混凝土夹芯板滑移与变形的理论计算及分析

对均布荷载作用下简支混凝土夹芯板的滑移及其对混凝土夹芯板变形挠度影响的理论计算进行了研究和分析,推导出了简支混凝土夹芯板的滑移和变形挠度的理论计算公式,该公式既能描述混凝土夹芯板的滑移规律,也能体现滑移对混凝土夹芯板变形挠度的影响。同时推导出了开裂弯矩的计算公式,确定了滑移和变形挠度计算公式的适用范围。通过与试验和有限元分析结果的比较表明:理论公式计算的结果与试验和有限元分析结果较吻合,可以在实际工程中用来计算混凝土夹芯板的滑移和弯曲变形。     

电压激励下四边简支压电层合板的振动分析

以压电陶瓷-金属-压电陶瓷对称层合板为研究对象,依据小挠度弯曲理论,根据Hamilton原理和Rayleigh-Ritz法推导出了电压激励下压电层合薄板的振动方程。以四边简支的压电层合薄板为算例,用ANSYS软件建立有限元模型并对其进行模态分析、瞬态动力学分析,仿真结果与理论值基本相符,验证了本文理论的正确性;通过改变电压幅值的大小分析其对中心节点位移响应幅值以及x,y方向应力幅值的影响。通过改变阻尼大小分析其对薄板横向位移的影响。数值模拟了薄板中心处节点x,y方向应力随时间的变化规律,并分析了薄板最大应力出现位置及随时间的变化规律,所得结论可为压电振子的设计和分析提供一定的理论参考。     

基于MEMS的静电微泵建模与仿真

对MEMS中应用广泛的静电微泵进行有限元建模分析．对于涉及多能量域下多场耦合的静电微泵建模,在仿真过程中进行了合理简化．其中在静态分析中,利用圆型薄板的小挠度变形理论和微机电系统中的静电力驱动理论来模拟静电-结构耦合过程;在泵膜的模态分析、谐响应分析以及非线性瞬态分析中,把腔内的流体当作附加质量作用在泵膜上,近似代替流场对泵膜的影响,从而减小计算量,提高了仿真效率．     

钢管混凝土构件在侧向冲击载荷作用下的挠度分析

运用大型显式动力有限元分析软件ANSYS/LS-DYNA对壁厚为3.5mm、3.8mm、4.5mm的钢管混凝土构件侧向冲击动力响应问题进行了仿真分析,对比了冲击点处残余挠度的模拟结果与试验结果,找出了挠度的主要影响因素,讨论了冲击局部变形和破坏问题。     

均布荷载作用下钢-混凝土组合梁滑移及变形的理论计算

对均布荷载作用下简支钢-混凝土组合梁的滑移及其对组合梁变形挠度影响的理论计算进行了研究。利用Goodman弹性夹层假设及弹性体变形理论,推导了简支钢-混凝土组合梁的界面滑移和挠度变形的理论计算公式。该理论公式既能描述组合梁的界面滑移规律,也体现了界面滑移对组合梁变形挠度的影响。该理论公式将为钢-混凝土组合结构极限承载力和变形挠度的有限元计算提供理论基础。     

作大范围运动矩形薄板的建模理论和有限元离散方法

研究了作大范围运动薄板的耦合动力学建模理论和离散化方法。对作大范围运动的薄板建立了耦合动力学模型，计及了在结构动力学中对薄板动力学特性影响很小的二次耦合变形量。用有限元方法对秉性薄板进行离散，基于Jourdain速度变分原理导出了作大范围运动薄板的动力学方程。计算了作旋转运动的薄板的变形，将仿真结果与不计二次耦合变形量的传统方法进行比较表明，随着转速的提高，仿真结果出现明显的差异。此外，将本文有限元与假设模态法的计算结果进行比较，揭示了高速旋转时假设模态法的局限性，表明取无大范围运动的高阶模态可以提高假设模态法的计算精度。     

柔性薄板件装配误差分析

为简化柔性薄板件装配分析过程和提高计算效率,在自由回弹的基础上,分析在"N-2-1"定位方式下,柔性薄板件夹具偏差经定位夹紧、自由回弹和焊接后对最终装配偏差的影响,建立柔性薄板件装配偏差模型.同时,分析装配过程中外力力矩作用下的偏转所引起的法向变形.最后,用MATLAB结合有限元软件ANSYS进行仿真,与CATIA TAA按传统装配过程分析的结果进行比对,验证装配偏差模型的有效性.     

