Eigenfunction expansion method of upper triangular operator matrixand application to two-dimensional elasticity problems based onstress formulation

This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example.

Simplification and improvement of prediction model for elastic modulus of particulate reinforced metal matrix composite

In this paper, we proposed a five-zone model to predict the elastic modulus of particulate reinforced metal matrix composite. We simplified the calculation by ignoring structural parameters including particulate shape, arrangement pattern and dimensional variance mode which have no obvious influence on the elastic modulus of a composite, and improved the precision of the method by stressing the interaction of interfaces with pariculates and maxtrix of the composite. The five- zone model can reflect effects of interface modulus on elastic modulus of composite. It overcomes limitations of expressions of rigidity mixed law and flexibility mixed law. The original idea of five zone model is to put forward the particulate/interface interactive zone and matrix/interface interactive zone. By organically integrating the rigidity mixed law and flexibility mixed law, the model can predict the engineering elastic constant of a composite effectively.

Simplified prediction model for elastic modulus of particulate reinforced metal matrix composites

Some structural parameters of the metal matrix composite, including particulate shape and distribution do not influence the elastic modulus. A prediction model for the elastic modulus of particulate reinforced metal matrix Al composite was developed and improved. Expressions of rigidity and flexibility of the rule of mixing were proposed. A five-zone model for elasticity performance calculation of the composite was proposed. The five-zone model is thought to be able to reflect the effects of the MMC interface on elastic modulus of the composite. The model overcomes limitations of the currently-understood rigidity and flexibility of the rule of mixing. The original idea of a five-zone model is to propose particulate/interface interactive zone and matrix/interface interactive zone. By integrating organically with the law of mixing, the new model is found to be capable of predicting the engineering elastic constants of the MMC composite.

Completeness of the system of eigenvectors of off-diagonal operator matrices and its applications in elasticity theory

This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block operators in the off-diagonal operator matrices. Using these results, the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed. Moreover, we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation.

Elastic and Plastic Behaviors of Laminated Ti-TiBw/Ti Composites

The novel laminated Ti-TiBw/Ti composites composed of pure Ti layers and TiBw/Ti composite layers have been successfully fabricated by reactive hot pressing. Herein, two-scale structures formed： the pure Ti layer and TiBw/Ti composite layer together constructed a laminated structure at a macro scale. Furthermore, TiBw reinforcement was distributed around Ti particles and then formed a network microstructure in TiBw/Ti composite layer at a micro scale. The laminated Ti-TiBw/Ti composites reveal a superior combination of high strength and high elongation due to two-scale structures compared with the pure Ti, and a further enhancement in ductility compared with the network structured composites. Moreover, the elastic modulus of the laminated composites can be predicted by H-S upper bound, which is consistent with the experimental values.

Propagation behavior of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with line defects

Using a stiffness matrix method, we in- vestigate the propagation behaviors of elastic waves in one-dimensional （1D） piezoelectric/piezomagnetic （PE/PM） phononic crystals （PCs） with line defects by calculating energy reflection/transmittion coefficients of quasi-pressure and quasi-shear waves. Line defects are created by the re- placement of PE or PM constituent layer. The defect modes existing in the first gap are considered and the influences on defect modes of the material properties and volume fraction of the defect layers, the type of incident waves, the location of defect layer and the number of structural layers are discussed in detail. Numerical results indicate that defect modes are the most obvious when the defect layers are inserted in the middle of the perfect PCs; the types of incidence wave and material properties of the defect layers have important effects on the numbers, the location of frequencies and the peaks of defect modes, and the defect modes are strongly de- pendent on volume fraction of the defect layers. We hope this paper will be found useful for the design of PE/PM acoustic filters or acoustic transducer with PCs structures.

Effect of negative permeability on elastic wave propagation in magnetoelastic multilayered composites

With the advent of left-handed magnetic materials, it is desirable to develop high-performance wave devices based on their novel properties of wave propagation. This letter reports the special properties of elastic wave propagation in magnetoelastic multilayered composites with negative permeability as compared to those in counterpart structures with positive permeability. These novel properties of elastic waves are discerned from the diversified dispersion curves, which represent the propagation and attenuation characteristics of elastic waves. To compute these dispersion curves, the method of reverberation-ray matrix is extended for the analysis of elastic waves in magnetoelastic multilayered composites. Although only the results of a single piezomagnetic and a binary magnetoelastic layers with mechanically free and magnetically short surfaces as well as perfect interface are illustrated in the numerical examples, the analysis is applicable to magnetoelastic multilayered structures with other kinds of boundaries/interfaces.

