Distributed multilevel optimization for complex structures

Optimization problems concerning complex structures with many design variables may entail an unacceptable computational cost. This problem can be reduced considerably with a multilevel approach: A structure consisting of several components is optimized as a whole (global) as well as on the component level. In this paper, an optimization method is discussed with applications in the assessment of the impact of new design considerations in the development of a structure. A strategy based on fully stressed design is applied for optimization problems in linear statics. A global model is used to calculate the interactions (e.g., loads) for each of the components. These components are then optimized using the prescribed interactions, followed by a new global calculation to update the interactions. Mixed discrete and continuous design variables as well as different design configurations are possible. An application of this strategy is presented in the form of the full optimization of a vertical tail plane center box of a generic large passenger aircraft. In linear dynamics, the parametrization of the component interactions is problematic due to the frequency dependence. Hence, a modified method is presented in which the speed of component mode synthesis is used to avoid this parametrization. This method is applied to a simple test case that originates from noise control.     

Integrated layout design of supports and structures

Based on the previously proposed techniques for the integrated layout optimization of multi-component system, this paper is to demonstrate further developments and applications of the related techniques in the integrated layout design of supports and structures. The design procedure mainly consists of two parts. Firstly, the layout of the supports is described with the positions of movable support components on the specified boundary of the design domain. These components are partially embedded into the design domain and subjected to the applied boundary conditions. Secondly, the layout optimization of the support components and the structure is carried out. Locations of the support components and the pseudo-densities defined on the density points are assumed as geometrical and topological design variables, respectively. Geometrical constraints are imposed to avoid the overlap of multiple components. The technique of embedded meshing is employed to adapt the topology optimization to the variation of the finite element mesh caused by the component movement. Varieties of numerical examples are finally tested to validate the proposed method. Both surface load and self-weight load are taken into account. More complexities of partially supported components are introduced in the presented examples.     

复杂圆柱壳结构参数化建模方法及模型库设计

针对船舶的主要结构形式——复杂圆柱壳结构,为研究其快速建模方法以实现船舶结构的优化设计,基于隐式参数化模型概念提出参数化模型表征方法,建立其分类和命名体系,给出其参数化建模方式和流程,利用数值仿真工具完成其参数化模型库设计和开发,并应用于某船舶结构的快速建模.算例表明:复杂圆柱壳参数化模型库设计合理,满足复杂圆柱壳结构快速建模和修改的要求.     

Integrated layout and topology optimization design of multi-frame and multi-component fuselage structure systems

The purpose of this paper is to present an extended integrated layout and topology optimization method dealing with the multi-frame and multi-component fuselage structure systems design. Considering an aircraft or aerospace fuselage system including main structure, numbers of frames and featured components located on the frames, a simultaneous optimization procedure is proposed here including geometrical design variables of components and frames as well as topological design variables of main structure and frame structures. The multi-point constraints (MPC) scheme is used to simulate the rivets or bolts connecting the components, frames and structures. The finite circle method (FCM) is implemented to avoid the overlaps among different components and frames. Furthermore, to deal with the difficulties of large numbers of non-overlapping constraints, a penalty method is used here to compose the global strain energy and non-overlapping constraints into a single objective function. To guarantee the fuselage system’s balance, the constraint on the system centroid is also introduced into the optimization. Different numerical examples are tested and the optimized solutions have demonstrated the validity and effectiveness of the proposed formulation.     

BLISS/S: a new method for two-level structural optimization

The paper describes a two-level method for structural optimization for a minimum weight under the local strength and displacement constraints. The method divides the optimization task into separate optimizations of the individual substructures (in the extreme, the individual components) coordinated by the assembled structure optimization. The substructure optimizations use local cross-sections as design variables and satisfy the highly nonlinear local constraints of strength and buckling. The design variables in the assembled structure optimization govern the structure overall shape and handle the displacement constraints. The assembled structure objective function is the objective in each of the above optimizations. The substructure optimizations are linked to the assembled structure optimization by the sensitivity derivatives. The method was derived from a previously reported two-level optimization method for engineering systems, e.g. aerospace vehicles, that comprise interacting modules to be optimized independently, coordination provided by a system-level optimization. This scheme was adapted to structural optimization by treating each substructure as a module in a system, and using the standard finite element analysis as the system analysis. A numerical example, a hub structure framework, is provided to show the new method agreement with a standard, no-decomposition optimization. The new method advantage lies primarily in the autonomy of the individual substructure optimization that enables concurrency of execution to compress the overall task elapsed time. The advantage increases with the magnitude of that task. Received December 5, 1999?Revised mansucript received April 26, 2000     