电力线缆自动化矫直的仿真和实验研究

为解决人工矫直线缆时矫直精度和标准化水平低的问题,对一种新型电力线缆的矫直过程进行了有限元仿真和实验分析,研究了线缆矫直过程中线缆挠度的变化规律。利用ANSYS workbench软件建立半圆状线缆有限元模型,采用瞬时动力学仿真分析压入量为0.5 mm时线缆矫直情况;在此基础上,分析在相同进给速度、不同线缆内径和相同线缆内径、不同进给速度下线缆的矫直过程,研究线缆挠度与线缆内径和进给速度的关系;制备了弯曲线缆试样,进行线缆矫直实验。结果表明：在0.5 mm给定压入量下,线缆矫直结果符合预期;线缆内径和进给速度对线缆挠度影响较大。线缆内径越大,进给速度越快,则线缆挠度越大,矫直精度越低且挠度变化趋势呈非线性。线缆挠度仿真值与实验值的误差在10%之内,验证了线缆矫直机有限元模型的准确性。研究结果可为提高线缆矫直机的矫直精度、工作效率及矫直机的优化设计提供参考。     

低速大质量球头弹冲击下薄板穿甲破坏机理数值分析

为探讨薄板穿甲破坏机理,采用动态非线性有限元,结合弹道冲击试验,分析了薄板在低速大质量球头弹体冲击下的穿甲破坏过程及其变形机理,薄板的变形吸能规律及破坏模式,并将有限元分析结果与实验结果进行了比较,有限元分析结果与实验结果吻合良好.结果表明:薄板穿甲破坏过程大致可分为三个阶段,即隆起变形阶段,碟形变形阶段和弹体贯穿阶段.其中薄板的隆起变形主要由剪力和弯矩引起的;隆起变形结束后,碟形变形区膜力逐渐增大,超过动态屈服极限,并随冲击速度的减小而增大,到弹道极限附近成为最主要的广义应力;低速冲击下碟型变形是靶板主要的变形吸能方式.大质量低速球头弹冲击下薄板的穿甲破坏模式可归纳为三种:隆起-碟形变形,隆起-碟形变形-贯穿破坏和隆起-贯穿破坏.     

基于B样条插值法的柔性矩形薄板的动力学分析

采用B样条插值方法研究柔性矩形薄板的动力学特性。考虑薄板的面外变形、面内变形以及面外变形引起的面内变形,利用B样条插值方法对柔性薄板的变形场进行离散,以拉格朗日方程为基础推导出作大范围运动柔性薄板的动力学方程,并运用MATLAB软件对薄板动力学仿真问题进行编程。通过动力学仿真,对比分析了B样条插值法、假设模态法以及有限元法的仿真结果,验证了B样条插值方法的正确性,并表明B样条插值法在处理柔性薄板的大变形问题的计算精度上具有优良性能和推广潜力。     

The surface effect on the strain energy release rate of buckling delamination in thin film-substrate systems

Gurtin-Murdoch continuum surface elasticity model is employed to study the buckling delamination of ultra thin film-substrate system. The effects of surface deformation and residual stress on the large deflection of ultra thin film are considered in analysis. A concept of effective bending rigidity (EBR) for ultra thin plate is proposed on the basis of Gurtin-Murdoch continuum theory and the principle of minimum potential energy. The governing equations with EBR are formally consistent with the classical plate theory, including both small deflection and large deflection. A surface effect factor is introduced to decide whether there is need to consider the surface effect or not. Combining the buckling theory and interface fracture mechanics, we obtain analytical solutions of the critical buckling load and the energy release rate of the interface crack in the film-substrate system. It is seen that the surface deformation and residual stress have significant effects on the buckling delamination of ultra thin film-substrate system.     

