Structural shape optimization using self-adjusted convex approximation

This study researches the applications of Self-Adjusted Convex Approximation (SACA) in structural shape optimization problems. The B-spline curve is adopted as the mathematical representation of the structural shapes. The SACA method is based on the CONvex LINearization (CONLIN) method and has better accuracy and convergent rate. Numerical examples are offered and the results show that the proposed method is effective in the structural shape design.     

Improved genetic algorithm with two-level approximation using shape sensitivities for truss layout optimization

Truss layout optimization is a procedure for optimizing truss structures under the combined influence of size, shape and topology variables. This paper presents an Improved Genetic Algorithm with Two-Level Approximation (IGATA) that uses continuous shape variables and shape sensitivities to minimize the weight of trusses under static or dynamic constraints. A uniform optimization model including continuous size/shape variables and discrete topology variables is established. With the introduction of shape sensitivities, the first-level approximations of constraint functions are constructed with respect to shape/topology/size variables. This explicit problem is solved by implementation of a real-coded GA for continuous shape variables and binary-coded GA for 0/1 topology variables. Acceleration techniques are used to overcome the convergence difficulty of the mixed-coded GA. When calculating the fitness value of each member in the current generation, a second-level approximation method is embedded to optimize the continuous size variables effectively. The results of numerical examples show that the usage of continuous shape variables and shape sensitivities improves the algorithm performance significantly.     

Gradient-based Pareto front approximation applied to turbomachinery shape optimization

Engineering with Computers - Multi-objective optimization has been rising in popularity, especially within an industrial environment, where several cost functions often need to be considered during...     

基于近似模型的整车气动外形优化

以类车体DrivAer的气动阻力因数为优化目标,选取影响其气动性能的5个形状参数作为设计变量,通过引入网格变形、试验设计(Design of Experiment,DOE)及近似模型等技术搭建自动仿真优化平台,探索气动性能最佳的参数匹配方案.优化后的DrivAer气动阻力因数降低4.5%,表明近似模型方法能够较好地取代实际仿真过程进行寻优.分析DOE的结果,发现影响气动阻力因数和气动升力因数的主要参数分别为行李箱高度与离去角,而多参数变化时的交互效应也会影响整车的气动性能.     

Time domain approximation using digital methods

Two digital methods are proposed for the solution of the time-domain approximation problem. Tho first method, based on a reeursivo algorithm for tho matrix pseudo-iriverso, determines the pulse transfer function of a discrete-timo system of a prescribed order providing the best fit in tho least squares sense at tho samplo points. Tho continuous-time system transfer function is then derived by using a simple transformation provided that tho sampling frequence oxeeeds tho Nyquist rate. Tho method is direct and computationally efficient. The second method is based on using an offieiont gradient search algorithm providing the best fit in the least pti sense at tho samplo points. A number of examples illustrato the methods     

Additive manufacturing scanning paths optimization using shape optimization tools

Structural and Multidisciplinary Optimization - This paper investigates path planning strategies for additive manufacturing processes such as powder bed fusion. The state of the art mainly studies...     

Zometool shape approximation

We present an algorithm that approximates 2-manifold surfaces with Zometool models while preserving their topology. Zometool is a popular hands-on mathematical modeling system used in teaching, research and for recreational model assemblies at home. This construction system relies on a single node type with a small, fixed set of directions and only 9 different edge types in its basic form. While being naturally well suited for modeling symmetries, various polytopes or visualizing molecular structures, the inherent discreteness of the system poses difficult constraints on any algorithmic approach to support the modeling of freeform shapes. We contribute a set of local, topology preserving Zome mesh modification operators enabling the efficient exploration of the space of 2-manifold Zome models around a given input shape. Starting from a rough initial approximation, the operators are iteratively selected within a stochastic framework guided by an energy functional measuring the quality of the approximation. We demonstrate our approach on a number of designs and also describe parameters which are used to explore different complexities and enable coarse approximations.     

