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为有效分析双轴受压反对称角铺设复合材料层压板在固支边界下的后屈曲性能, 由渐近修正几何非线性理论推导其双耦合四阶偏微分方程(即应变协调方程和稳定性控制方程), 通过双Fourier级数将耦合非线性控制偏微分方程转换为系列非线性常微分方程, 从而获得相对简单的求解方法。使用广义Galerkin方法求解与角交铺设复合层合板相关的边界值问题, 研究了模态跃迁前后不同复杂程度的后屈曲模式。对四层固支边界复合层合板的数值模拟结果表明: 该解析法与有限元方法在主后屈曲区域的线性屈曲荷载计算结果吻合良好; 有限元方法在解靠近二次分岔点时失去收敛性, 而解析方法可深入后屈曲区域, 准确捕捉模态跃迁现象; 对于反对称角铺设层合板, 可仅用纯对称模态来定性预测主后屈曲分支、二次分岔荷载及远程跃迁路径。 相似文献
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含脱层单向铺设层合梁非线性后屈曲分析 总被引:1,自引:0,他引:1
采用四分区模型,将含脱层单向铺设复合材料层合板梁分为4个子梁,根据复合材料层合理论,考虑后屈曲路径上位于脱层界面上、下子梁之间的局部受力与变形机制,建立了子梁之间接触力与变形之间的非线性定量关系。在此基础上,结合可伸长梁的几何非线性理论,推导出了计及接触效应的各子梁的非线性后屈曲控制方程。设定简支板梁的边界条件以及脱层前沿处各子梁之间力和位移的连续性条件,通过对控制方程和定解条件归一化,采用小参数摄动法求解,并根据梁的平衡微分方程的特点,解析其通解与特解的构造,获得了含脱层单向铺设层合梁受轴向压力作用的临界屈曲荷载及后屈曲平衡路径的理论解。通过对含脱层单向铺设的复合材料层合梁进行数值分析,综合讨论了脱层长度和深度等对层合板梁的临界屈曲载荷及接触性能的影响,并将所得的理论解与ABAQUS有限元分析得到的结果进行对比,结果表明二者高度吻合。研究发现梁的屈曲模态包含宏观的整体失效模态和界面的微观屈曲模态。梁的屈曲荷载和接触性能都是其固有属性,前者受梁的几何参数和材料参数的影响较显著,而后者则主要受脱层的位置和大小影响。 相似文献
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从动力学观点,浅拱受冲击是一种无穷维或者连续的动力系统,论文针对抛物线浅拱,应用有关薄壁结构的基本理论和非线性几何关系推导并建立其控制微分方程。然后,利用时滞惯性流形的思想,提出一种求解这类强非线性偏微分方程的新方法,即基于时滞惯性流形的非线性Galerkin方法。通过这种方法,把原始方程的解投影到由控制方程中线性算子的特征函数所张成的完备空间内,并构造出无限维子空间内的动力行为与有限维子空间内的动力行为之间的耦合作用,该耦合作用认为高低阶分量间的相互作用并不是一种简单的瞬时行为,而是与模态发展的历史有关。通过数值分析得到:系统存在两个稳定平衡位置,与传统的Galerkin方法相比,所提出的基于时滞惯性流形的非线性Galerkin方法可以大幅度地降低方程的维数,提高计算速度,有效地降低对计算机内存的需求和减少计算时间。某种程度上,时滞惯性流形为系统的非线性动力行为如屈曲、分岔、突跳等动态模拟和数值分析提供了一个新的更为合理的研究手段。 相似文献
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大展弦比夹芯翼大攻角颤振分析 总被引:4,自引:0,他引:4
首先导出大展弦比复合材料梁弯扭耦合模态的半解析解,对具有NACA0012翼型的大展弦比的夹芯翼,在模态空间内建立了运动方程。然后采用半经验的ONERA非线性气动力模型描述空气动力,形成了对大展弦比夹芯翼大攻角气动弹性问题的描述。通过结构求解器和空气动力求解器联合求解来完成非线性颧振边界的计算。为了验证非线性颤振边界的求解方法,还利用ONERA气动力模型中的线性部分建立了夹芯翼的线性颤振方程。结果表明:零翼根攻角时,线性颤振速度与用非线性颧振边界求解方法得到的颧振速度完全一致;颤振速度随翼根攻角的增加而迅速减小;复合层铺设方式对颤振速度有较大影响。 相似文献
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研究具有几何非线性的旋转复合材料薄壁梁的自由振动。梁的变形引入了Von Kármán几何非线性, 基于Hamilton原理和变分渐进法 (Variational-Asymptotical Method -VMA),导出旋转复合材料薄壁梁的非线性振动偏微分方程组。采用Galerkin法将振动方程离散化为常微分方程组。借助于谐波平衡法 (Harmonic Balance Method -HBM) 建立自由振动的振幅-非线性固有频率关系方程。将上述方程化为非线性特征值问题,采用迭代算法进行求解。将所建立的旋转复合材料薄壁梁非线性自由振动分析模型和计算方法,应用于周向均匀刚度配置(Circumferentially Uniform Stiffness –CUS) 构型复合材料薄壁梁,通过数值计算揭示了纤维铺层角、旋转速度对非线性振动固有频率-振幅关系的影响。 相似文献
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本文基于高阶变形理论和修正型Hahn-Tsai非线性本构模型,提出一种复合材料层合板非线性热屈曲分析方法.针对四边简支反对称角铺设复合材料层合板,导出了非线性热屈曲临界温度封闭解.数值结果表明:材料非线性能显著降低层合板临界温度. 相似文献
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该文导出了面内热载荷作用下, 梁在其过屈曲构形附近微幅振动的解析解。首先基于经典梁理论, 推导了控制轴向和横向变形的基本方程。然后, 将2 个非线性方程化为一个关于横向挠度的四阶非线性积分-微分方程。假设梁的振幅以及由此引起的附加应变为无限小, 另设其响应为谐振, 则该非线性积分-微分方程将化为两组耦合的微分方程:一组控制非线性静态响应;另一组就是叠加于梁屈曲构形之上的线性振动方程。直接求解这些问题, 可以得到梁热过屈曲构形以及固有频率的解析解, 这些解是外加热载荷的函数。该文得到的精确解可以用于验证或改进各类近似理论和数值方法。 相似文献
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根据Euler-Bernoulli梁理论和粘弹性材料的Kelvin-Voigt理论建立风力机叶片挥舞—摆振耦合非线性动力学方程。将位移视为静态位移和动态位移的叠加,进而将非线性动力学方程线性化为动态位移的线性方程,得到叶片耦合振动特征方程。使用基于加权残值的Galerkin方法求解特征方程,分析叶片气弹稳定性,讨论风速、安装角、耦合效应和材料阻尼对叶片颤振稳定性和非线性自激振动行为的影响。结果表明:摆振方向易出现不稳定振动,通过设置安装角,利用挥舞—摆振耦合可以控制不稳定振动,但当安装角太大时,挥舞—摆振耦合会引起不稳定振动。 相似文献
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Nonlinear torsional vibrations of thin-walled beams exhibiting primary and secondary warpings are investigated. The coupled nonlinear torsional–axial equations of motion are considered. Ignoring the axial inertia term leads to a differential equation of motion in terms of angle of twist. Two sets of torsional boundary conditions, that is, clamped–clamped and clamped-free boundary conditions are considered. The governing partial differential equation of motion is discretized and transformed into a set of ordinary differential equations of motion using Galerkin’s method. Then, the