An Efficient Numerical Method for Calculation of Elastic and Thermo-Elastic Fields in a Homogeneous Medium with Several Heterogeneous Inclusions

The work is devoted to calculation of static elastic and thermo-elastic fields in a homogeneous medium with a finite number of isolated heterogeneous inclusions. Firstly, the problem is reduced to the solution of inte-gral equations for strain and stress fields in the medium with inclusions. Then, Gaussian approximating func-tions are used for discretization of these equations. For such functions, the elements of the matrix of the dis-cretized problem are calculated in explicit analytical forms. The method is mesh free, and only the coordi-nates of the approximating nodes are the geometrical information required in the method. If such nodes compose a regular grid, the matrix of the discretized problem obtains the Toeplitz properties. By the calcula-tion of matrix-vector products with such matrices, the Fast Fourier Transform technique may be used. The latter accelerates essentially the process of the iterative solution of the disretized problem. The results of calculations of elastic fields in 3D-medium with an isolated spherical heterogeneous inclusion are compared with exact solutions. Examples of the calculation of elastic and thermo-elastic fields in the medium with several inclusions are presented.

Influence of Axial Loads to Propagation Characteristics of the Elastic Wave in a Non-Uniform Shaft

The vibration propagates through the shaft in the form of elastic waves. The propagation characteristics of the elastic waves are a ected by the axial loads. The influence of the axial loads to the propagation characteristics of the elastic waves is studied in this paper. Firstly, the transfer matrix of the elastic waves for the non-uniform shaft with axial loads is deduced by combining the transfer matrix without axial load and the additional equation caused by the axial load. And then, a numerical method is used to study the influence of the axial load, non-uniformity and the rotating speed to the propagation characteristics of the elastic waves. It’s found that a new Stop Band will appear due to the axial force, and the central frequency of which will decrease as the increase of the force, while the band width of which remains the same. The central frequency of the new Stop Band will also increase as the increase of the cross-section area ratio;however, the rotating speed of the shaft doesn’t a ect the propagation characteristics of the elastic waves obviously. Finally, an experimental rig is built up for further study, even though there are some small local errors, the results of experiments match well with the numerical ones, which indicates the validation of the theoretical results. The result can help to study the influence of the axial load to the dynamics of a non-uniform shaft and help to reveal the vibration propagating mechanism in such a shaft.

Prediction of Effective Elastic Modulus of Biphasic Composite Materials

Two semi-empirical approaches for prediction of elastic modulus of biphasic composites have been proposed. Developed relations are for pore free matrix and pore free filler and found to depend on nonlinear contribution of volume fraction of constituents as well as ratio of elastic properties of individual phases. These relations are applied for the calculation of effective elastic modulus mainly for Al2O3-NiAl, SiC-Al, Alumina-Zirconia, Al-Al2O3, W-glass and Flax-Resin composite materials. Theoretical predictions using developed relations are compared with experimental data. It is found that the predicted values of effective elastic modulus using modified relations are quite close to the experimental results.

A CLOSED-FORM ALGORITHM FOR THE STEADY-STATE RESPONSE OF ELASTIC MECHANISMS

This paper presents a closed-form algorithm for the steady-state response of elastic mecha-nisms. Based on an analytic expression of the initial conditions, the steady-state response can beobtained by just one cycle of integration, thus the algorithm is of high efficiency. The algorithm isthen verified by comparing the computational results with the previously published experimental re-sults.

