Shape and topology optimization for periodic problems

The present paper deals with the implementation of an optimization algorithm for periodic problems which alternates shape and topology optimization; the theoretical background about shape and topological derivatives was developed in Part I (Barbarosie and Toader, Struct Multidiscipl Optim, 2009). The proposed numerical code relies on a special implementation of the periodicity conditions based on differential geometry concepts: periodic functions are viewed as functions defined on a torus. Moreover the notion of periodicity is extended and cases where the periodicity cell is a general parallelogram are admissible. This approach can be adapted to other frameworks (e.g. Bloch waves or fluid dynamics). The numerical method was tested for the design of periodic microstructures. Several examples of optimal microstructures are given for bulk modulus maximization, maximization of rigidity for shear response, maximization of rigidity in a prescribed direction, minimization of the Poisson coefficient.     

Mathematical models for assessment of the safety of steel beams based on average strains from long gage optic sensors

Most fiber optic sensors are point sensors that can measure the strain only at a local point of a beam, although strain distribution is non-uniform along the length of a beam. Long gage fiber optic sensors that measure integrated strain over a relatively long length can consider strain variation. This type of sensor was found to be efficient and useful for monitoring large-scale structures. On the other hand, the maximum strain in a beam cannot be measured with long gage optic sensors; the safety of a steel beam is analyzed by a comparison between the maximum stress measured during monitoring and the allowable stress of the beam calculated by a design code. Therefore, in this paper, simple mathematical models are presented for the determination of the maximum values of strains or stresses in a beam based on the average strains measured by long gage optic sensors. The model was tested in an experiment by comparing the maximum strain directly obtained from electrical gages and the calculated maximum strain from long gage optic sensors.     

Experimental study on use of nickel powder-filled Portland cement-based composite for fabrication of piezoresistive sensors with high sensitivity

Nickel powder-filled Portland cement-based composite was prepared by adding nickel powder as functional filler into conventional Portland cement-based materials, and piezoresistive sensors were fabricated by embedding four loop electrodes in the nickel powder-filled Portland cement-based composite. The relationship between the fractional change in electrical resistivity and the stress/strain of piezoresistive sensors was established for the compressive stress and was found to be in the range from 0 to 12.5 MPa. Experimental results indicate that the electrical resistivity of nickel powder-filled Portland cement-based composite under uniaxial compression decreases by 62.6144% within elastic regime, which justifies the use of this composite in the fabrication of piezoresistive sensors with high sensitivity to stress and sensitivity to strain (gauge factor). The sensitivity of piezoresistive sensors to compressive stress is higher than 0.050092 MPa^?1 and goes up to 0.123648 MPa^?1. The gauge factor of piezoresistive sensors is higher than 895.450 and goes up to 1929.500. It is therefore concluded that the newly developed piezoresistive sensors have a high sensitivity to stress/strain, and they can be used for measurement of stress/strain or force/deformation.     

A nonlinear model of center-wound rolls incorporating refined boundary conditions

This article presents a novel approach for determining the displacement, strains and stresses developed in a center-wound roll. The approach consists of a nonlinear model and some refined boundary conditions. The investigation starts with a linear, displacement-based formulation and refined boundary conditions previously developed by the author. The choice of displacement-based formulation, unlike the stress-, or strain-based counterpart, allows for easy determination of relative and absolute displacements, and stress and strain components caused by the relative displacement and by the wound-in stress. The refined boundary conditions, on the other hand, take into account radial displacement compatibility at the core-roll interface, as well as between the current outer surface of the roll and the next wound-on lap, resulting in relaxation of the wound-in stress, or the loss of it. Conventional boundary conditions, on the contrast, consider only radial displacement compatibility at the core-roll interface. The nonlinear model incorporates nonlinear radial modulus of elasticity of the wound roll. It is linearized lap-by-lap, translating the nonlinear problem into a series of linear equations of banded structure. A number of examples are chosen to demonstrate that the approach is accurate, rather simple, able to account for wound-in stress loss and capable of updating web thickness. Furthermore, it can accommodate any form of nonlinear radial modulus of elasticity and any profile of wound-in stress.     

