Topology optimization of beam cross-section considering warping deformation

The beam cross-section optimization problems have been very important as beams are widely used as efficient load-carrying structural components. Most of the earlier investigations focus on the dimension and shape optimization or on the topology optimization along the axial direction. An important problem in beam section design is to find the location and direction of stiffeners, for the introduction of a stiffener in a closed beam section may result in a topologically different configuration from the original; the existing section shape optimization theory cannot be used. The purpose of this paper is to formulate a section topology optimization technique based on an anisotropic beam theory considering warping of sections and coupling among deformations. The formulation and corresponding solving method for the topology optimization of beam cross-sections are proposed. In formulating the topology optimization problem, the minimum averaged compliance of the beam is taken as objective, and the material density of every element is used as design variable. The schemes to determine the rigidity matrix of the cross-sections and the sensitivity analysis are presented. Several kinds of topologies of the cross-section under different load conditions are given, and the effect of load condition on the optimum topology is analyzed.     

Bending of beams of arbitrary cross sections - optimal design by analytical formulae

The paper deals with the conceptual design of a beam under bending. The common problem of designing a beam in a state of pure bending is discussed in the framework of Pareto-optimality theory. The analytical formulation of the Pareto-optimal set is derived by using a procedure based on the reformulation of the Fritz John Pareto-optimality conditions. The shape of the cross section of the beam is defined by a number of design variables pertaining to the optimization process by means of efficiency factors. Such efficiency factors are able to describe the bending properties of any beam cross section and can be used to derive analytical formulae. Design performance is determined by the combination of cross section shape, material and process. Simple expressions for the Pareto-optimal set of a beam of arbitrary cross section shape under bending are derived. This expression can be used at the very early stage of the design to choose a possible cross section shape and material for the beam among optimal solutions.     

Two-dimensional field analysis for CAD of Rotman-type beam-forming lenses

A general procedure for design and analysis of a Rotman-type beam-forming lens using 2-dimensional field analysis is proposed. Evaluation of reflection coefficients, coupling between ports, main beam direction, 3-dB beam width and side lobe level are described. The results for a sample case are in agreement with the experimental results. The procedure developed is suitable for CAD implementation leading to optimization of Rotman lens layout configuration.     

嵌入多层黏弹性胶膜复合材料阻尼工字梁的多目标设计优化

针对嵌入多层黏弹性胶膜的复合材料阻尼工字梁,传统的混合单元法在进行结构动态分析与设计优化时存在很大困难的问题,采用基于离散层理论的多层梁单元建模分析复合材料阻尼工字梁.通过对正交各向异性铺层和腹板进行等效处理的方法,对工字梁凸缘嵌入单层阻尼层模型进行参数化分析;分别对嵌入多层或单层阻尼层的模型建立多目标优化模型,优化目标为模态损耗因子和固有频率最大化,设计变量为阻尼层层数（厚度）及其嵌入位置;应用多目标遗传算法进行优化求解.结果表明：基于离散层理论的阻尼梁单元计算精度好且易于优化,对于嵌入单层较厚阻尼和嵌入多层较薄阻尼的复合材料工字梁,获得的阻尼效果与动刚度损失基本相当,但对于高阻尼的方案,前者比后者的动刚度损失更大.     

Nonsmooth and nonconvex structural analysis algorithms based on difference convex optimization techniques

The impact of difference convex optimization techniques on structural analysis algorithms for nonsmooth and non-convex problems is investigated in this paper. Algorithms for the numerical solutions are proposed and studied. The relation to more general optimization techniques and to computational mechanics algorithms is also discussed. The theory is illustrated by a composite beam delamination example.     

相控阵测量雷达波控系统优化设计

以某型相控阵雷达为例,从雷达波束控制的实现方法出发,对雷达波控信号完整性(SI)进行了理论分析.通过天线小阵实验,讨论了天线阵面电磁场对雷达波控信号的影响,实现了对雷达波控系统的优化设计.     

A stochastic beam search for the berth allocation problem

In this paper, the optimization of the Berth Allocation Problem (BAP) is transformed into a multiple stage decision making procedure and a new multiple stage search method, namely stochastic beam search algorithm, is proposed to solve it. New techniques such as an improved beam search scheme, a two-phase node goodness estimation, and a stochastic node selection criteria are proposed. Real-life information provided by Singapore Port was collected as our test data. Experimental results show that the proposed stochastic beam search is more accurate and efficient than both the state-of-the-art meta-heuristic and the traditional determinist beam search.     

Optimal design of elastic-plastic beams with additional supports

An optimization problem of elastic-plastic beams is discussed. An additional support, whose location must be selected so as to minimize the compliance of the beam, is introduced to the beam. The problem is solved with the aid of the optimal control theory. A new optimality condition is presented. Two example problems are solved.     

