Shape optimization of two-dimensional elastic structures with optimal thicknesses for fixed parts

Shape optimization of two-dimensional elastic structures is treated in this paper. B-spline function is used as the shape function and design element technique is adapted simultaneously. An interesting comparison is done between sizing optimization and shape optimization. Shape optimization of two-dimensional elastic structures with optimal thicknesses for fixed parts is lighter in structural weight than that for one of uniform thickness. Four examples are solved using two or three design elements and the hybrid approximation technique in combination with the dual method from mathematical programming.     

Large scale structural optimization: Computational methods and optimization algorithms

Summary The objective of this paper is to investigate the efficiency of various optimization methods based on mathematical programming and evolutionary algorithms for solving structural optimization problems under static and seismic loading conditions. Particular emphasis is given on modified versions of the basic evolutionary algorithms aiming at improving the performance of the optimization procedure. Modified versions of both genetic algorithms and evolution strategies combined with mathematical programming methods to form hybrid methodologies are also tested and compared and proved particularly promising. Furthermore, the structural analysis phase is replaced by a neural network prediction for the computation of the necessary data required by the evolutionary algorithms. Advanced domain decomposition techniques particularly tailored for parallel solution of large-scale sensitivity analysis problems are also implemented. The efficiency of a rigorous approach for treating seismic loading is investigated and compared with a simplified dynamic analysis adopted by seismic codes in the framework of finding the optimum design of structures with minimum weight. In this context a number of accelerograms are produced from the elastic design response spectrum of the region. These accelerograms constitute the multiple loading conditions under which the structures are optimally designed. The numerical tests presented demonstrate the computational advantages of the discussed methods, which become more pronounced in large-scale optimization problems.     

Integrated design optimization of base-isolated concrete buildings under spectrum loading

Base isolation has become a practical control strategy for protecting structures against seismic hazards. Most previous studies on the optimum design of base-isolated structures have been focused on the design optimization of either the base isolation or the superstructure. It is necessary to simultaneously optimize both the base isolation and the superstructure as a whole to seek the most cost-efficient design for such structures. This paper presents an effective numerical optimization technique for the seismic design of base-isolated concrete building structures under spectrum loading. Attempts have been made to automate the integrated spectrum analysis and design optimization procedure and to minimize the total cost of the base-isolated building subject to design performance criteria in terms of the interstory drifts of the superstructure and the lateral displacement of the isolation system. In the optimal design problem formulation, the cost of the superstructure can be expressed in terms of concrete member sizes while assuming all these members to be linearly elastic under earthquake actions. However, the isolation system is assumed to behave nonlinearly, and its cost can be related to the effective horizontal stiffness of each isolator. Using the principle of virtual work, the lateral drift responses of concrete base-isolated buildings can be explicitly formulated and the integrated optimization problem can be solved by the optimality criteria method. The technique is capable of achieving the optimal balance between the costs of the superstructure and the isolation system while the design performance criteria can be simultaneously satisfied. One practical building example with and without base isolation is used to illustrate the effectiveness of the optimal design technique.     

Nonlinear analysis and optimal design of structures via force method and genetic algorithm

In this paper analysis, design and optimization of structures are performed considering material and geometric nonlinearity. For this purpose, the force method, energy concepts and genetic algorithm are employed. The first part of this paper contains the formulation of the problem based on the force method and energy principles using linear analysis. In this method, the material nonlinearity is also included. The formulations are examined by simple illustrative examples. Reduction of the complementary energy is efficiently incorporated in this approach. The second part of the article combines the process of the analysis and design to achieve specified stress ratios for the members of the structure. This problem is especially important in the seismic deign of structures. Geometric nonlinearity is then formulated, in the third part by employing two approaches. Considering the energy term next to the weight of the structure, optimal dimensions of the structures are selected. In each part, the efficiency of the methods is illustrated by means simple examples.     

基于无网格径向点插值方法的简谐激励下的连续体结构拓扑优化

针对用有限元法进行连续体结构拓扑优化时需不断重构网格来处理网格畸变和网格移动,且存在数值计算不稳定等问题,基于无网格径向点插值方法(Radial Point Interpolation Method,RPIM)对简谐激励下的连续体结构进行拓扑优化.选取节点的相对密度作为设计变量,以结构动柔度最小化为目标函数,基于带惩罚的各向同性固体微结构(Solid Isotropic Microstructure with Penalization,SIMP)模型建立简谐激励下的优化模型;采用伴随法求解得到目标函数的敏度分析公式;利用优化准则法求解优化模型.经典的二维连续体结构拓扑优化算例证明该方法的可行性和有效性.     