基于短栅区光纤光栅传感器的油气管线腐蚀在线监测系统研究

基于短栅区光纤光栅传感器设计了一种油气管线腐蚀在线监测系统。对应油气管线外表面周向非线性应变,该系统可以测量油气管线腐蚀缺陷,保障管线安全运行。通过对管线圆柱型腐蚀缺陷周向应变特性及光纤光栅应变传感模型的理论分析,设计了3mm短栅区光纤光栅的应变传感阵列,并在模拟油气管道上验证了测量圆柱型缺陷表面周向非线性应变的可行性。结合波分复用、时分复用技术及光纤光栅解调系统可以组成解调7×7个应变及1个温度补偿共计50个光纤光栅传感器的在线监测系统。该系统已应用于中海油渤南龙口天然气终端处理厂,监测结果表明该在线监测系统稳定可靠,是监测油气管线腐蚀状况,保障管线安全运行的一种有效可靠方法。     

丁基橡胶密封环形状和材料黏弹性对结构密封性能的影响

为确保橡胶密封结构的可靠性,避免因经验设计带来的密封失效,在考虑丁基橡胶材料的超弹性和黏弹性的基础上,采用数值模拟方法分析密封环的形状和密封材料的应力松弛等因素对结构密封性能的影响. 研究结果表明:矩形密封环和梯形密封环的接触应力分布均匀、密封面宽,密封效果优于O形密封环; 但压缩量较大时,矩形密封环外角点处较大的剪切应力会造成密封环局部撕裂,进而影响到整体结构的密封性能. 短时松弛过程中装配预紧力变化的计算结果与试验测试数据吻合较好. 该方法能够预测不同形状密封环在压缩过程中的变形和应力等特征参数,有助于加深了解密封环的密封性能,对同类密封结构设计有一定指导意义.     

Comparative study on directional sensitivity of patch‐antenna‐based strain sensors

In this article, we present a comparative study into the directional sensitivity of patch‐antenna‐based strain sensors. Two linearly‐polarized (LP) patch sensors vs a circularly‐polarized (CP) patch sensor with identical configurations are demonstrated. The strain occurred in real structures is commonly uncertain, the usefulness of LP‐patch sensor becomes limited. Like the conventional strain gauges, it can only be used if the strain direction is known beforehand. Therefore, a nearly‐square CP‐patch sensor for multi‐directional strain monitoring is proposed here. In order to obtain high sensitivity, three novel strain sensing methods are proposed for strain monitoring. Multi‐directional strain sensing is achieved by a proof‐of‐concept prototype. The simulated results verified by experimental results show that high sensitivities of these three methods were achieved.     

Adaptive topology optimization of elastoplastic structures

Material topology optimization is applied to determine the basic layout of a structure. The nonlinear structural response, e.g. buckling or plasticity, must be considered in order to generate a reliable design by structural optimization. In the present paper adaptive material topology optimization is extended to elastoplasticity. The objective of the design problem is to maximize the structural ductility which is defined by the integral of the strain energy over a given range of a prescribed displacement. The mass in the design space is prescribed. The design variables are the densities of the finite elements. The optimization problem is solved by a gradient based OC algorithm. An elastoplastic von Mises material with linear, isotropic work-hardening/softening for small strains is used. A geometrically adaptive optimization procedure is applied in order to avoid artificial stress singularities and to increase the numerical efficiency of the optimization process. The geometric parametrization of the design model is adapted during the optimization process. Elastoplastic structural analysis is outlined. An efficient algorithm is introduced to determine the gradient of the ductility with respect to the densities of the finite elements. The overall optimization procedure is presented and verified with design problems for plane stress conditions.     

