bend splitting. These are explored within the framework of the Collaborative Research Centre (CRC) 666. The geometry of such products can be parameterized by means of free form surfaces whereas their mechanical behaviour is described by the three dimensional linear elasticity equations. The associated PDE-constrained problem for optimizing the stiffness of the structure is formulated and an algorithm for solving this problem using exact constraints and a globalization strategy based on adaptive cubic regularization is presented. Numerical results for an example are given. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Design of planar articulated mechanisms using branch and bound

This paper considers an optimization model and a solution method for the design of two-dimensional mechanical mechanisms. The mechanism design problem is modeled as a nonconvex mixed integer program which allows the optimal topology and geometry of the mechanism to be determined simultaneously. The underlying mechanical analysis model is based on a truss representation allowing for large displacements. For mechanisms undergoing large displacements elastic stability is of major concern. We derive conditions, modeled by nonlinear matrix inequalities, which guarantee that a stable equilibrium is found and that buckling is prevented. The feasible set of the design problem is described by nonlinear differentiable and non-differentiable constraints as well as nonlinear matrix inequalities.To solve the mechanism design problem a branch and bound method based on convex relaxations is developed. To guarantee convergence of the method, two different types of convex relaxations are derived. The relaxations are strengthened by adding valid inequalities to the feasible set and by solving bound contraction sub-problems. Encouraging computational results indicate that the branch and bound method can reliably solve mechanism design problems of realistic size to global optimality.     

Steady and Unsteady Jet Wiping Processes

The jet wiping process is widely used in continuous coating applications to remove the excess amount of liquid entrained by a sheet moving out of a liquid bath. Typical fields of applications are hot dip galvanization of metal strips and coating of photographic films. The process is based on the impact of a gas jet onto the liquid film carried by the solid substrate. In the present study the process is investigated for the case of strictly two‐dimensional flow. It is assumed that inertia effects on the film flow can be neglected, whereas the effects of the pressure gradient and the shear stress distribution of the impinging jet and the surface tension of the liquid film are taken into account. As a result it is possible to derive a single kinematic wave equation which governs the distribution of the film thickness. Numerical results for representative steady and unsteady processes including the formation of shock discontinuities are presented.     

Using artificial reaction force to design compliant mechanism with multiple equality displacement constraints

Monolithic compliant mechanisms are elastic workpieces which transmit force and displacement from an input position to an output position. Continuum topology optimization is suitable to generate the optimized topology, shape and size of such compliant mechanisms. The optimization strategy for a single input single output compliant mechanism under volume constraint is known to be best implemented using an optimality criteria or similar mathematical programming method. In this standard form, the method appears unsuitable for the design of compliant mechanisms which are subject to multiple outputs and multiple constraints. Therefore an optimization model that is subject to multiple design constraints is required. With regard to the design problem of compliant mechanisms subject to multiple equality displacement constraints and an area constraint, we here present a unified sensitivity analysis procedure based on artificial reaction forces, in which the key idea is built upon the Lagrange multiplier method. Because the resultant sensitivity expression obtained by this procedure already compromises the effects of all the equality displacement constraints, a simple optimization method, such as the optimality criteria method, can then be used to implement an area constraint. Mesh adaptation and anisotropic filtering method are used to obtain clearly defined monolithic compliant mechanisms without obvious hinges. Numerical examples in 2D and 3D based on linear small deformation analysis are presented to illustrate the success of the method.     

Analysis of optimal metal flow in incremental sheet forming

Sheet metal forming processes are manufacturing processes in which a piece of sheet metal is shaped to a specified geometry, e.g. a car door. A promising new forming process is incremental sheet metal forming, in which the deformation is imposed by a progressive, localised plastic deformation induced by a pin-like forming tool that moves under numerical control along a pre-defined trajectory. This process offers the possibility to control the metal flow by adjusting the trajectory of the forming tool. Mathematically, sheet metal forming processes can be considered as a mapping between the initial, undeformed sheet metal and the final, deformed state. In most applications the surface area of the sheet metal is enlarged during the deformation. In this case, an ideal mapping would produce a homogeneous stretching of the sheet metal such that the final sheet thickness is the same everywhere. In this work, we analyze the following question: for each point in the initial configuration, what must be its location on the final geometry such that the thickness is the same everywhere? We construct a special type of surface evolution that combines flow along the surface normal with appropriate tangential velocity corrections, and show that the flow yields a constant sheet thinning on a sheet metal. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Efficient topology optimization of thermo-elasticity problems using coupled field adjoint sensitivity analysis method