Gradientless shape optimization using artificial neural networks

In this paper a new zero order method of structural shape optimization, in which material shrinks or grows perpendicular to the design boundary, has been proposed in order to satisfy fully stressed design criteria. To avoid mesh distortion that results in undesirable shape, design element concept and for nodal movement and convergence checking, fuzzy set theory have been used. To accelerate the convergence, artificial neural networks are employed. The proposed approach, named as GSN technique, has been incorporated in a FORTRAN software GSOANN. Using this software shape optimization of four structures are carried out. It is demonstrated that proposed technique overcomes most of the shortcomings of mundane zero order methods.     

Applications of one-shot methods in PDEs constrained shape optimization

The paper deals with applications of numerical methods for optimal shape design of composite materials structures and devices. We consider two different physical models described by specific partial differential equations (PDEs) for real-life problems. The first application relates microstructural biomorphic ceramic materials for which the homogenization approach is invoked to formulate the macroscopic problem. The obtained homogenized equation in the macroscale domain is involved as an equality constraint in the optimization task. The second application is connected to active microfluidic biochips based on piezoelectrically actuated surface acoustic waves (SAWs). Our purpose is to find the best material-and-shape combination in order to achieve the optimal performance of the materials structures and, respectively, an improved design of the novel nanotechnological devices. In general, the PDEs constrained optimization routine gives rise to a large-scale nonlinear programming problem. For the numerical solution of this problem we use one-shot methods with proper optimization algorithms and inexact Newton solvers. Computational results for both applications are presented and discussed.     

Level set topology and shape optimization by density methods using cut elements with length scale control

Structural and Multidisciplinary Optimization - The level set and density methods for topology optimization are often perceived as two very different approaches. This has to some extent led to two...     

Estimation and marginalization using the Kikuchi approximation methods

In this letter, we examine a general method of approximation, known as the Kikuchi approximation method, for finding the marginals of a product distribution, as well as the corresponding partition function. The Kikuchi approximation method defines a certain constrained optimization problem, called the Kikuchi problem, and treats its stationary points as approximations to the desired marginals. We show how to associate a graph to any Kikuchi problem and describe a class of local message-passing algorithms along the edges of any such graph, which attempt to find the solutions to the problem. Implementation of these algorithms on graphs with fewer edges requires fewer operations in each iteration. We therefore characterize minimal graphs for a Kikuchi problem, which are those with the minimum number of edges. We show with empirical results that these simpler algorithms often offer significant savings in computational complexity, without suffering a loss in the convergence rate. We give conditions for the convexity of a given Kikuchi problem and the exactness of the approximations in terms of the loops of the minimal graph. More precisely, we show that if the minimal graph is cycle free, then the Kikuchi approximation method is exact, and the converse is also true generically. Together with the fact that in the cycle-free case, the iterative algorithms are equivalent to the well-known belief propagation algorithm, our results imply that, generically, the Kikuchi approximation method can be exact if and only if traditional junction tree methods could also solve the problem exactly.     

Numerical method for shape optimization using meshfree method

A numerical method for continuum-based shape design sensitivity analysis and optimization using the meshfree method is proposed. The reproducing kernel particle method is used for domain discretization in conjunction with the Gauss integration method. Special features of the meshfree method from a sensitivity analysis viewpoint are discussed, including the treatment of essential boundary conditions, and the dependence of the shape function on the design variation. It is shown that the mesh distortion that exists in the finite element-based design approach is effectively resolved for large shape changing design problems through 2-D and 3-D numerical examples. The number of design iterations is reduced because of the accurate sensitivity information.     