基于纹理和草图的图像铅笔画绘制

针对目前铅笔画生成方法中的线条不够灵活、纹理缺少方向感的问题,提出了一种基于带方向的纹理和线条草图将一幅图像转换为铅笔画风格的方法。首先,对输入图像进行直方图匹配得到图像的色调图,并将图像分割为多个区域,对每个区域,根据其颜色和形状计算其色调和方向,以此决定铅笔纹理的色调和方向;然后,通过可调整的线性卷积方法得到铅笔画的线条草图;最后,将纹理和草图结合得到铅笔画效果。运用提出的方法对不同类型的自然图像进行了铅笔画的转换,并与已有的线卷积积分方法和基于色调的方法进行了对比。实验结果表明带方向的区域纹理能更好地模拟手工铅笔画纹理的方向,可调整的线条能够更好地模拟手工铅笔画的线条的随意性和灵活性。     

光纤Bragg光栅传感器高速冲击试验研究

光纤Bragg光栅是一种性能优良的敏感元件,光纤Bragg光栅传感器在很多领域得到了应用.通过霍普金森压杆上的冲击试验研究了光纤光栅的动态响应能力.试验表明Bragg光栅能够正确响应不同频率的冲击信号,解调仪能够正确并快速解调出高速动态激励信号,同时Bragg光栅在受拉和受压时以及动态和静态灵敏度基本一致.光纤光栅传感器能够应用于武器侵彻爆炸等强冲击、恶劣环境下动态应力应变的测试.     

Optimal structural remodeling of multi-objective systems

The paper describes a statistical formulation for the structure modification problems, where two or more performance measuring functions (e.g. stiffness, strength, frequency, modeshape, weight, etc.) can be specified at several points on the structure. “Optimal Remodeling” refers to the best possible form of modification which would satisfy the prescribed limits imposed on these performance measures. The design variables may be any parameter associated with a generic finite element model such as sectional, material, geometric, or shape properties. The formulation is based on statistical system identification methods and penalty approaches that move as many performance measures as possible into an acceptable region. As an illustration of these concepts, examples have been chosen from two types of problems: (a) shape optimization to minimize stress concentrations and (b) fully stressed design (FSD).     

Physiological cost of horizontal materials handling while seated

Experiments were carried out in the course of which during seated work a load of 2 kg had to be lifted repeatedly 24 times per minute from 3 different beginning points within the outward reach over a distance of 38 cm to a fixed point near the body. In order to measure the physiological cost strictly due to unweighted movements, identical tasks had been performed by handling an almost weightless article (i.e. 0 kg). Besides oxygen consumption and heart rate as integral measures for stress and strain, electromyographic activity (EA) of 7 muscle groups was registered continuously from each of 11 subjects participating in the test sessions. EA was standardized with the help of EA-values obtained from preceding maximum voluntary contractions (MVC).

The results show extensive and consistent reactions of the global and local indicators of strain. Dependent on direction, even manual movements without external load induced strain, elucidated in significant minimum values of all parameters at 30° (measured from the frontal plane of the subjects). The local strain of the 7 monitored muscles shows a more or less distinct dependence of the direction. Almost only the dynamic component is influenced, yet to a degree which is much higher than the reaction of the integral physiological parameters. Correlations between EA-values and those of the oxygen consumption as well as the work pulses indicate that electromyography is an efficient method for determining local muscular strain, which can be assessed very precisely. Furthermore, multi-channel electromyography proved to enable detection of bottle-necks in muscular strain.     

Time–frequency analysis of signals using support adaptive Hermite–Gaussian expansions