An elastic-plastic analysis of short-leg shear wall structures during earthquakes

Short-leg shear wall structures are a new form of building structure that combine the merits of both frame and shear wall structures. Its architectural features, structure bearing and engineering cost are reasonable. To analyze the elastic-plastic response of a short-leg shear wall structure during an earthquake, this study modified the multiple-vertical-rod element model of the shear wall, considered the shear lag effect and proposed a multiple-vertical-rod element coupling beam model with a new local stiffness domain. Based on the principle of minimum potential energy and the variational principle, the stiffness matrixes of a short-leg shear wall and a coupling beam are derived in this study. Furthermore, the bending shear correlation for the analysis of different parameters to describe the structure, such as the beam height to span ratio, short-leg shear wall height to thickness ratio, and steel ratio are introduced. The results show that the height to span ratio directly affects the structural integrity; and the short-leg shear wall height to thickness ratio should be limited to a range of approximately 6.0 to 7.0. The design of short-leg shear walls should be in accordance with the ＂strong wall and weak beam＂ principle.

STUDY ON Ni_(25)Ti_(50)Cu_(25) SHAPE MEMORY PARTICLE/Al MATRIX COMPOSITE

Ni_(25)Ti_(50)Cu_(25) shape memory particle/Al matrix composite was prepared by hot pressing and further extrusion.The Ni_(25)Ti_(50)Cu_(25) particles embeded in Al matrix still keep B19 and B19 structure,and have a good thermal-elastic martensitic transition with 6K thermal hysteresis,the phase transition temperatures remaining constant during cycling. The scratching force of Ni_(25)Ti_(50)Cu_(25) particle is two times that of Al matrix,When the scratching force is larger than 4.2N, the Ni_(25)Ti_(50)Cu_(25) particle is separated from Al matrix.

故障关联矩阵下弹性配电网可靠性评估

配电网弹性是指系统受到干扰后恢复原有状态的能力,而自然灾害的频发要求配电网不仅在正常条件下能够可靠运行,而且还能够在极端灾害出现时保持必要能力。据此,提出一种基于故障关联矩阵(fault incidence matrix,FIM)的弹性配电网可靠性评价方法。通过建立FIM,使用简化的矩阵代数、布尔运算即可实现配电系统可靠性、弹性和供电能力的显式解析计算,避免了评估过程中故障枚举的重复性搜索工作,节省了计算时间,并且可适用于结构复杂的配电网,易于扩展。最后结果表明:采用文中方法的计算时间仅为约0.055 s,相较于故障扩散算法和分块算法分别减少87%和75%的时间。

基于时变价格弹性矩阵的深谷电价多目标定价策略

随着碳中和、碳达峰目标的提出,构建高比例新能源的新型电力系统已成为未来能源电力的发展形态,由此导致的高比例新能源渗透使系统净负荷曲线呈现剧烈的波动性和显著的深谷特征,对电力系统安全运行以及供需平衡提出了新挑战。为此,提出了一种基于时变价格弹性矩阵的需求侧深谷电价多目标定价模型。首先,确立基于模糊隶属度的深谷时段划分方法,并利用贝叶斯判别法对时段划分结果进行合理性评估。其次,针对用户需求响应的动态性,建立具有时变特征的价格弹性矩阵模型衡量用户的响应程度。最后,以用户满意度和系统峰谷差作为待优化的两个目标,建立多目标混合整数规划的深谷电价定价模型,并用非支配排序遗传算法求解模型并得到其Pareto最优解。为了检验所提模型的有效性,将其应用于中国华东地区某省的实际场景进行仿真分析。结果表明,上述模型可在高比例新能源渗透情景下降低峰谷差,促进用户用电行为向深谷时段转移,缓解电力系统在深谷时段的运行压力。

人工神经网络和电阻抗谱法压电材料快速表征

压电材料作为重要的功能材料,广泛应用于社会的各领域,但其弹性常数的偏差会导致应用过程中出现错误的设计,弹性常数的正确表征对压电器件的正确设计尤为重要。与其他测量方法相比,电阻抗谱仅需要阻抗分析仪即可实现测量,通过测量阻抗谱反演获得压电材料的弹性常数。传统电阻抗谱法通过不断修正材料参数,使得测量阻抗谱和计算阻抗谱最大程度吻合,该过程需要多次迭代,计算量大,耗时较长。该文提出采用神经网络建立阻抗谱到弹性常数的正向模型,测量得到阻抗谱后仅需一次正向计算即可得到弹性常数。使用Comsol和Matlab联合仿真建立数据集,引入丢弃法避免模型过拟合,利用Pytorch建立模型,经过训练后,最大谐振频率偏差从初始2.8%降至0.8%。该技术为压电材料弹性常数精密测量提供可靠的理论与实践途径。