Regularization of shape optimization problems using FE-based parametrization

This paper introduces a general fully stabilized mesh based shape optimization strategy, which allows for shape optimization of mechanical problems on FE-based parametrization. The well-known mesh dependent results are avoided by application of filter methods and mesh regularization strategies. Filter methods are successfully applied to SIMP (Solid Isotropic Material with Penalization) based topology optimization for many years. The filter method presented here uses a specific formulation that is based on convolution integrals. It is shown that the filter methods ensure mesh independency of the optimal designs. Furthermore they provide an easy and robust tool to explore the whole design space with respect to optimal designs with similar mechanical properties. A successful application of optimization strategies with FE-based parametrization requires the combination of filter methods with mesh regularization strategies. The latter ones ensure reliable results of the finite element solutions that are crucial for the sensitivity analysis. This presentation introduces a new mesh regularization strategy that is based on the Updated Reference Strategy (URS). It is shown that the methods formulated on this mechanical basis result in fast and robust mesh regularization methods. The resulting grids show a minimum mesh distortion even for large movements of the mesh boundary. The performance of the proposed regularization methods is demonstrated by several illustrative examples.     

Two-level optimization of airframe structures using response surface approximation

In this paper, a two-level optimization approach is developed for the preliminary and conceptual design of airframe structures. The preliminary design, involving a single objective multidisciplinary optimization, constitutes the lower level where ASTROS (Automated STRuctural Optimization System) is employed for multidisciplinary optimization. The conceptual design, which is carried out at the upper level, aims mainly at configuration design. The multiple objectives are incorporated as a single objective function by using the K-S function formulation. The objective function and constraints at the upper level are modelled through response surface approximation. During the upper level optimization process, the branch and bound method is applied for solving the problem with discrete design variables. The proposed strategy is demonstrated by the optimization of an Intermediate Complexity Wing (ICW) model. Received June 23, 1999     

A study of direct vs. approximation methods in structural optimization

This note discusses the performances and applications of two methods generally used in structural optimization. One is the direct method which applies a nonlinear programming (NLP) algorithm directly to the structural optimization problem. The other is the approximation method which utilizes the engineering sense very well. The two methods are compared through standard structural optimization problems with truss and beam elements. The results are analysed based on the convergence performances, the number of function calculations, the quality of the cost functions, etc. The applications of both methods are also discussed.     

Geometric constraint satisfaction using optimization methods

The numerical approach to solving geometric constraint problems is indispensable for building a practical CAD system. The most commonly-used numerical method is the Newton–Raphson method. It is fast, but has the instability problem: the method requires good initial values. To overcome this problem, recently the homotopy method has been proposed and experimented with. According to the report, the homotopy method generally works much better in terms of stability. In this paper we use the numerical optimization method to deal with the geometric constraint solving problem. The experimental results based on our implementation of the method show that this method is also much less sensitive to the initial value. Further, a distinctive advantage of the method is that under- and over-constrained problems can be handled naturally and efficiently. We also give many instructive examples to illustrate the above advantages.     

Geometry-aware bases for shape approximation

We introduce a new class of shape approximation techniques for irregular triangular meshes. Our method approximates the geometry of the mesh using a linear combination of a small number of basis vectors. The basis vectors are functions of the mesh connectivity and of the mesh indices of a number of anchor vertices. There is a fundamental difference between the bases generated by our method and those generated by geometry-oblivious methods, such as Laplacian-based spectral methods. In the latter methods, the basis vectors are functions of the connectivity alone. The basis vectors of our method, in contrast, are geometry-aware since they depend on both the connectivity and on a binary tagging of vertices that are "geometrically important" in the given mesh (e.g., extrema). We show that, by defining the basis vectors to be the solutions of certain least-squares problems, the reconstruction problem reduces to solving a single sparse linear least-squares problem. We also show that this problem can be solved quickly using a state-of-the-art sparse-matrix factorization algorithm. We show how to select the anchor vertices to define a compact effective basis from which an approximated shape can be reconstructed. Furthermore, we develop an incremental update of the factorization of the least-squares system. This allows a progressive scheme where an initial approximation is incrementally refined by a stream of anchor points. We show that the incremental update and solving the factored system are fast enough to allow an online refinement of the mesh geometry