Cost-weight trades for modular composite structures

A design approach for airframe structures is formulated based on the concept of modularity allowing trade-offs and optimization between cost and weight. A modular structure can be created by replacing a collection of parts which all have a unique design by a collection of parts where the same design repeats multiple times. Structures with high levels of modularity have higher weight since it is harder to design a weight-efficient structure when the amount of design options is limited, but this weight increase might be worth the associated decrease in manufacturing cost. In modular design, cost reductions are achieved through learning curve effects and through reduction of the non-recurring cost, for example, due to lower tooling costs. Based on dynamic programming, an approach to determine the optimum number of repeating designs was determined and applied to a composite fuselage structure. Two examples are given where the cost-weight efficiency at different modularity levels is assessed for a composite airframe: the stringers and the frames in a fuselage. The corresponding cost-weight diagrams indicated that the modularity concept provides a useful methodology for designing more cost- weight efficient structures. In both cases it was possible to replace a large amount of designs and increase the level of modularity of the structure, yielding significant reductions in recurring and non-recurring manufacturing costs while keeping the associated weight increase of the structure to a minimum.     

Optimal design of steel frames subject to gravity and seismic codes' prescribed lateral forces

Allowable stress design of two-dimensional braced and unbraced steel frames based on AISC specifications subject to gravity and seismic lateral forces is formulated as a structural optimization problem. The nonlinear constrained minimization algorithm employed is the feasible directions method. The objective function is the weight of the structure, and behaviour constraints include combined bending and axial stress, shear stress, buckling, slenderness, and drift. Cross-sectional areas are used as design variables. The anylsis is performed using stiffness formulation of the finite element analysis method. Equivalent static force and response spectrum analysis methods of seismic codes are considered. Based on the suggested methodology, the computer program OPTEQ has been developed. Examples are presented to illustrate the capability of the optimal design approach in comparative study of various types of frames subjected to gravity loads and seismic forces according to a typical code.     

Stochastic optimal coupling-control of adjacent building structures

A stochastic optimal coupling-control method for adjacent building structures is proposed. The coupled structures with control devices under random seismic excitation are condensed to form a reduced-order model for the control analysis. The stochastic averaging method is applied to the reduced model to obtain Itô stochastic differential equations with respect to structural modal vibration energies. Then the stochastic dynamical programming principle is applied to the energy processes to establish a dynamical programming equation, by which the optimal coupling-control law is determined. The seismic response mitigation is achieved through the structural energy control and the dimension of optimal control problem is reduced. The seismic excitation spectrum is taken into account according to the stochastic dynamical programming principle. The random response of the non-linear controlled structures is predicted by using the stochastic averaging method and is compared with that of the uncontrolled structures to evaluate the control efficacy. A numerical study is conducted to demonstrate the response reduction capacity of the proposed stochastic optimal coupling-control method for adjacent building structures.     

Bidirectional Evolutionary Structural Optimization (BESO) based design method for lattice structure to be fabricated by additive manufacturing

Unlike traditional manufacturing methods, additive manufacturing can produce parts with complex geometric structures without significant increases in fabrication time and cost. One application of additive manufacturing technologies is the fabrication of customized lattice-skin structures which can enhance performance of products while minimizing material or weight. In this paper, a novel design method for the creation of periodic lattice structures is proposed. In this method, Functional Volumes (FVs) and Functional Surfaces (FSs) are first determined based on an analysis of the functional requirements. FVs can be further decomposed into several sub-FVs. These sub-FVs can be divided into two types: FV with solid and FV with lattice. The initial design parameters of the lattice are selected based on the proposed guidelines. Based on these parameters, a kernel based lattice frame generation algorithm is used to generate lattice wireframes within the given FVs. At last, traditional bidirectional evolutionary structural optimization is modified to optimize distribution of lattice struts’ thickness. The design method proposed in this paper is validated through a case study, and provides an important foundation for the wide adoption of additive manufacturing technologies in the industry.     

Simultaneous size and geometry optimization of steel trusses under dynamic excitations

During the past decades, the main focus of the research in steel truss optimization has been tailored towards optimal design under static loading conditions and limited work has been devoted to investigating the optimum structural design considering dynamic excitations. This study addresses the simultaneous size and geometry optimization problem of steel truss structures subjected to dynamic excitations. Using the well-known big bang-big crunch algorithm, the minimum-weight design of steel trusses is conducted under both periodic and non-periodic excitations. In the case of periodic excitations, in order to examine the effect of the exciting period of the dynamic load on the final results, the design instances are optimized under different exciting periods and the obtained results are compared. It is observed that by increasing the excitation period of the considered sinusoidal loading as well as the finite rise time of the non-periodic step force, the optimization results approach the minimum design weight obtained under the static loading counterpart. However, in the case of the studied rectangular periodic excitation, the results obtained do not approach the optimum design associated with the static loading case even for higher values of the exciting period.     

