A new model for wrinkling and collapse analysis of membrane inflated beam

A new model is proposed to accurately predict the wrinkling and collapse loads of a membrane inflated beam. In this model, the pressure effects are considered and a modified factor is introduced to obtain an accurate prediction. The former is achieved by modifying the pressure-related structural parameters based on elastic small strain considerations, and the modified factor is determined by our test data. Compared with previous models and our test data, the present model, named as shell-membrane model, can accurately predict the wrinkling and collapse loads of membrane inflated beams.     

Derivation of a second-order model for Reynolds stress using renormalization group analysis and the two-scale expansion technique

With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Yakhot-Orszag renormalization group method to analyze the fluctuating field,the Reynolds-average terms in the Reynolds stress transport equation,such as the convective term,the pressure-gradient-velocity correlation term and the dissipation term,are modeled.Two numerical examples:turbulent flow past a backward-facing step and the fully developed flow in a rotating channel,are presented for testing the efficiency of the proposed second-order model.For these two numerical examples,the proposed model performs as well as the Gibson-Launder (GL) model,giving better prediction than the standard k-ε model,especially in the abilities to calculate the secondary flow in the backward-facing step flow and to capture the asymmetric turbulent structure caused by frame rotation.     

Surface effects of adsorption-induced resonance analysis on micro/nanobeams via nonlocal elasticity

The governing differential equation of micro/nanbeams with atom/molecule adsorption is derived in the presence of surface effects using the nonlocal elasticity.The effects of the nonlocal parameter,the adsorption density,and the surface parameter on the resonant frequency of the micro/nanobeams are investigated.It is found that,in addition to the nonlocal parameter and the surface parameter,the bending rigidity and the adsorption-induced mass exhibit different behaviors with the increase in the adsorption density depending on the adatom category and the substrate material.     

A three-layer structure model for the effect of a soft middle layer on Love waves propagating in layered piezoelectric systems

A three-layer structure model is proposed for investigating the effect of a soft elastic middle layer on the propagation behavior of Love waves in piezoelectric layered systems, with "soft" implying that the bulk-shear-wave velocity of the middle layer is smaller than that of the upper sensitive layer. Dispersion equations are obtained for unelectroded and traction-free upper surfaces which, in the limit, can be reduced to those for classical Love waves. Systematic parametric studies are subsequently carried out to quantify the effects of the soft middle layer upon Love wave propagation, including its thickness, mass density, dielectric constant and elastic coefficient. It is demonstrated that whilst the thickness and elastic coefficient of the middle layer affect significantly Love wave propagation, its mass density and dielectric constant have negligible influence. On condition that both the thickness and elastic coefficient of the middle layer are vanishingly small so that it degenerates into an imperfectly bonded interface, the three-layer model is also employed to investigate the influence of imperfect interfaces on Love waves propagating in piezoelectric layer/elastic substrate systems. Upon comparing with the predictions obtained by employing the traditional shear-lag model, the present three-layer structure model is found to be more accurate as it avoids the unrealistic displacement discontinuity across imperfectly bonded interfaces assumed by the shearlag model, especially for long waves when the piezoelectric layer is relatively thin.     

基于多重子域代理模型的结构可靠性分析

基于合理子域概念,构建多重代理模型。多重代理模型在合理子域内采用经典响应面模型,在合理子域外采用经典Kriging模型,能够充分利用两种经典模型各自的优势。多重代理模型能够合理规避经典响应面模型中响应函数采取事先假定形式带来的可靠度评估风险,同时能够有效避免经典Kriging模型中试验点组合爆炸的问题。相比经典响应面模型,多重代理模型所需试验点数量并未增加,计算效率与经典响应面模型大体相同。算例表明,本文方法的计算结果与MCS的计算结果几乎一致,具有较好的计算精度。     

Effects of bottom shear stresses on the wave-induced dynamic response in a porous seabed：PORO-WSSI （shear） model