Postbuckling response and failure of symmetric laminates under in-plane shear

This paper summarizes a study aimed at understanding the postbuckling behaviour and progressive failure of thin, simply supported symmetric rectangular laminates with various possible in-plane boundary conditions and under the action of in-plane shear loads. First-order shear deformation theory and geometric non-linearity, in the von-Karman sense, is used with a finite-element procedure. The 3D Tsai–Hill criterion is used to predict failure of lamina and the maximum stress criterion is used to predict the onset of delamination at the interface of two adjacent layers. The effect of in-plane boundary conditions, plate lay-ups, plate aspect ratio, fiber orientations and lamina material properties on the load deflection response, buckling load, first-ply failure load, ultimate load and the maximum transverse displacement associated with failure loads is presented.     

Extended rotation‐free plate and beam elements with shear deformation effects

This paper describes a methodology for extending rotation‐free plate and beam elements to accounting for transverse shear deformation effects. The ingredients for the element formulation are a Hu–Washizu‐type mixed functional, a linear interpolation for the deflection and the shear angles over standard finite elements and a finite volume approach for computing the bending moments and the curvatures over a patch of elements. As a first application of the general procedure, we present an extension of the three‐noded rotation‐free basic plate triangle (BPT) originally developed for thin plate analysis to account for shear deformation effects of relevance for thick plates and composite‐laminated plates. The nodal deflection degrees of freedom (DOFs) of the original BPT element are enhanced with the two shear deformation angles. This allows to compute the bending and shear deformation energies leading to a simple triangular plate element with three DOFs per node (termed BPT+ element). For the thin plate case, the shear angles vanish and the element reproduces the good behaviour of the original thin BPT element. As a consequence the element is applicable to thick and thin plate situations without exhibiting shear locking effects. The numerical solution for the thick case can be found iteratively starting from the deflection values for the Kirchhoff theory using the original thin BPT element. A two‐noded rotation‐free beam element termed CCB+ applicable to slender and thick beams is derived as a particular case of the plate formulation. The examples presented show the robustness and accuracy of the BPT+ and the CCB+ elements for thick and thin plate and beam problems. Copyright © 2010 John Wiley & Sons, Ltd.     

钢筋混凝土矩形薄板徐变效应分析

基于弹性薄板理论和按龄期调整的有效模量法思想,分析钢筋混凝土矩形薄板徐变效应,建立了考虑混凝土徐变和钢筋约束影响的时变弹性曲面微分方程,并给出了四边简支和四边夹支的钢筋混凝土矩形薄板的徐变效应计算公式,可方便求解任意时刻薄板挠度和混凝土、钢筋的应力.     

薄板在周期热流作用下的热响应(Ⅱ)——变形响应

考虑高频周期热流作用下引起传热过程的非Fourier效应,基于线性热弹性理论和经典的薄板理论,建立了周边简支矩形板在动态温度场下的控制方程,利用Nowacki方法和Navier级数解法求解得到了相应的拟静态变形和考虑惯性动力项作用的动态变形的解析表达式。通过算例,分析讨论了非Fourier效应、热流频率及惯性项对薄板变形的影响。     

Nonlinear elastic mechanics of the ball-loaded blister test

The nonlinear elastic mechanics of spherically capped shaft or ball-loaded blister tests is presented. In the test model, a thin film is attached to a substrate with a circular hole running through the thickness of the substrate. A central load is applied to the film through the hole by a spherically capped shaft or a ball with a finite radius. The deformed blister is divided into two parts: a circular region in contact with the sphere of the cap or ball and an outer noncontact annulus. The Reissner’s plate theory is employed to describe the deformation of the contact part and the von Kármán plate theory for the noncontact annulus. A constitutive equation of coupled linear springs is obtained to quantify the effect of the substrate deformation on the blister deflection. For small deflection, the analytical solution of load-deflection is derived. For large deflection, an iteration approach is adopted to predict numerically the load-deflection curve. Finite-element analysis is conducted to verify the analytical and numerical solutions. The influence of the substrate deformation, residual stress, radius of the spherical cap or ball and the friction between the film and ball on the load-deflection relation is investigated.     