Since Hermite–Gaussian (HG) functions provide an orthonormal basis with the most compact time–frequency supports (TFSs), they are ideally suited for time–frequency component analysis of finite energy signals. For a signal component whose TFS tightly fits into a circular region around the origin, HG function expansion provides optimal representation by using the fewest number of basis functions. However, for signal components whose TFS has a non-circular shape away from the origin, straight forward expansions require excessively large number of HGs resulting to noise fitting. Furthermore, for closely spaced signal components with non-circular TFSs, direct application of HG expansion cannot provide reliable estimates to the individual signal components. To alleviate these problems, by using expectation maximization (EM) iterations, we propose a fully automated pre-processing technique which identifies and transforms TFSs of individual signal components to circular regions centered around the origin so that reliable signal estimates for the signal components can be obtained. The HG expansion order for each signal component is determined by using a robust estimation technique. Then, the estimated components are post-processed to transform their TFSs back to their original positions. The proposed technique can be used to analyze signals with overlapping components as long as the overlapped supports of the components have an area smaller than the effective support of a Gaussian atom which has the smallest time-bandwidth product. It is shown that if the area of the overlap region is larger than this threshold, the components cannot be uniquely identified. Obtained results on the synthetic and real signals demonstrate the effectiveness for the proposed time–frequency analysis technique under severe noise cases.     

最大化个人偏好的多目标优化进化算法

针对多目标优化过程中如何将个人偏好信息融入寻优搜索过程的问题,本文提出一种最大化个人偏好 以确定搜索方向的多目标优化进化算法．该算法首先采用权重和法将多目标问题转换为单目标问题,再利用遗传算 法进行全局搜索,在满足个人偏好约束条件下,每一代进化结束后通过解约束优化问题获得能够使种群综合适应度 具有最大方差的权重组合,从而最大化个人偏好以选择综合最优的个体进行遗传操作．按照不同个人偏好应用于传 动系统进行控制器设计,仿真结果表明该算法能够获得满足个人偏好约束条件下的全局最优解．     

Optimal topology design for stress-isolation of soft hyperelastic composite structures under imposed boundary displacements

Soft hyperelastic composite structures that integrate soft hyperelastic material and linear elastic hard material can undergo large deformations while isolating high strain in specified locations to avoid failure. This paper presents an effective topology optimization-based methodology for seeking the optimal united layout of hyperelastic composite structures with prescribed boundary displacements and stress constraints. The optimization problem is modeled based on the power-law interpolation scheme for two candidate materials (one is soft hyperelastic material and the other is linear elastic material). The ?-relaxation technique and the enhanced aggregation method are employed to avoid stress singularity and improve the computational efficiency. Then, the topology optimization problem can be readily solved by a gradient-based mathematical programming algorithm using the adjoint variable sensitivity information. Numerical examples are given to show the importance of considering prescribed boundary displacements in the design of hyperelastic composite structures. Moreover, numerical solutions demonstrate the validity of the present model for the optimal topology design with a stress-isolated region.     

基于纳米晶软磁合金的电感式应变花的研究

利用纳米晶软磁合金良好的压磁特性,设计了一种用于测量平面应力的电感式应变计。首先,介绍了这种应变计的结构和工作原理,并推导出其输出数学模型。其次,进行了可行性试验。试验表明,应变计每一测量轴的输出电压主要取决于该测量方向的应变,其灵敏度可达3.86 mV/με,线性度为1.03%F.S,重复误差与迟滞误差均小于1%F.S。在平面应力状态时,不同方向应变相互耦合对测量精度的影响,通过标定补偿灵敏度系数对应变计的输出加以修正。与传统的电阻式应变计相比,这种电感式应变计具有结构简单,工作可靠,使用寿命长,适应性强,灵敏度和测量精度较高等特点。     

Silicon micro-cantilever chemical sensors fabricated in double-layer silicon-on-insulator (SOI) wafer

Micro-cantilever piezoresistive sensors are optimally designed and fabricated in a double-layer silicon-on-insulator (SOI) wafer. The sensor geometry is optimized by placing the sensing piezoresistor at the cantilever root region to increase effective piezoreisistive sensing area. According to finite-element simulation results, high sensitivity can be obtained by design the cantilever into a wide and short shape. In order to use single-crystalling silicon to fabricate both the cantilever and the piezoresistor for high sensitivity, double-layer SOI wafer, which has two active layers and two insulating layers, is proposed to fabricate the self-sensing micro-cantilever sensor. The piezoresistor is made of the top active-layer single-crystalline silicon. Without p–n junction isolation, such a piezoresistor can be free from leakage-current relative noise that helps to achieve fine sensing resolution. The bottom active-layer is used to form the cantilever, with well controlled cantilever thickness and high fabrication yield. With the top surface of the micro-cantilever is modified with the functionalized self-assembled monolayer, detection of trace-concentration Trinitrotoluene (TNT) vapor is experimentally carried out, with reproducible sensing response to 7.6 ppb TNT.     