When ocean waves propagate over the sea floor,dynamic wave pressures and bottom shear stresses exert on the surface of seabed.The bottom shear stresses provide a horizontal loading in the wave-seabed interaction system,while dynamic wave pressures provide a vertical loading in the system.However,the bottom shear stresses have been ignored in most previous studies in the past.In this study,the effects of the bottom shear stresses on the dynamic response in a seabed of finite thickness under wave loading will be examined,based on Biot’s dynamic poro-elastic theory.In the model,an "u-p" approximation will be adopted instead of quasi-static model that have been used in most previous studies.Numerical results indicate that the bottom shear stresses has certain influences on the wave-induced seabed dynamic response.Furthermore,wave and soil characteristics have considerable influences on the relative difference of seabed response between the previous model(without shear stresses) and the present model(with shear stresses).As shown in the parametric study,the relative differences between two models could up to 10% of p0,depending on the amplitude of bottom shear stresses.     

基于刚度损伤并考虑强度退化的钢筋模型

Clough本构广泛应用于现浇节点的滞回模拟中,针对原始Clough本构中的应力可能会超出材料自身极限强度的问题,提出了一种根据节点刚度损伤来推导钢筋本构的算法。该算法依次建立现浇节点刚度退化与构件中钢筋模量退化间的关系及梁端位移角与钢筋应变的关系,根据以上关系建立钢筋强度退化的表达式,并得到钢筋的本构模型。使用Fortran语言编写自定义纤维单元材料子程序,利用有限元软件ABAQUS进行两个算例验证,得到的模拟滞回曲线具有捏缩现象,形状与试验吻合良好,耗能和延性等方面可与试验接近,在峰值点位移角的预测方面也具备一定的优势,同时,本构在二维和三维模型中均有良好的收敛性,且精度较高,可以应用于实际工程中。     

电子封装元件的高阶层离散均匀化分析

将均匀化理论应用于具有非完全(单层内)周期性微结构的倒装焊底充胶电子封装元件,建立了高阶逐层离散层板模型,用解析法分析热载荷下结构的温度应力. 计算结果与有限元解的比较表明,该分析模型和方法是有效的,而且比较简便. 算例分析结果显示,胶层厚度、焊点密度、胶与焊点材料的模量比和体积比,对于焊点温度应力有明显影响.     

A model of acoustic absorption in fluids based on a continuous distribution of relaxation times

This work extends the quasi-equilibrium relaxation theory of sound absorption in liquids to the case of continuous distribution of relaxation times. Such extension is needed when absorption mechanisms are not confined to the action of viscosity and heat conduction, but are mainly due to the excitation of a large number of internal molecular degrees of freedom. In this case the conventional Navier-Stokes equations are not sufficient to describe the fluid motion, and additional equations are required to model normal relaxation stresses. When relaxation frequencies form a sufficiently dense distribution, as is the case for many biological fluids, it makes sense to consider the limit of continuously distributed relaxation frequencies, in order to obtain the required equation for normal relaxation stresses.In contrast to its discrete counterparts, the proposed method avoids the use of a potentially infinite number of relaxation equations for a given set of distinct relaxation frequencies. Instead, these are replaced by a single evolution equation of Boltzmann type whose right-hand side is a linear combination of the time derivatives of density and entropy. The rheological functions appearing before these derivatives are expressed in terms of the absorption coefficient. Since the dependence of absorption coefficient on sound frequency is measurable experimentally, these rheological coefficients can be recovered from experimental data.The key feature of the present study is that a closed system of equations of motion can be formulated directly from absorption measurement data on the basis of the theory proposed for the very wide range of absorption laws that can occur in practice.As an illustration of the generality of the present method, a number of absorption laws documented in the experimental literature are considered in detail, in order to derive the coefficients of the related systems of equations of motion for these liquids. For example, the methodology based on modelling of acoustic absorption in biologically soft tissue by the employment of fractional derivatives, which has been recently developed in the literature, is shown to be a special case of the proposed theory.     

