Quantum-Inspired Evolutionary Algorithm for Topology Optimization of Modular Cabled-Trusses

This article proposes an alternative optimization framework applied to topology optimization of modular lightweight cabled-truss structures. These structures are described as a system of intrinsically positioned cables and triangular bar formations jointed at their ends by hinged connections to form a rigid framework. The optimized topologies are determined through a stochastic discrete optimization procedure that uses ground structure approach, nonlinear finite element analysis, and quantum-inspired evolutionary algorithms. The optimization searches for optimal mass reduction with minimal losses in stiffness, such relation, is expressed by the stiffness-to-mass ratio parameter. Nonlinear finite element analysis is used to evaluate the static structural response. In order to decrease computation time, kinematically instable and structurally invalid individuals are filtered before evaluation. Modular design approach is taken into consideration to reduce the number of design variables and increase the productibility of cabled-trusses. Symmetric structural response is desired since in several mechanical applications forces can assume different directions during the working cycle. A modular ground structure with 300 elements is optimized, and optimal truss and cabled-truss topologies are compared. Complementary analyses comprise the investigation of the structural performance under different number of modules and slenderness ratios. The results indicate that the proposed optimization framework leads to optimized structures. In addition, it was observed that cabled trusses presented significant improvements in structural performance when compared with trusses.     

考虑接头作用的全复合材料桁架结构多尺度分析

为提高全复合材料桁架分析的精度和效率,引入结构多尺度有限元思想,对接头进行精细化建模,通过建立两点位移约束实现不同尺度模型连接,从而将接头模型嵌入宏观桁架模型,并针对具体制备工艺赋予桁架材料属性。为验证多尺度模型的优势,同时进行全复合材料桁架实验,以及分别基于全部梁单元模型和全部实体单元模型的有限元分析。对比相关模型的计算精度与效率,结果表明多尺度模型能够较好地兼顾计算精度与效率。该文针对全复合材料桁架的结构多尺度有限元建模方法,可精确分析全复合材料桁架承载性能,并且能够提供有效的局部信息,可用于分析其他包含复杂细节构造的大尺度复合材料结构。     

Model updating based on an affine scaling interior optimization algorithm

Finite element model updating is usually considered as an optimization process. Affine scaling interior algorithms are powerful optimization algorithms that have been developed over the past few years. A new finite element model updating method based on an affine scaling interior algorithm and a minimization of modal residuals is proposed in this article, and a general finite element model updating program is developed based on the proposed method. The performance of the proposed method is studied through numerical simulation and experimental investigation using the developed program. The results of the numerical simulation verified the validity of the method. Subsequently, the natural frequencies obtained experimentally from a three-dimensional truss model were used to update a finite element model using the developed program. After updating, the natural frequencies of the truss and finite element model matched well.     

Analysis of one-dimensional stochastic finite elements using neural networks

This paper explores the applicability of neural networks for analyzing the uncertainty spread of structural responses under the presence of one-dimensional random fields. Specifically, the neural network is intended to be a partial surrogate of the structural model needed in a Monte Carlo simulation, due to its associative memory properties. The network is trained with some pairs of input and output data obtained by some Monte Carlo simulations and then used in substitution of the finite element solver. In order to minimize the size of the networks, and hence the number of training pairs, the Karhunen–Loéve decomposition is applied as an optimal feature extraction tool. The Monte Carlo samples for training and validation are also generated using this decomposition. The Nyström technique is employed for the numerical solution of the Fredholm integral equation. The radial basis function (RBF) network was selected as the neural device for learning the input/output relationship due to its high accuracy and fast training speed. The analysis shows that this approach constitutes a promising method for stochastic finite element analysis inasmuch as the error with respect to the Monte Carlo simulation is negligible.     

Hybrid real-code population-based incremental learning and approximate gradients for multi-objective truss design

In this article, real-code population-based incremental learning (RPBIL) is extended for multi-objective optimization. The optimizer search performance is then improved by integrating a mutation operator of evolution strategies and an approximate gradient into its computational procedure. RPBIL and its variants, along with a number of established multi-objective evolutionary algorithms, are then implemented to solve four multi-objective design problems of trusses. The design problems are posted to minimize structural mass and compliance while fulfilling stress constraints. The comparative results based on a hypervolume indicator show that the proposed hybrid RPBIL is the best performer for the large-scale truss design problems.     