Bending of a Thin Rectangular Isotropic Micropolar Plate

In this note, deflection of a thin rectangular isotropic micropolar plate is observed under the influence of transverse loading. From the properties of asymptotic solution, a set of hypotheses is considered and the corresponding governing equations of bending are derived. The solutions are validated by comparing the numerical results and with their counterparts reported in literature for classical Timoshenko plate theory and the Kirchhoff’s theory of plate deformation.     

基于解析试函数的各向异性材料厚薄通用板单元

该文采用满足Kirchhoff假设的薄板理论,推导了各向异性材料系列解析试函数,并利用该系列解析试函数构造了一个四边形应力杂交板单元。首先,该文从薄板理论的基本方程出发,推导了各向异性材料薄板中面挠度w应满足的特征微分方程。然后,从该方程出发求得w的系列特征通解,由w特征通解可进一步求得广义位移、广义应变和广义应力的解析试函数。同时,根据广义应力利用平衡条件构造了相应的横向剪力解析试函数。最后,根据已有的广义应力和横向剪力解析试函数构造了一个四边形应力杂交板单元ATF-PH4。数值算例表明:上述方法构造出的单元模型有很好的精度、收敛性,且对网格畸变不敏感,同时能较好地解决板单元的厚薄通用性问题。     

A non-classical third-order shear deformation plate model based on a modified couple stress theory

A non-classical third-order shear deformation plate model is developed using a modified couple stress theory and Hamilton’s principle. The equations of motion and boundary conditions are simultaneously obtained through a variational formulation. This newly developed plate model contains one material length scale parameter and can capture both the size effect and the quadratic variation of shear strains and shear stresses along the plate thickness direction. It is shown that the new third-order shear deformation plate model recovers the non-classical Reddy-Levinson beam model and Mindlin plate model based on the modified couple stress theory as special cases. Also, the current non-classical plate model reduces to the classical elasticity-based third-order shear deformation plate model when the material length scale parameter is taken to be zero. To illustrate the new model, analytical solutions for the static bending and free vibration problems of a simply supported plate are obtained by directly applying the general forms of the governing equations and boundary conditions of the model. The numerical results show that the deflection and rotations predicted by the new plate model are smaller than those predicted by its classical elasticity-based counterpart, while the natural frequency of the plate predicted by the former is higher than that by the latter. It is further seen that the differences between the two sets of predicted values are significant when the plate thickness is small, but they are diminishing with increasing plate thickness.     

Enhanced modeling of laminated and sandwich plates via strain energy transformation

An enhanced first-order shear deformation theory has been developed for the deformation and stress recovery of laminated and sandwich plates. Based on the definition of Reissner–Mindlin’s plate theory, the relationships between three-dimensional and first-order shear deformation theories have been derived. It is assumed that the displacements, in-plane strains and stresses of Reissner–Mindlin’s plate theory can approximate those of three-dimensional theory, in the least-square sense. Their relationships have been systematically established and verified through the strain energy transformation. These relationships provide the closed-form recovering relations for three-dimensional variables expressed in terms of the variables of Reissner–Mindlin’s plate theory. An efficient higher-order plate theory is utilized to obtain the in-plane warping functions. Comparisons of deflection, stresses and shear correction factors of both laminated and sandwich plates using the present theory are made with the original first-order shear deformation theory and three-dimensional exact solutions.