双向地震激励下隔震结构抗倾覆特性的数值分析

为研究叠层橡胶支座隔震建筑的抗倾覆性能,建立隔震结构在双向地震激励下倾覆力矩时域响应动力分析模型.在对该模型进行简化的基础上,利用结构设计反应谱探讨结构高宽比和结构基本周期等因素对隔震结构抗倾覆力矩与倾覆力矩比值的影响.给出多层和小高层隔震结构在双向地震作用下的抗倾覆安全因数随地震烈度、场地土类别的变化规律.利用本课题...     

Optimization of reinforced concrete frames subjected to historical time-history loadings using DMPSO algorithm

In this paper, the seismic design of reinforced concrete (RC) frames subjected to time-history loadings was formulated as an optimization problem. Because finding the optimum design is relatively difficult and time-consuming for structural dynamics problems, an innovative algorithm combining multi-criterion decision-making (DM) and Particle Swarm Optimization (PSO), called DMPSO, was presented for accelerating convergence toward the optimum solution. The effectiveness of the proposed algorithm was illustrated in some benchmark reinforced concrete optimization problems. The main goal was to minimize the cost or weight of structures subjected to time-history loadings while satisfying all design requirements imposed by building design codes. The results confirmed the ability of the proposed algorithm to find the optimal solutions for structural optimization problems subjected to time-history loadings.     

Optimal topology design of internal stiffeners for machine pedestal structures using biological branching phenomena

Naturally evolved biological structures exhibit the optimal characteristics of light weight, high stiffness, and high strength. Based on the growth mechanism of biological branch systems in nature, an optimization method for internal stiffener plate distribution in box structures is suggested. Under the given load and support conditions, the internal stiffener plates of machine pedestal structures grow, bifurcate, and degenerate towards the direction of maximum overall structural stiffness in accordance with the adaptive growth law. The optimal and distinct distribution of internal stiffener plates with the most effective load path is thus obtained. Based on this, a size optimization for lightweight design is conducted, in which the self-weight of the structures is taken as the design objective, and the natural vibration frequency and static stiffness in the direction that is sensitive to machining accuracy are set as constraints. Finally, an optimized structure is obtained. The effectiveness of the proposed method is verified by using a precision grinder bed as an example. The results of numerical simulation and 3D–printed model experiment indicate that both the dynamic and the static performance of the optimized structure are improved, while the structural weight is reduced by compared with the initial structure. The suggested design method provides a new solution approach for the design optimization of machine pedestal structures.     

On objective functions of minimizing the vibration response of continuum structures subjected to external harmonic excitation

This work deals with the topological design of vibrating continuum structures. The vibration of continuum structure is excited by time-harmonic external mechanical loading with prescribed frequency and amplitude. In comparison with well-known compliance minimization in static topology optimization, various objective functions are proposed in literature to minimize the response of vibrating structures, such as power flow, vibration transmission, and dynamic compliances, etc. Even for the dynamic compliance, different definitions are found in literature, which have quite different formulations and influences on the optimization results. The aim of this paper is to provide a comparison of these different objective functions and propose reference forms of objective functions for design optimization of vibration problems. Analytical solutions for two degrees of freedom system and topological design of plane structures in numerical examples are compared using different optimization formulations for given various excitation frequencies. The results are obtained by the finite element method and gradient based optimization using analytical sensitivity analysis. The optimized topologies and vibration response of the optimized structures are presented. The influence of excitation frequencies and the eigenfrequencies of the structure are discussed in the numerical examples.     

多孔模型设计方法

多孔模型质量轻,且具有优秀的力热磁等复合性能。采用多孔模型有望突破传统设计极限,获得 综合性能优异的机械部件,满足先进工业级产品对结构的极致物理性能追求。近年来,增材制造技术的发展与成 熟,大幅推动了多孔模型的工业应用,多孔模型已经在航空航天部件、医疗器械等重要装备或仪器中发挥出独特 且卓越的工业价值。因此,以多孔模型设计方法为落脚点,分别从基于几何建模的多孔模型正向设计方法、基于 拓扑优化的多孔模型逆向设计方法 2 方面阐述相关工作。前者论述了多孔模型的离散体素表示、连续参数表示、 连续隐式表示、其他及混合表示等建模方法,后者论述了多孔模型微结构单元优化设计方法、多孔模型结构设计 方法,并探讨了 2 方面多孔模型设计的发展趋势。     

School-based optimization for performance-based optimum seismic design of steel frames