Topology optimization of structures with integral compliant mechanisms for mid-frequency response

The purpose of this paper is to present a method for developing new truss-like sandwich structures that exhibit desirable mid-frequency vibratory characteristics. Specifically, a genetic algorithm optimization routine is used to determine candidate small scale structural topologies, i.e. unit cells, that may be used in the design of larger scale periodic sandwich structures. This multi-scale procedure is demonstrated starting with several unit cell topology optimization examples. From these examples a specific optimal unit cell is selected for further investigation and integration into a periodic sandwich beam. Computational results indicate that the proposed optimization approach is effective when used to design new structures for reduced mid-frequency vibratory response.     

Improvement of numerical instabilities in topology optimization using the SLP method

In this paper, we present a method for preventing numerical instabilities such as checkerboards, mesh-dependencies and local minima occurring in the topology optimization which is formulated by the homogenization design method and in which the SLP method is used as optimizer. In the present method, a function based on the concept of gravity (which we named “the gravity control function”) is added to the objective function. The density distribution of the topology is concentrated by maximizing this function, and as a result, checkerboards and intermediate densities are eliminated. Some techniques are introduced in the optimization procedure for preventing the local minima. The validity of the present method is demonstrated by numerical examples of both the short cantilever beam and the MBB beam. Received February 23, 1999     

Simultaneous optimization of photostrictive actuator locations,numbers and light intensities for structural shape control using hierarchical genetic algorithm

The present paper introduces an investigation into simultaneous optimization of the PbLaZrTi-based actuator configuration and corresponding applied light intensity for morphing beam structural shapes. A finite element formulation for multiphysics analysis of coupled opto-electro-thermo-mechanical fields in PbLaZrTi ceramics is derived and verified with the theoretical solution and the commercial software ANSYS. This element is then used to simulate beam bending shape control using the orthotropic PbLaZrTi actuators and the simultaneous optimization. In this procedure, the controlling and geometrical variables are simultaneously optimized via a hierarchical genetic algorithm. A bi-coded chromosome is proposed in a hierarchical mode, which consists of some control genes (i.e. actuator location and number) and parametric genes (i.e. applied light intensity). Whether the parametric gene is activated or not is managed by the value of the first-grade control genes. The numerical results demonstrate that the achieved beam bending shapes correlate remarkably well with the expected ones and the simultaneous optimization of photostrictive actuator locations, numbers and light intensities can result in optimal actuator layout with less PbLaZrTi actuators and irradiated light energy. The simulation results also show that the hierarchical genetic algorithm has more superior performance over the conventional real-coded genetic algorithm.     

An optimum preliminary strength design of reinforced concrete frames

An optimization procedure is organized for the preliminary design of a multistory-multibay, moment-resisting reinforced concrete frame. A reduced set of collapse mechanisms are used to define the kinematic constraints, special constraints are defined in order to satisfy building code requirements and practical design considerations. In the proposed optimum preliminary design the total volume of reinforcing steel required by the members of the structure is minimized. A strong column—weak beam design results from the optimization study. An example is presented to illustrate the proposed method.     

Genetic algorithm design for nonperiodic planar graphene leaky-wave antennas in THz

The aim of this paper is proposing a new fast designing method for planar graphene leaky-wave antennas without periodical changes. Thus, Floquet theory cannot be used for designing, an optimization in numerical EM solver is needed. Since leaky-wave antennas are electrically long, their simulation using commercial EM simulators needs a large number of meshes, also the optimization of the large number of parameters (slot lengths and their distances) needs huge amount of memory and computation time. To resolve this problem, the method of Moments, implemented in MATLAB, which has been accelerated by applying some techniques, has been used in the design procedure. The antenna comprises a slotted graphene micro ribbon with a specific pattern, which is placed on two dielectric substrates and a PEC reflector. Graphene is used in the proposed LWA, instead of the electric conductor, because of its wonderful properties. The suitable pattern of slots on the graphene microstrip, is obtained using optimization by MATLAB Genetic algorithm tool. The usefulness and performance of the proposed designing approach, is verified in one example. It has been shown that the presented antenna, compared with one of the new successful similar antennas, has a better gain, radiation efficiency, and a wider range of beam scanning.     

Design and optimization of RF ICs with embedded linear macromodels of multiport MEMS devices

In this paper, we demonstrate efficient modeling approach for simulation, analysis, design, and optimization of multiport radio frequency microelectromechanical systems (RF MEMS) resonating structures embedded in RF circuits. An in‐house finite element method (FEM) solver is utilized to develop accurate and efficient macromodels that capture all the essential characteristics of the device. Using the datasets generated from the FEM simulations, the artificial neural network models are trained for two‐way mapping between the physical input and electrical output parameters. Realized model is implemented in a circuit simulator, enabling a simple yet accurate circuit simulator compatible modeling and optimization procedure instead of memory and time demanding FEM analysis. The derivation of dynamic macromodels with preserved electromechanical behavior of the multiport resonating structures is also presented. Capabilities of the proposed approach are demonstrated with several examples featuring capacitively actuated MEMS resonating structures: a clamped–clamped beam, a free–free beam, and a coupled clamped–clamped beam. © 2007 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2007.     