A unified stochastic framework for robust topology optimization of continuum and truss-like structures

In this article, a unified framework is introduced for robust structural topology optimization for 2D and 3D continuum and truss problems. The uncertain material parameters are modelled using a spatially correlated random field which is discretized using the Karhunen–Loève expansion. The spectral stochastic finite element method is used, with a polynomial chaos expansion to propagate uncertainties in the material characteristics to the response quantities. In continuum structures, either 2D or 3D random fields are modelled across the structural domain, while representation of the material uncertainties in linear truss elements is achieved by expanding 1D random fields along the length of the elements. Several examples demonstrate the method on both 2D and 3D continuum and truss structures, showing that this common framework provides an interesting insight into robustness versus optimality for the test problems considered.     

Parallel computational strategies for structural optimization

The objective of this paper is to investigate the efficiency of various computational algorithms implemented in the framework of structural optimization methods based on evolutionary algorithms. In particular, the efficiency of parallel computational strategies is examined with reference to evolution strategies (ES) and genetic algorithms (GA). Parallel strategies are implemented both at the level of the optimization algorithm, by exploiting the natural parallelization features of the evolutionary algorithms, as well as at the level of the repeated structural analysis problems that are required by ES and GA. In the latter case the finite element solutions are performed by the FETI domain decomposition method specially tailored to the particular type of problems at hand. The proposed methodology is generic and can be applied to all types of optimization problems as long as they involve large‐scale finite element simulations. The numerical tests of the present study are performed on sizing optimization of skeletal structures. The numerical tests demonstrate the computational advantages of the proposed parallel strategies, which become more pronounced in large‐scale optimization problems. Copyright © 2003 John Wiley & Sons, Ltd.     

Hybrid optimization and Bayesian inference techniques for a non‐smooth radiation detection problem

We propose several algorithms to recover the location and intensity of a radiation source located in a simulated 250 × 180 m block of an urban center based on synthetic measurements. Radioactive decay and detection are Poisson random processes, so we employ likelihood functions based on this distribution. Owing to the domain geometry and the proposed response model, the negative logarithm of the likelihood is only piecewise continuous differentiable, and it has multiple local minima. To address these difficulties, we investigate three hybrid algorithms composed of mixed optimization techniques. For global optimization, we consider simulated annealing, particle swarm, and genetic algorithm, which rely solely on objective function evaluations; that is, they do not evaluate the gradient in the objective function. By employing early stopping criteria for the global optimization methods, a pseudo‐optimum point is obtained. This is subsequently utilized as the initial value by the deterministic implicit filtering method, which is able to find local extrema in non‐smooth functions, to finish the search in a narrow domain. These new hybrid techniques, combining global optimization and implicit filtering address, difficulties associated with the non‐smooth response, and their performances, are shown to significantly decrease the computational time over the global optimization methods. To quantify uncertainties associated with the source location and intensity, we employ the delayed rejection adaptive Metropolis and DiffeRential Evolution Adaptive Metropolis algorithms. Marginal densities of the source properties are obtained, and the means of the chains compare accurately with the estimates produced by the hybrid algorithms. Copyright © 2016 John Wiley & Sons, Ltd.     

Safety factor maximization for trusses subjected to fatigue stresses

This article presents a mathematical model for sizing optimization of undamped trusses subjected to dynamic loading leading to fatigue. The combined effect of static and dynamic loading, at steady state, is considered. An optimization model, whose objective is the maximization of the safety factor of these trusses, is developed. A new quantity (equivalent fatigue strain energy) combining the effects of static and dynamic stresses is presented. This quantity is used as a global measure of the proximity of fatigue failure. Therefore, the equivalent fatigue strain energy is minimized, and this seems to give a good value for the maximal equivalent static stress. This assumption is verified through two simple examples. The method of moving asymptotes is used in the optimization of trusses. The applicability of the proposed approach is demonstrated through two numerical examples; a 10-bar truss with different loading cases and a helicopter tail subjected to dynamic loading.     

Truss topology optimization with static and dynamic constraints using modified subpopulation teaching–learning-based optimization

In this study, an improved version of the teaching–learning-based optimization (TLBO) algorithm is proposed for truss topology optimization (TTO), with static and dynamic constraints on planar and space trusses. The basic TLBO algorithm is improved to enhance its exploration and exploitation abilities by considering various factors such as the number of teachers, adaptive teaching, tutorial learning and self-motivated learning. The TTO problems are considered with multiple load conditions and subjected to constraints for natural frequencies, element stresses, nodal displacements, Euler buckling criteria and kinematic stability conditions. TTO is achieved with the removal of superfluous elements and nodes from the ground structure, and results in a mass saving. In this method, difficulties arise owing to singular solution and unnecessary analysis; therefore, the finite element model is reformed to resolve these issues. A single-stage optimization approach is used, in which size and topology optimization are considered simultaneously. The results obtained are compared with the best solutions obtained by the algorithm. The results reveal that the modified subpopulation teaching–learning-based optimization (MS-TLBO) algorithm is more effective than other state-of-the-art algorithms.     