method of multiple scales is used to solve the time domain equations and derive the equations governing the modulation of the amplitudes and phases of the vibration modes. The obtained results are compared with the available results in the literature that are obtained from boundary element and finite element methods, which reveals an excellent agreement between different solution methodologies. Finally, the internal resonance and the stability of coupled and uncoupled nonlinear modes are investigated. This study can be a preliminary step in the understanding of complex dynamics of such systems in internal resonance excited by external resonant excitations. 相似文献
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《International Journal of Engineering Science》2003,41(3-5):231-247
Pulsatile flows of micropolar fluids with stretch whose microelements can undergo expansions and contractions besides translations and rotations in straight circular tubes are considered. The governing field equations for such flows of linear microstretch fluids turn out to be a nonlinear coupled partial differential system. Solutions are sought for this system starting with a reasonable initial approximation for microinertia and the consequent linearization of the field equations. One of the coupled equations governing the microstretch and microinertia is solved approximately by the method of Laplace transforms taken with respect to the time variable. Making use of this approximate solution, the other coupled equation is solved leading to explicit higher order approximation solutions for microinertia, microstretch and micropressure. Next, the coupled equations governing the velocity and the microrotation fields are solved by employing the finite Hankel transform operators on a space variable and their inversions, and higher order approximation solutions are determined. All the above-mentioned explicit solutions are obtained in computationally suitable forms. These solutions have the promise of application to many practically important physical situations such as flows of polymeric fluids with deformable springy suspensions and flows of biological fluids including blood with deformable cell suspensions in small arteries. 相似文献
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G. C. Tsiatas 《Acta Mechanica》2010,209(1-2):141-152
In this paper a boundary integral equation solution to the nonlinear problem of non-uniform beams resting on a nonlinear triparametric elastic foundation is presented, which permits also the treatment of nonlinear boundary conditions. The nonlinear subgrade model which describes the foundation includes the linear and nonlinear Winkler (normal) parameters and the linear Pasternak (shear) foundation parameter. The governing equations are derived in terms of the displacements for nonlinear analysis in the deformed configuration and for linear analysis in the undeformed one. Moreover, as the cross-sectional properties of the beam vary along its axis, the resulting coupled nonlinear differential equations have variable coefficients which complicate the mathematical problem even more. Their solution is achieved using the analog equation method of Katsikadelis. Several beams are analyzed under various boundary conditions and load distributions, which illustrate the method and demonstrate its efficiency and accuracy. Finally, useful conclusions are drawn from the investigation of the nonlinear response of non-uniform beams resting on nonlinear elastic foundation. 相似文献
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In this paper the analog equation method (AEM) is applied to nonlinear analysis of elastic membranes with arbitrary shape.