基于修正Park-Ang模型的圆钢管构件地震损伤评估

为合理评估薄壁圆钢管构件的地震损伤程度,基于Park-Ang地震损伤模型,通过修正相关参数,建立了适用于圆钢管构件的地震损伤模型。利用圆钢管构件在低周反复荷载作用下的骨架曲线,给出了损伤模型中各待定参数的计算方法,在此基础上通过反演构件破坏点损伤因子为1.0时的模型组合系数,并利用曲线拟合法得到模型组合系数与构件轴压比、长细比和径厚比等参数间的关系式,从而建立构件的地震损伤评估模型。结果表明,修正的Park-Ang损伤模型可较好地评估圆钢管构件的损伤程度,构件达到极限破坏时的损伤因子值收敛于1.0且离散性较小,构件的破坏程度可划分为基本完好、轻微与中等破坏、严重破坏和失效破坏,对应的损伤因子界限值分别为0.02,0.41和1.00。     

分数阶黏弹性土层中分数阶三维轴对称桩的竖向振动

将桩基和土体视为三维连续介质,桩基和土体的应力一应变关系采用分数阶黏弹性模型描述。在三维轴对称情况下,利用三维弹性理论和连续介质力学理论,运用分离变量法和分数阶导数的性质,得到了分数阶黏弹性土层中分数阶黏弹性桩基的三维轴对称解;并分析了相关参数对桩顸动态刚度和等效阻尼的影响。研究结果表明：与土体相比,桩基的相关参量对桩顶复刚度的影响较大;桩基和土体的密度比、模量比对桩顶复刚度都有较大的影响。     

Stability analysis of helical rod based on exact Cosserat model

Helical equilibrium of a thin elastic rod has practical backgrounds, such as DNA, fiber, sub-ocean cable, and oil-well drill string. Kirchhoff's kinetic analogy is an effective approach to the stability analysis of equilibrium of a thin elastic rod. The main hypotheses of Kirchhoff's theory without the extension of the centerline and the shear deformation of the cross section are not adoptable to real soft materials of biological fibers. In this paper, the dynamic equations of a rod with a circular cross section are established on the basis of the exact Cosserat model by considering the tension and the shear deformations. Euler's angles are applied as the attitude representation of the cross section. The deviation of the normal axis of the cross section from the tangent of the centerline is considered as the result of the shear deformation. Lyapunov's stability of the helical equilibrium is discussed in static category. Euler's critical values of axial force and torque are obtained. Lyapunov's and Euler's stability conditions in the space domain are the necessary conditions of Lyapunov's stability of the helical rod in the time domain.     

基于区间分析的结构非概率可靠性模型

本文用非概率的凸集模型模拟结构的不确定性,将结构的不确定参数描述为区间变量,基于区间分析,提出了一种新的非概率可靠性度量体系分析方法,从物理、几何意义等方面解释了文中理论的合理性,其计算方法简便,衫,给出了算例分析。     

基于等效阻尼理论的金属橡胶弹性迟滞力学模型及实验研究

针对弹性多孔金属橡胶非线性迟滞特性力学行为,将迟滞恢复力-位移曲线分解为非线性单值曲线和椭圆,并将等效阻尼理论用于动态力学性能参数识别,从而建立了一种新型的适用于黏弹性阻尼材料的宏观唯象力学模型。采用不同相对密度的环形金属橡胶进行动态实验测试,以验证理论模型的准确性,结果表明该模型可将具有非线性特性的金属橡胶系统进行降阶处理,提高金属橡胶力学模型的预测效率,并能很好地描述金属橡胶的迟滞力学行为。另外,研究了在不同激励频率条件下金属橡胶的阻尼耗能特性。实验结果表明:在高频加载的条件下,黏性阻尼系数对动态加载频率不敏感,阻尼耗能与加载幅值之间呈线性正相关。基于等效阻尼理论的弹性迟滞力学模型具有一定的普适性,可进一步推广应用于类似弹性多孔材料的力学性能表征,为其工程应用提供理论基础。     