地震作用下空间网架结构考虑损伤累积效应的弹塑性分析

考虑钢材的损伤累积效应和应变强化效应,应用塑性应变和能量耗损理论建立了钢材的损伤力学模型;在此模型基础上,推导了网架结构考虑损伤累积效应的单元弹塑性刚度矩阵和结构动力平衡微分方程,编制了相应的有限元分析计算程序,并对一空间网架结构算例进行了数值仿真分析。结果表明,考虑损伤累积效应对空间网架结构的弹塑性地震反应有着显著的影响,其中有损伤杆件的应力减小、应变增大;无损伤杆件的应力、应变均增大;在不同方向组合地震的作用下,考虑与不考虑损伤累积效应,网架结构的内力和变形趋势相同;不同的地震作用,考虑损伤累积效应时对网架结构的内力和变形的影响也较大。     

Ballistic resistance of hybrid-cored sandwich plates: Numerical and experimental assessment

The impact responses and ballistic resistance of sandwich plates having three different types of hybrid cores are investigated. The hybrid cores include metallic pyramidal lattice trusses, metallic pyramidal lattice trusses with ceramic prism insertions, and metallic pyramidal lattice trusses with ceramic prism insertions and void-filling epoxy resin. Three-dimensional (3D) finite element (FE) simulations are carried out for each sandwich type impacted by a hemispherical projectile. Upon validating the FE simulation results with experimental measurements, the ballistic limit velocity, energy absorption and failure mechanisms for each type of the sandwich as well as the influence of key material, structural and topological parameters are investigated systematically. Sandwich plates having metallic pyramidal lattice core with ceramic insertions and epoxy resin filling void spaces are found to outperform the other two sandwich types. It is also demonstrated that the back face-sheet plays a more significant role than the front face-sheet in resisting ballistic impacts.     

基于有限元和神经网络的杂交建模

针对复杂非线性结构动力学系统提出了一种基于有限元与神经网络相结合的杂交建模方法。依据该方法,首先将系统中的线性结构部分采用有限元建模,非线性或难以机理建模的结构部件采用神经网络描述。其次,再通过力和位移边界联接条件将有限元模型部分和神经网络模型部分结合从而得到整个系统的杂交模型,且杂交模型的物理结构明确,精度较高,网络规模较小。在一非线性隔振系统的杂交建模算例仿真中,用所建杂交模型对正弦及宽带随机激励进行了预测检验分析,结果良好,该杂交建模方法为主体结构为线弹性结构而又包含有强非线性器件的非线性动力学系统提供了一种有效的建模途径。     

Swarm algorithms for single- and multi-objective optimization problems incorporating sensitivity analysis

Swarm algorithms such as particle swarm optimization (PSO) are non-gradient probabilistic optimization algorithms that have been successfully applied for global searches in complex problems such as multi-peak problems. However, application of these algorithms to structural and mechanical optimization problems still remains a complex matter since local optimization capability is still inferior to general numerical optimization methods. This article discusses new swarm metaphors that incorporate design sensitivities concerning objective and constraint functions and are applicable to structural and mechanical design optimization problems. Single- and multi-objective optimization techniques using swarm algorithms are combined with a gradient-based method. In the proposed techniques, swarm optimization algorithms and a sequential linear programming (SLP) method are conducted simultaneously. Finally, truss structure design optimization problems are solved by the proposed hybrid method to verify the optimization efficiency.     

Experimental and numerical investigations on full-scale adhesively bonded timber trusses

Timber architecture, taking advantage of modern production techniques, is increasingly moving towards free forms; however, traditional joining techniques are not yet adapted to echo the new expression at the level of the details. This paper reports on adhesively bonded joints as a way to help architects fully unleash their creative potential. For this purpose, experimental and numerical investigations on full-scale adhesively bonded timber trusses were performed, in which adhesive bonds were compared to traditional doweled connections. The adhesively bonded trusses achieved significantly higher failure load and stiffness. Tests on small clear specimens were conducted to determine input parameters for finite element analyses. The sole timber connection was characterised, giving valuable insights into the mechanical behaviour of this truss component. At this end, the influence of the embedded length of the applied sleet plates was experimentally determined, delivering data to benchmark the subsequent dimensioning method. The trusses were then modeled and excellent agreement was found between numerical and experimental results. Finally, a dimensioning method, based on a realistic multi-axial failure criterion coupled with size effects was implemented and yielded very good agreement when with experimental results. The reported investigation demonstrates the high potential of adhesive bonding in timber structures.     