We develop a unified and efficient adjoint design sensitivity analysis (DSA) method for weakly coupled thermo-elasticity problems. Design sensitivity expressions with respect to thermal conductivity and Young's modulus are derived. Besides the temperature and displacement adjoint equations, a coupled field adjoint equation is defined regarding the obtained adjoint displacement field as the adjoint load in the temperature field. Thus, the computing cost is significantly reduced compared to other sensitivity analysis methods. The developed DSA method is further extended to a topology design optimization method. For the topology design optimization, the design variables are parameterized using a bulk material density function. Numerical examples show that the DSA method developed is extremely efficient and the optimal topology varies significantly depending on the ratio of mechanical and thermal loadings.     

Topology and material orientation optimization based on evolution equations

Many modern high-performance materials have inherent anisotropic elastic properties and its local material orientation can be considered to be an additional design variable for the topology optimization [1–3]. We extend our previous model for topology optimization with variational controlled growth [4–6] for linear elastic anisotropic materials, for which the material orientation is introduced as an additional design variable. We solve the optimization problem purely with the principles of thermodynamics by minimizing the Gibbs energy. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Topology optimization methods for guided flow – comparison of optimality criteria vs. phase-field method

Optimization of guided flow problems is an important task for industrial applications especially those with high Reynolds numbers. There exist several optimization methods to increase the energy efficiency of these problems. Different optimization methods are shown bei Klimetzek [1], Hinterberger [2] and Pingen [3]. In recent years the phase-field method has been shown to be an applicable method for different kinds of topology optimization [4, 5]. We present results of topology optimization methods with optimality criterion and by using a phase-field model in the area of guided fluid flow problems. The two methods aim on the same main target reducing the pressure drop between the inlet and outlet of the flow domain. The first method is based on local optimality criterion, preventing the backflow in the flow domain [1, 6, 7]. The second method is based on a phase field model, which describes a minimization problem and uses a specially constructed driving force to minimize the total energy of the system [4, 5]. We investigate the capabilities and limits of both methods and present examples of different resulting geometries. The initial configurations are prepared in a way that the same optimization problem is solved with both methods. We discuss these results regarding the shape of the improved flow geometry. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Topology Optimization Procedure Based on Structure Stress History

The structure design points stress analysis for succeeding optimization steps is the base of the topology optimization algorithm. Because the material density of the material is proportional to the strain energy we can predict how to change the density for each design point for the next optimization steps. Proposed procedure make the optimization process faster and final topology is finally more optimal than topology obtained using standard optimization procedures. This stress analyzing procedure, can be treated as a hardware of the sensors being the part of the smart structure for the real time structure reconstruction. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

应力和位移约束下连续体结构拓扑优化

同时考滤应力和位移约束的连续体结构拓扑优化问题,很难用现有的均匀方法或变密度方法等求解。主要困难在于难以建立应力和位移约束与拓扑设计变量间显式关系式;即使建立了这种关系,也由于优化问题规模过大,利用常规的数学规划方法难以求解。隋允康、杨德庆曾提出了基于独立连续拓扑变量及映射变换（ＩＣＭ）的桁架结构拓扑优化模型。本文在此基础上,建立了以重量为目标,考虑应力和位移约束的连续体结构拓扑优化模型,并推导出     

A new approach for sheet nesting problem using guided cuckoo search and pairwise clustering

The nesting problem is commonly encountered in sheet metal, clothing and shoe-making industries. The nesting problem is a combinatorial optimization problem in which a given set of irregular polygons is required to be placed on a rectangular sheet. The objective is to minimize the length of the sheet while having all polygons inside the sheet without overlap. In this study, a methodology that hybridizes cuckoo search and guided local search optimization techniques is proposed.     

Optimality criteria coupled adaptive mesh method for optimal shape design of Stokes flow

An adaptive mesh method combined with the optimality criteria algorithm is applied to optimal shape design problems of fluid dynamics. The shape sensitivity analysis of the cost functional is derived. The optimization problem is solved by a simple but robust optimality criteria algorithm, and an automatic local adaptive mesh refinement method is proposed. The mesh adaptation, with an indicator based on the material distribution information, is itself shown as a shape or topology optimization problem. Taking advantages of this algorithm, the optimal shape design problem concerning fluid flow can be solved with higher resolution of the interface and a minimum of additional expense. Details on the optimization procedure are provided. Numerical results for two benchmark topology optimization problems are provided and compared with those obtained by other methods. Copyright © 2016 John Wiley & Sons, Ltd.