A thin-walled box beam finite element for curved bridge analysis

Practical design of single and multispan curved bridges requires an analysis procedure which is easy and economical to use, and provides a physical insight into structural response under general loading conditions. In the work presented, the thin-walled beam theory has been directly combined with the finite element technique to provide a new thin-walled box beam element. The beam element includes three extra degrees-of-freedom over the normal six degrees-of-freedom beam formulation, to take into account the warping and distortional effects as well as shear. The beam may be curved in space and variable cross-sections may be included. The performance of the box beam element has been compared favourably against results obtained from full 3D shell element analysis, differential equation solutions and experimental results.     

Design and FEM simulation study of the electro-thermal excitation resonant beam with slit-structure

This paper proposes a slit-resonant beam based on the double clamped resonant beam theory of silicon micro-machined resonant pressure sensors. The slit structure can enhance surface alternating stress in the root area of beam while vibrating. Finite element method (FEM) is applied to calculate the stress concentration magnification, and we carry out a computational study of the effects of size and location of slit structure in terms of mechanical properties of resonant beam, such as stress concentration on resonant beam and natural frequency of resonant beam, as well as sensing performance, such as resonant beam amplitude sensitivity. Our simulations show that the slit structure could strengthen the stress concentration and increase the amplitude detection sensitivity, and the variations of these parameters can substantially influence the performance of slit structure. The research of stress concentration, caused by silt structure, could provide reference for further optimization and design for the resonant beam.     

Optimal Matching Control of a Low Energy Charged Particle Beam in Particle Accelerators

Particle accelerators are devices used for research in scientific problems such as high energy and nuclear physics. In a particle accelerator, the shape of particle beam envelope is changed dynamically along the forward direction. Thus, this reference direction can be considered as an auxiliary "time" beam axis. In this paper, the optimal beam matching control problem for a low energy transport system in a charged particle accelerator is considered. The beam matching procedure is formulated as a finite "time" dynamic optimization problem, in which the Kapchinsky-Vladimirsky (K-V) coupled envelope equations model beam dynamics. The aim is to drive any arbitrary initial beam state to a prescribed target state, as well as to track reference trajectory as closely as possible, through the control of the lens focusing strengths in the beam matching channel. We first apply the control parameterization method to optimize lens focusing strengths, and then combine this with the time-scaling transformation technique to further optimize the drift and lens length in the beam matching channel. The exact gradients of the cost function with respect to the decision parameters are computed explicitly through the state sensitivity-based analysis method. Finally, numerical simulations are illustrated to verify the effectiveness of the proposed approach.      

Topology and detail geometry optimization for beam structures using homotopy modeling

This paper describes a novel design concept and an algorithm for topology and detail geometry design of a beam structure. Topology, layout, cross-sectional shape and size of each element are treated as a design variable. Homotopy theory is used to classify a topological type of a beam structure. In the design concept, not topology itself of a structure but a detail geometry design space defined by topology is transformed. By introducing the novel concept of an algebraic topology expression and the topology metamorphosis algorithm, active topology transformation becomes possible. A numerical example of topology, layout and cross-sectional optimization of reinforcement for a beam structure is illustrated.     

A reliability-based multidisciplinary design optimization procedure based on combined probability and evidence theory

To address the reliability-based multidisciplinary design optimization (RBMDO) problem under mixed aleatory and epistemic uncertainties, an RBMDO procedure is proposed in this paper based on combined probability and evidence theory. The existing deterministic multistage-multilevel multidisciplinary design optimization (MDO) procedure MDF-CSSO, which combines the multiple discipline feasible (MDF) procedure and the concurrent subspace optimization (CSSO) procedure to mimic the general conceptual design process, is used as the basic framework. In the first stage, the surrogate based MDF is used to quickly identify the promising reliable regions. In the second stage, the surrogate based CSSO is used to organize the disciplinary optimization and system coordination, which allows the disciplinary specialists to investigate and optimize the design with the corresponding high-fidelity models independently and concurrently. In these two stages, the reliability-based optimization both in the system level and the disciplinary level are computationally expensive as it entails nested optimization and uncertainty analysis. To alleviate the computational burden, the sequential optimization and mixed uncertainty analysis (SOMUA) method is used to decompose the traditional double-level reliability-based optimization problem into separate deterministic optimization and mixed uncertainty analysis sub-problems, which are solved sequentially and iteratively until convergence is achieved. By integrating SOMUA into MDF-CSSO, the Mixed Uncertainty based RBMDO procedure MUMDF-CSSO is developed. The effectiveness of the proposed procedure is testified with one simple numerical example and one MDO benchmark test problem, followed by some conclusion remarks.     

Statistical confidence intervals for fuzzy data

The application of fuzzy sets theory to statistical confidence intervals for unknown fuzzy parameters is proposed in this paper by considering fuzzy random variables. In order to obtain the belief degrees under the sense of fuzzy sets theory, we transform the original problem into the optimization problems. We provide the computational procedure to solve the optimization problems. A numerical example is also provided to illustrate the possible application of fuzzy sets theory to statistical confidence intervals.