Erratum to: New efficient method for dynamic modeling and simulation of flexible multibody systems moving in plane

Efficient, precise dynamic analysis for general flexible multibody systems has become a research focus in the field of flexible multibody dynamics. In this paper, the finite element method and component mode synthesis are introduced to describe the deformations of the flexible components, and the dynamic equations of flexible bodies moving in plane are deduced. By combining the discrete time transfer matrix method of multibody system with these dynamic equations of flexible component, the transfer equations and transfer matrices of flexible bodies moving in plane are developed. Finally, a high-efficient dynamic modeling method and its algorithm are presented for high-speed computation of general flexible multibody dynamics. Compared with the ordinary dynamics methods, the proposed method combines the strengths of the transfer matrix method and finite element method. It does not need the global dynamic equations of system and has the low order of system matrix and high computational efficiency. This method can be applied to solve the dynamics problems of flexible multibody systems containing irregularly shaped flexible components. It has advantages for dynamic design of complex flexible multibody systems. Formulations as well as a numerical example of a multi-rigid-flexible-body system containing irregularly shaped flexible components are given to validate the method.     

New efficient method for dynamic modeling and simulation of flexible multibody systems moving in plane

Efficient, precise dynamic analysis for general flexible multibody systems has become a research focus in the field of flexible multibody dynamics. In this paper, the finite element method and component mode synthesis are introduced to describe the deformations of the flexible components, and the dynamic equations of flexible bodies moving in plane are deduced. By combining the discrete time transfer matrix method of multibody system with these dynamic equations of flexible component, the transfer equations and transfer matrices of flexible bodies moving in plane are developed. Finally, a high-efficient dynamic modeling method and its algorithm are presented for high-speed computation of general flexible multibody dynamics. Compared with the ordinary dynamics methods, the proposed method combines the strengths of the transfer matrix method and finite element method. It does not need the global dynamic equations of system and has the low order of system matrix and high computational efficiency. This method can be applied to solve the dynamics problems of flexible multibody systems containing irregularly shaped flexible components. It has advantages for dynamic design of complex flexible multibody systems. Formulations as well as a numerical example of a multi-rigid-flexible-body system containing irregularly shaped flexible components are given to validate the method.     

复合材料磁悬浮列车车体结构数值模拟(III)——车体结构性能的参数化数值模拟

在磁悬浮列车车体参数化数值模型的基础上,开展参数变化对车体结构性能影响的数值试验,研究复合材料梁截面几何参数对车体刚度和频率的影响。在典型荷载工况下,研究关键设计参数对车体结构性能、结构部件连接模型的力学性能、车体频率和振型、车体结构线性屈曲性能的影响,确定关键设计参数对复合材料车体结构性能的影响趋势,为车体优化设计奠定基础,验证将参数化车体数值模型作为车体结构性能研究的有效性。     

平面全柔性3-DOF过驱动并联机构的最优综合

以设计全柔性多自由度过驱动并联机构为目标,研究了平面3-DOF 4RRR过驱动并联机构的最优综合问题．从一般四分支3-DOF平面并联机构出发,建立了机构的运动学模型;给出了机构的4种可能拓扑结构分类,对不同拓扑结构类型机构的运动学和力学性能进行了分析比较．建立了并联机构全工作空间操作性改善优化模型,采用遗传算法进行优化设计并给出了实例,根据优化实例的结果设计制造了平面全柔性三自由度过驱动并联机构．以上方法对其它全柔性并联机构的优化设计具有参考价值．     

A new experiential learning electromagnetism-like mechanism for numerical optimization

The Electromagnetism-like Mechanism algorithm (EM) is a population-based search algorithm which has shown good achievements in solving various types of complex numerical optimization problems so far. To date, the study on experience-based local search mechanism is relatively limited, and there is no study in the literature to integrate experience-based features into the EM. This work introduces an experience-learning feature into the EM for the first time. A new Experiential Learning Electromagnetism-like Mechanism algorithm (ELEM) is proposed in this paper. The ELEM is integrated with two new components. The first component is the particle memory concept which allows the particles to remember the details of their past search experience. The second component is the experience analysing and decision making mechanisms which enables the particles to adjust the settings for the coming iterations. Combining the advantages of this strong exploitation strategy and the powerful exploration mechanism of the EM, the proposed ELEM strikes a good balance in providing well diversified solutions with high accuracy. The results from extensive numerical experiments carried out using 21 challenging test functions show that ELEM is able to provide very competitive solutions and significantly outperforms other optimization techniques. It can thus be concluded from the results that the proposed ELEM performs well in solving high dimensional numerical optimization problems.     