Development of a wireless stress/strain measurement system integrated with pressure-sensitive nickel powder-filled cement-based sensors

A wireless stress/strain measurement system is developed by integrating with pressure-sensitive sensors for health monitoring of concrete structures. The pressure-sensitive stress/strain sensors are fabricated by using nickel powder-filled cement-based composite. The wireless stress/strain measurement system integrated with these sensors is tested with compressive stress/strain in the range from 0 MPa/0 μ to 2.5 MPa/311.5 μ for performance evaluation. Experimental results indicate that the electrical resistivity of pressure-sensitive nickel powder-filled cement-based stress/strain sensors changes linearly and reversibly with the compressive stress/strain, and its fractional change goes up to 42.719% under uniaxial compression. The relationship between input (compressive stress/strain) and output (the fractional change in electrical resistivity) of the wireless stress/strain measurement system integrated with pressure-sensitive sensors is Δρ = −0.16894σ/Δρ = −1336.5. The wireless stress/strain measurement system can be used to achieve a sensitivity to stress/strain of 16.894% MPa⁻¹/0.13365%μ⁻¹ (a gauge factor of 1336.5) and a stress/strain resolution of 150 Pa/0.02 μ. The newly developed wireless stress/strain measurement system integrated with pressure-sensitive nickel powder-filled cement-based sensors has such advantages as high sensitivity to stress/strain, high stress/strain resolution, simple circuit and low energy consumption.     

Shape estimation of distorted flexible structures

The present work discusses the optimal placement of sensors in truss structures in order to obtain best possible information regarding the distortions of the structure. The estimation goal is to reconstruct the deformed shape of the structure, at the controlled degrees of freedom, from the sensor readings. A basic assumption is that the structure is subjected to a parametric disturbance field. We distinguish between disturbances which cause uniform or arbitrary distortions of the structure, and disturbances which cause structured distortions. Uniform distortions can be construed as white noise, that is, distortions which have no characteristics. Structured distortions are chromatic, they have some characteristics which can be helpful in estimating the shape. Although the disturbance in either case is random it is assumed that its magnitude is confined to a hyper sphere. The estimator is based on the least squares method, hence the estimated shape is the one with least RMS displacement for the given sensor readings. To evaluate the performance of each set of sensors a measure is derived based on the concept of the worst case distortion. The measure is the largest possible error between the estimated and the actual displacements, at the CDOF. For small number of sensors all possible arrangements can be generated and compared. Larger trusses with a moderate number of sensors generate prohibitively large number of possible configurations, hence heuristic search techniques are employed. The theory has been applied to 2D and 3D flexible trusses. Results show that for reasonable shape estimation a relatively large number of sensors is needed. It is also shown that when using sensors which measure mainly the distortions of the controlled degrees of freedom, significant improvements in the shape estimation can be obtained.     

Printed radiating structures and transitions in multilayered substrates

This article reviews an integral equation technique to efficiently solve printed structures consisting of conducting patches, slots, and ground planes residing in a stratified medium. The integral equation is cast into a mixed potential form and solved in the space domain. Both the electric and magnetic surface currents are considered as general two-dimensional surface currents with no prescribed or preferred direction. Thus, arbitrary shapes for patches and slots can be considered. After the formulation in the space domain, the integral equation is solved using the method of moments. Theoretical results are compared with measurements for three structures. These structures are: a wide slot antenna excited by a microstrip line; a microstrip line-slot line-microstrip line transition; and transitions between microstrip lines embedded at different levels of a multilayered media. © 1992 John Wiley & Sons, Inc.