基于凸集模型的结构地震多维易损性分析

将凸集模型应用于结构的地震多维易损性分析。建立钢筋混凝土框架结构模型,选择最大层间位移角和最大层加速度两种参数建立多维性能极限状态方程。通过平均信息熵理论,获得两种参数的区间估计。考虑椭球模型和区间模型两种形式的凸集模型,在标准空间内通过拉丁超立方抽样生成样本点,通过矩阵变换将其映射到凸集空间内,建立结构地震响应的凸集模型。将凸集变量样本点代入极限状态方程,进行了易损性分析。采用概率模型进行对比计算,研究表明,与概率模型相比,当PGA较小时,凸集模型的破坏概率较大,而PGA较大时,凸集模型的破坏概率较小;椭球模型和凸集模型的分析结果差距较小,在各个PGA下破坏概率差值仅为0.05~0.1,因此可以不考虑凸集类型不同对易损性分析结果的差异。     

Semi-permeable crack analysis in a 2D magnetoelectroelastic medium based on the EMPS model

For a crack in a magnetoelectroelastic plane under the electrically and magnetically semi-permeable boundary condition, we derive the non-linear analytical solution of the strip electric–magnetic polarization saturation (EMPS) model. Using the extended dislocation theory and integral equation method, we obtain the electric and magnetic yielding zones, as well as the field intensity factor and local J-integral. Adapting an iterative method, numerical examples were performed to analyze the effect of different boundary conditions and the electric–magnetic saturated properties on the electric displacement and magnetic induction in the crack cavity, electric and magnetic yielding zones, stress intensity factor and local J-integral.     

基于弹塑性模型的群桩-土-结构动力非线性数值分析

提出一种群桩-土弹塑性模型,结合动力文克尔理论,推导出了与桩(筏)-土属性及SSI体系频率相关的各项弹簧-阻尼单元动力阻抗,建立了三维框架土-结构相互作用有限元简化分析模型。针对不同地震激励,在不同桩-土条件下对模型进行了动力非线性时程分析,结果表明,在某些地震动和土-基础条件下,上部结构非线性作用效应结果可能大于固基假定情形,且桩-土弹塑性模型对上部结构柔弱层位置产生影响。应用本文简化方法可以快速、较准确有效地进行复杂的上下部结构动力时程分析及抗震评估。     

聚氯乙烯弹性体静动态力学性能及本构模型

为揭示聚氯乙烯弹性体在静、动态载荷下的力学性能,采用万能材料试验机和改进的分离式霍普金森压杆实验装置获得了材料在应变率为0.001、0.01、0.1、1 510、2 260和3 000 s⁻¹下的应力应变曲线,并以屈服强度为整形器优选参数,对比了紫铜、铜版纸和铅等3种整形器材料的整形效果。使用修正的ZWT非线性黏弹性本构模型描述聚氯乙烯弹性体在静、动态载荷下的力学性能。结果表明：聚氯乙烯弹性体在静态载荷下具有应变率效应和显著的超弹性特性,动态载荷下表现出较明显的应变率效应和较强的抗变形能力,且静动态载荷下的力学行为受应变历史影响较大。3种整形器材料中铜版纸的整形效果最好。修正后的ZWT非线性黏弹性本构模型能够得到统一参数的本构表达式,且各应变率下的拟合结果与实验结果具有较好的一致性。

     

Free vibration characteristics of sectioned unidirectional/bidirectional functionally graded material cantilever beams based on finite element analysis

Advancements in manufacturing technology, including the rapid development of additive manufacturing (AM), allow the fabrication of complex functionally graded material (FGM) sectioned beams. Portions of these beams may be made from different materials with possibly different gradients of material properties. The present work proposes models to investigate the free vibration of FGM sectioned beams based on onedimensional (1D) finite element analysis. For this purpose, a sample beam is divided into discrete elements, and the total energy stored in each element during vibration is computed by considering either the Timoshenko or Euler-Bernoulli beam theory. Then, Hamilton's principle is used to derive the equations of motion for the beam. The effects of material properties and dimensions of FGM sections on the beam's natural frequencies and their corresponding mode shapes are then investigated based on a dynamic Timoshenko model (TM). The presented model is validated by comparison with three-dimensional (3D) finite element simulations of the first three mode shapes of the beam.