Integration of design and manufacturing for structural shape optimization

This paper presents an integrated design and manufacturing approach that supports shape optimization of structural components. The approach starts from a primitive concept stage, where boundary and loading conditions of the structural component are given to the designer. Topology optimization is conducted for an initial structural layout. The discretized structural layout is smoothed using parametric B-Spline surfaces. The B-Spline surfaces are imported into a CAD system to construct parametric solid models for shape optimization. Virtual manufacturing (VM) techniques are employed to ensure that the optimized shape can be manufactured at a reasonable cost. The solid freeform fabrication (SFF) system fabricates physical prototypes of the structure for design verification. Finally, a computer numerical control (CNC) machine is employed to fabricate functional parts as well as mold or die for mass production of the structural component. The main contribution of the paper is incorporating manufacturing into the design process, where manufacturing cost is considered for design. In addition, the overall design process starts from a primitive stage and ends with functional parts. A 3D tracked vehicle roadarm is employed throughout this paper to illustrate the overall design process and various techniques involved.     

On the emergence of intelligent global behaviours from simple local actions

Artificial intelligence focuses on the question of how to design systems to exhibit intelligent behaviour in complex environments. Complex global behaviours can emerge from simple systems acting in a complex environment; however, this emergence requires that the systems' internal structure reflects essential structures in the environment This paper examines the algebraic structure of a system's actions. We find that these actions often possess a self-similar local neighbourhood structure that permits analysis and synthesis to be performed locally and yet produces global intelligent behaviours. A procedure for finding this local structure is presented and illustrated with examples.     

Improved method of synthesis of an automaton from its specification in the language L

A modification of an algorithm for synthesis of an automaton from its logical specification is proposed. This algorithm is based on a procedure of splitting components of a disjunctive form. Improvements are aimed at decreasing the number of most complex procedures used during synthesis and at reducing the complexity of formulas processed by the procedures. Moreover, the modification enhances the natural parallelism of the algorithm.     

Optimization of hole reinforcements by doublers

For various technical reasons, cutouts such as holes in thin-walled structures are inevitable and are of significant technical relevance. Unfortunately holes lead to an undesired stress concentration at the hole vicinity and a reduced strength of the structure. Therefore in practice a local reinforcement is usually applied around the hole. The increasing requirements for modern structures in terms of low weight and high strength lead to the question of an optimal reinforcement design. The present paper addresses the well-approved techniques of mathematical structural optimization to determine the aforementioned optimal design of the reinforcement. Thus it is necessary to set up an optimization model, as well as an appropriate structural model, to obtain the structural response (displacements, stresses ...). In this work, the finite element method has been applied for the structural analysis. The optimization procedure described has been utilized for a number of different reinforcement alternatives under various load cases. The numerical procedure implemented works with good reliability and efficiency and gives optimal reinforcement designs that are very useful for the direct engineering application. The results obtained illustrate the necessity and usefulness of the applied optimization procedure. Received April 28, 1999     

面向复杂装备精密产品质量特性的Kriging-RBDO可靠性优化设计

不确定设计参数情形下的复杂装备柔顺机构精密产品质量特性波动与可靠性疲劳退化是精密微机电系统领域的基础性工程难题.针对这一基础性工程难题,提出一种面向复杂装备柔顺机构精密产品可靠性优化设计模型.利用拉丁超立方试验设计(Latin hypercube design,LHD)构建试验设计组合方案,通过有限元数值模拟获取各试验设计组合方案的质量特性值.据此,采用Kriging代理模型建立质量特性与不确定设计参数之间复杂非线性函数关系模型.在此基础上,引入基于可靠性优化设计(Reliability-based design optimization,RBDO)策略,构建面向复杂装备柔顺机构精密产品Kriging-RBDO可靠性优化设计模型.算例表明,所提出的方法在不确定设计参数情形下的复杂装备柔顺机构精密产品早期质量设计方面具有良好的抗疲劳退化特性.     