In this case the transverse deflections influence the inplane stress resultants and the three partial differential equations
governing the response of the membrane are coupled and nonlinear. The present formulation, being in terms of the three displacements
components, permits the application of geometrical inplane boundary conditions. The membrane is prestressed either by prescribed
boundary displacements or by tractions. Using the concept of the analog equation the three coupled nonlinear equations are
replaced by three uncoupled Poisson's equations with fictitious sources under the same boundary conditions. Subsequently,
the fictitious sources are established using a procedure based on BEM and the displacement components as well as the stress
resultants are evaluated from their integral representations at any point of the membrane. Several membranes are analyzed
which illustrate the method and demonstrate its efficiency and accuracy. Moreover, useful conclusions are drawn for the nonlinear
response of the membranes. The method has all the advantages of the pure BEM, since the discretization and integration is
limited only to the boundary.
Received 21 November 2000 相似文献
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通过数值方法研究超临界速度下,两端固定边界的轴向运动梁平面耦合非线性振动固有频率。发展有限差分法,确定在超临界范围轴向运动梁的径向与横向耦合平面内非平凡静平衡位形。基于非平凡静平衡位形,经坐标变换,建立超临界轴向运动梁连续陀螺系统的标准控制方程。运用高阶Galerkin截断,研究超临界运动状态下梁平面振动的固有频率;并研究Galerkin截断阶数对计算结果的影响。 相似文献
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The post-buckling response of thin plates made of linear viscoelastic materials is investigated. The employed viscoelastic material is described with fractional order time derivatives. The governing equations, which are derived by considering the equilibrium of the plate element, are three coupled nonlinear fractional partial evolution type differential equations in terms of three displacements. The nonlinearity is due to nonlinear kinematic relations based on the von Kármán assumption. The solution is achieved using the analog equation method (AEM), which transforms the original equations into three uncoupled linear equations, namely a linear plate (biharmonic) equation for the transverse deflection and two linear membrane (Poisson’s) equations for the inplane deformation under fictitious loads. The resulting initial value problem for the fictitious sources is a system of nonlinear fractional ordinary differential equations, which is solved using the numerical method developed recently by Katsikadelis for multi-term nonlinear fractional differential equations. The numerical examples not only demonstrate the efficiency and validate the accuracy of the solution procedure, but also give a better insight into this complicated but very interesting engineering plate problem 相似文献
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G. A. Armstrong R. S. Ferguson J. Flynn 《International journal for numerical methods in engineering》1986,23(4):635-649
The proposed algorithm solves equations governing the behaviour of semiconductor devices using a finite element technique. Electrostatic potential and the hole and electron quasi-Fermi potentials are chosen as the solution variables. The equation set is written in a steady-state form using these three variables and this gives rise to a system of three nonlinear partial differential equations. The equations, which are intimately coupled, are solved simultaneously using a weighted residual formulation. Convergence of the nonlinear solution procedure using any initial guess is guaranteed by employing ‘incremental loading’ coupled to a test for divergence that is applied at each iterative step. The triangular elements used in the program are automatically generated from a mesh of eight-node isoparametric elements that is itself an automatically generated subdivision of a small number of eight-node (super) elements. A novel method of generating an initialisation state using the boundary element method is also described. 相似文献
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《Engineering Analysis with Boundary Elements》2001,25(8):655-667
In this paper, the analog equation method (AEM) is applied to nonlinear analysis of heterogeneous orthotropic membranes with arbitrary shape. In this case, the transverse deflections influence the in-plane stress resultants and the three partial differential equations governing the response of the membrane are coupled and nonlinear with variable coefficients. The present formulation, being in terms of the three displacement components, permits the application of geometrical in-plane boundary conditions. The membrane may be prestressed either by prescribed boundary displacements or by tractions. Using the concept of the analog equation, the three coupled nonlinear equations are replaced by three uncoupled Poisson's equations with fictitious sources under the same boundary conditions. Subsequently, the fictitious sources are established using a procedure based on the BEM and the displacement components as well as the stress resultants are evaluated from their integral representations at any point of the membrane. Several membranes are analyzed which illustrate the method, and demonstrate its efficiency and accuracy. Moreover, useful conclusions are drawn for the nonlinear response of heterogeneous anisotropic membranes. The method has all the advantages of the pure BEM, since the discretization and integration are limited only to the boundary. 相似文献