The performance-based optimum seismic design of steel frames is one of the most complicated and computationally demanding structural optimization problems. Metaheuristic optimization methods have been successfully used for solving engineering design problems over the last three decades. A very recently developed metaheuristic method called school-based optimization (SBO) will be utilized in the performance-based optimum seismic design of steel frames for the first time in this study. The SBO actually is an improved/enhanced version of teaching–learning-based optimization (TLBO), which mimics the teaching and learning process in a class where learners interact with the teacher and between themselves. Ad hoc strategies are adopted in order to minimize the computational cost of SBO results. The objective of the optimization problem is to minimize the weight of steel frames under interstory drift and strength constraints. Three steel frames previously designed by different metaheuristic methods including particle swarm optimization, improved quantum particle swarm optimization, firefly and modified firefly algorithms, teaching–learning-based optimization, and JAYA algorithm are used as benchmark optimization examples to verify the efficiency and robustness of the present SBO algorithm. Optimization results are compared with those of other state-of-the-art metaheuristic algorithms in terms of minimum structural weight, convergence speed, and several statistical parameters. Remarkably, in all test problems, SBO finds lighter designs with less computational effort than the TLBO and other methods available in metaheuristic optimization literature.

     

Reliability based structural optimization: A simplified safety index approach

A probabilistic optimal design methodology for complex structures modelled with finite element methods is presented. The main emphasis is on developing probabilistic analysis tools suitable for optimization. An advanced second-moment method is employed to evaluate the failure probability of the performance function. The safety indices are interpolated using the information at the mean and most probable failure point. The minimum weight design with an improved safety index limit is achieved by using the extended interior penalty method of optimization. Numerical examples covering beam and plate structures are presented to illustrate the design approach. The results obtained by using the proposed approach are compared with those obtained by using the existing probabilistic optimization techniques.     

Isogeometric configuration design optimization of shape memory polymer curved beam structures for extremal negative Poisson’s ratio

Using a continuum-based design sensitivity analysis (DSA) method, a configuration design optimization method is developed for curved Kirchhoff beams with shape memory polymers (SMP), from which we systematically synthesize lattice structures achieving target negative Poisson’s ratio. A SMP phenomenological constitutive model for small strains is utilized. A Jaumann strain, based on the geometrically exact beam theory, is additively decomposed into elastic, stored, and thermal parts. Non-homogeneous displacement boundary conditions are employed to impose mechanical loadings. At each equilibrium configuration, an additional nonlinear analysis is performed to calculate the Poisson’s ratio and its design sensitivity of the SMP material. The design objectives are twofold: for purely elastic materials, lattice structures are designed to achieve prescribed Poisson’s ratios under finite compressive deformations. Also, SMP-based lattice structures are synthesized to possess target Poisson’s ratios in specified temperature ranges. The analytical design sensitivity of the Poisson’s ratio is verified through comparison with finite difference sensitivity. Several configuration design optimization examples are demonstrated.     

Damage-reduction-based structural optimum design for seismic RC frames

The development of structural seismic design is briefly reviewed with an emphasis on different conceptual approaches and their success in practical engineering applications. The concept of damage-reduction-based seismic design is proposed, in which the whole structural system is either physically or functionally designed as two parts, the main-function part and the damage-reduction part. The main-function part satisfies the serviceability requirements of the structural system. The damage-reduction part is composed of several damage-reduction elements, which work under hazard loads to ensure the safety of the main-function part, and further maintain the serviceability of the structural system by specific damage-reduction techniques or even by failure of damage-reduction elements. The formulation of damage-reduction-based optimum design for seismic structures is presented and some related issues are addressed, including a simplified approach to reliability analysis, the evaluation of the structural loss expectation, and the modified enumeration method. Numerical examples of RC frames are examined. The results show that several measures of structural seismic performance, including the life-cycle cost, severe earthquake action, and the story-drift reliability index of the weakest story, can be improved by damage-reduction-based design compared with conventional design.     

Modified-modal-pushover-based seismic optimum design for steel structures considering life-cycle cost

A modified-modal-pushover-based optimization technique is presented to design steel moment resisting frame buildings for minimizing the life-cycle cost based on the framework of performance based earthquake engineering. Modified modal pushover analysis (MMPA) procedure capturing the higher mode effect well is utilized to analyze the inelastic seismic demands of the structures subjected to the considered design earthquakes in terms of the Chinese seismic code for buildings, especially for the medium- to high-rise buildings. Furthermore, the life-cycle cost is formulated as the summation of the initial material cost and the future expected damage loss, which can be stated as a function of seismic performance levels and their corresponding failure probability by means of a statistical model. Meanwhile, the damage loss is explicitly and continuously expressed by the defined interstory drift index using the fuzzy-decision theory. Moreover, the powerful adaptive simulated annealing algorithm is applied to solve the discrete optimization problem due to the discreteness of standard steel sections. Finally, a 9-story planar steel frame is provided to illustrate the effectiveness of the proposed optimization design technique, which achieves not only more cost-effective design but greatly improves the robustness of the optimum design as well.