A bilevel integer programming method for blended composite structures

This paper proposes a new approach for the design of a composite structure. This approach is formulated as an optimization problem where the weight of the structure is minimized such that a reserve factor is higher than a threshold. The thickness of each region of the structure is optimized together with its stacking sequence and the ply drop-offs. The novelty of this approach is that, unlike in common practice, the optimization problem is not simplified and split into two steps, one for finding the thicknesses and one for the stacking sequence. The optimization problem is solved without any simplification assumption. It is formulated as a bilevel integer programming and it uses the backtracking procedure to satisfy the blending and the manufacturing rules. Some numerical experiments are performed to show the efficiency of the proposed optimization method over complex cases which cannot be solved with the existing methods.     

A hierarchical design concept for shape optimization based on the interaction of CAGD and FEM

The numerical treatment of shape optimization problems requires sophisticated software tools such as Computer Aided Design (CAD), the Finite Element Method (FEM) and a suitable Mathematical Programming (MP) algorithm. Efficiency of the overall procedure is guaranteed if these tools interact optimally. The theoretical and numerical effort for sensitivity analysis reflect the complexity of this engineering problem.In this paper we outline a general modelling concept for shape optimization problems. Hierarchical design models within Computer Aided Geometrical Design (CAGD) and the interaction of geometry and FEM lead to an efficient overall optimization procedure. Our concept has been derived, implemented and tested for shell structures but it is seen to be generally applicable.After a short introduction containing the state of the art we give an overview of the numerical tools used and outline the interaction of CAGD and FEM within the overall optimization procedure.The paper is mainly devoted to the hierarchical design space based on a hierarchical geometrical modelling. The major part of computational effort is consumed by sensitivity analysis related to the number of design variables. Therefore, this number should be limited and only few powerful design variables corresponding to the special interests of the considered problem should be defined. This procedure may lead to a considerable limitation of the design space. Based on a hierarchy in the geometrical model different types of design variables are introduced: design variables with global, regional and local influence. The new method is based on successive activation of these types of design variables. This procedure leads to a considerable reduction of computational time for the sensitivity analysis without loss of geometrical flexibility.A new method of geometrical refinement and a successive adaptively driven expansion and reduction of the design space is described. It is based on the degree elevation or degree reduction of parametric curves and surfaces, respectively.A numerical example illustrates the new method and the efficiency of the overall optimization procedure.     

Multi-module satellite component assignment and layout optimization

In previous optimization methods for multi-module satellite equipment (component) layout optimization problem, each component was limited to certain module or supporting surface and could only search its position there. Components could not migrate from one module or supporting surface to another. In this case, the layout design of components within satellite module was seriously hindered from further improvement. In this study a component assignment and layout integration optimization algorithm is presented to deal with this problem, which can assign components to each module of satellite dynamically during optimization procedure. The aim of this paper is to expand the solution space of component layout optimization so as to further improve the component layout design. The proposed component assignment and layout integration optimization algorithm is inspired from the idea of stepwise regression in multiple regression analysis, which allows independent variables to enter or leave regression equation freely. In the proposed algorithm components enter the satellite module one by one in descending order of the product of mass and height. For all supporting surfaces within satellite module, each component will try all of them through layout optimization together with these components have been in the satellite module, and finally select the one with the best fitness as its initial assignment. At the same time, these components have been in the satellite module will be evaluated by their moment of inertia to decide whether they leave the current supporting surfaces and move to another or not. The layout optimization algorithm uses the differential evolution (DE) and random mutation operation to optimize the coordinates and orientations of components, respectively. The performance of the proposed algorithm is finally evaluated on a simplified satellite case. Experimental results show the proposed algorithm outperforms other two algorithms that did not consider component assignment in computational accuracy.     

Application of layout optimization to the design of additively manufactured metallic components

Additive manufacturing (‘3D printing’) techniques provide engineers with unprecedented design freedoms, opening up the possibility for stronger and lighter component designs. In this paper ‘layout optimization’ is used to provide a reference volume and to identify potential design topologies for a given component, providing a useful alternative to continuum based topology optimization approaches (which normally require labour intensive post-processing in order to realise a practical component). Here simple rules are used to automatically transform a line structure layout into a 3D continuum. Two examples are considered: (i) a simple beam component subject to three-point bending; (ii) a more complex air-brake hinge component, designed for the Bloodhound supersonic car. These components were successfully additively manufactured using titanium Ti-6Al-4V, using the Electron Beam Melting (EBM) process. Also, to verify the efficacy of the process and the mechanical performance of the fabricated specimens, a total of 12 beam samples were load tested to failure, demonstrating that the target design load could successfully be met.