机械弹性储能用永磁同步电机多源谐波提取及统一抑制

针对柔性涡簧振动和电力电子装置等引起机械弹性储能(MEES)系统机械侧谐波难以准确建模、多源谐波无法整体表征及统一抑制的问题,该文提出MEES用永磁同步电机多源谐波提取及统一抑制方法。首先,建立MEES系统数学模型,利用电机转速谐波对多源谐波进行整体表征;然后,提出融合奇异值差分的矩阵束算法,利用其对含噪实测转速数据进行处理以获取包含不同频率成分的多源谐波信息;最后,设计定子电流矢量定向下基于反推控制的多源谐波统一抑制算法,完成对不同频率成分谐波的同时抑制。仿真和实验结果表明,利用融合奇异值差分的矩阵束算法能快速、准确地识别转速信号中的多源谐波成分,统一抑制算法有效降低了多源谐波导致的电磁转矩脉动,改善了系统运行性能。

完全匹配层在矩阵式波动方程SBP-SAT方法应用

数值离散方法和截断边界效果是地震动模拟实现的关键。基于分部求和(summation-by-parts,SBP)和一致逼近(simultaneous approximation term,SAT)的SBP-SAT方法具有较高的稳定性,这使得该方法具备了较高的应用前景和价值。此外,完全匹配层(perfect matching layer,PML)是一种应用广泛用于模拟截断边界的技术,但引入匹配层可能会破坏原始方程的稳定性,特别是在各向异性介质或曲线域模型中。首先基于数理推导,给出弹性波动方程系数矩阵的对称形式。在此基础上,引入多轴完全匹配层(multi-axis perfect matching layer,MPML),并建立相应的匹配层方程。通过本征值分析,我们可以判断阻尼函数对原方程特征根实部的走向和取值范围的影响。然后,我们采用SBP-SAT方法对矩阵对称形式匹配层方程进行离散,并在频域中采用能量法进行稳定性评估。通过对不同模型的数值仿真,表明所提出的离散框架具有整合度高、稳定性好和拓展性强等特点。此外,多轴匹配层可以与SBP-SAT方法结合,可以稳定地模拟曲线域中的波传播。

基于动态分时电价引导的电动汽车需求侧响应

为激励电动汽车(electric vehicles,EVs)参与需求侧响应以减小电网负荷峰谷差,同时提高电动汽车用电经济性,首先,利用蒙特卡罗法模拟出电动汽车无序充电负荷,再根据电动汽车是否受电网调控或者受价格信号引导,将电动汽车分为3类进行处理;然后,以电网峰谷差均方值最小和用户充放电费用最小为目标,搭建基于电价需求弹性矩阵的动态分时电价(time-of-use,TOU)需求响应模型;最后,根据湖南某地区历史负荷数据对一天的电价进行分段,再通过仿真分析,验证考虑实时负荷反馈的动态分时电价可以有效地应对负荷波动,并且对于减小峰谷差和降低用户用电成本的效果更明显。

基于DLP工艺的柔弹性点阵吸能支架研究

面向微小多功能支架结构设计与原型制造需求,开展了基于数字光处理(Digital Light Processing,DLP)快速成形工艺的柔弹性点阵支架设计与制备研究。以胞元结构几何拓扑设计为主线,利用Timoshenko梁理论对胞元结构建立等效力学模型,得到预测能量吸收的数学模型,聚焦分析胞元几何尺寸和承载方向对其影响规律。配置新颖柔弹性光敏树脂为成形材料,选用DLP成形工艺,实现对应点阵结构的高精、高效制备。结合数值模拟和物理实验,着重探究了杆径、胞元边长、点阵层数对点阵结构吸能特性的影响。结果表明,该点阵结构面外压缩较面内压缩具有显著优越的吸能特性,且胞元边长越小,杆径越大,点阵层数越多,吸能特性越佳。理论分析、数值模拟和物理实验所得规律基本一致,可为后续皮肤组织工程支架的研制提供相关理论参考。