不均匀随机参数桁架结构的随机反应分析

以随机荷载作用下的不均匀随机参数桁架结构为研究对象,提出了求解结构反应数字特征的矩法。从结构有限元方程出发,推导出结构刚度矩阵对各单元的弹性模量、横截面积以及各节点坐标的导数,进一步导得结构位移反应对各随机参数的敏度。利用随机变量函数的矩法,导出了结构位移反应的均值和方差,依据单元位移应力的转换表达式,分析了应力反应的均值和方差。算例表明,结构反应的方差取决于各随机参数的分散性和参数间的相关性。     

Design sensitivity analysis and optimization of non‐linear transient dynamics. Part I—sizing design

A continuum‐based sizing design sensitivity analysis (DSA) method is presented for the transient dynamic response of non‐linear structural systems with elastic–plastic material and large deformation. The methodology is aimed for applications in non‐linear dynamic problems, such as crashworthiness design. The first‐order variations of the energy forms, load form, and kinematic and structural responses with respect to sizing design variables are derived. To obtain design sensitivities, the direct differentiation method and updated Lagrangian formulation are used since they are more appropriate for the path‐dependent problems than the adjoint variable method and the total Lagrangian formulation, respectively. The central difference method and the finite element method are used to discretize the temporal and spatial domains, respectively. The Hughes–Liu truss/beam element, Jaumann rate of Cauchy stress, rate of deformation tensor, and Jaumann rate‐based incrementally objective stress integration scheme are used to handle the finite strain and rotation. An elastic–plastic material model with combined isotropic/kinematic hardening rule is employed. A key development is to use the radial return algorithm along with the secant iteration method to enforce the consistency condition that prevents the discontinuity of stress sensitivities at the yield point. Numerical results of sizing DSA using DYNA3D yield very good agreement with the finite difference results. Design optimization is carried out using the design sensitivity information. Copyright © 2000 John Wiley & Sons, Ltd.     

基于完全概率的随机桁架固有频率的可靠性分析

对随机桁架固有频率的概率密度函数提出了一种求解方法。考虑结构物理参数和几何参数的随机性，通过构建随机参数桁架结构的有限元模型，利用瑞利商公式获得了结构固有频率随机函数的计算表达式，应用随机函数的概率分布函数表达式，通过确定积分区间、变量替换、积分顺序变换等一系列数学上的处理，获得结构固有频率的概率密度函数，进而实现对结构固有频率可靠度的精确计算。箅例的结果与Monte-Carlo模拟法结果比较，表明该方法的正确性和有效性。     

Application of hybrid Trefftz finite element method to non‐linear problems of minimal surface

This investigation provides a hybrid Trefftz finite element approach for analysing minimal surface problems. The approach is based on combining Trefftz finite element formulation with radial basis functions (RBF) and the analogue equation method (AEM). In this method, use of the analogue equation approach avoids the difficulty of treating the non‐linear terms appearing in the soap bubble equation, making it possible to solve non‐linear problems with the Trefftz method. Global RBF is used to approximate the inhomogeneous term induced from non‐linear functions and other loading terms. Finally, some numerical experiments are implemented to verify the efficiency of this method. Copyright © 2006 John Wiley & Sons, Ltd.     

Experimental studies on roof trusses made of glubam

This paper presents experimental and analytical studies on trusses made of glue-laminated bamboo or glubam, which is a new type of structural material unlike conventional steel or timber. Six full-scale model trusses with two types of configurations and sizes were tested to failure under gradually increased vertical load. The failure of the model trusses was caused by lateral buckling of the top compressive chords. Tests show that the model glubam trusses have adequate stiffness and strength. Analyses were also conducted to model the truss behavior with considering different joint conditions, such as pinned, rigid as well as semi-rigid joint using fictitious members. The analytical results for deformation at the design load level agree with the test results favorably well using all types of joint models. The semi-rigid joint model provides a slightly better prediction to the load carrying capacities of the model trusses. However, the analytical truss model based on pinned joints generally provides conservative prediction to load carrying capacities.