共查询到18条相似文献,搜索用时 125 毫秒
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反对称角铺设复合材料层合板热后屈曲和模态跃迁分析 总被引:1,自引:0,他引:1
为有效分析反对称角铺设复合材料层压板热后屈曲性能,由渐近修正几何非线性理论推导双耦合四阶偏微分方程(即协调方程和动态控制方程),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。通过四边简支、面内不可移边界下复合层合板的数值计算表明:该解析法与有限元方法在主后屈曲区域的计算结果有很好的吻合性;有限元方法在解靠近二次分岔点时失去收敛性,而解析法仍具有深入探索后屈曲区域和准确捕捉模态跃迁现象的能力。 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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各向异性复合材料对称角铺设层合板非线性弯曲强迫振动 总被引:1,自引:0,他引:1
笔者曾经研究讨论了各向异性复合材料反对称角铺设层合板的非线性弯曲强迫振动问题[1]。本文是这一研究领域的继续和扩展。在这里,笔者详细研究了各向异性复合材料对称角铺设层合板在简谐激振力作用下的非线性弯曲强迫振动问题,做了包括算例的全解析过程分析,得到了各向异性对称角铺设层合板在各种量级载荷作用下的幅一频关系,分析了对称角铺设层合板结构的铺设方向角对非线性弯曲强迫振动的幅一频关系影响,所求得的解析形式结果保证了结果的可靠性。本文无疑是对复合材料层合板非线性强迫振动问题研究的一个有意义的深入扩展,它们对于探讨其它复合材料结构的非线性动力问题具有一定的意义。 相似文献
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提出了一种等效理论来分析含损伤碳纤维增强树脂T300/QY8911复合材料层合板的分层屈曲。针对含贯穿脱层层合板产生面外弯曲后的受力特点,引入损伤界面的接触效应,根据精确模型所给出的多尺度变形失效机制,提出了一个基于刚度等效理论来分析损伤层合板结构失效的力学性能。通过将含脱层的区域等效成一个几何形状和铺设方式完全一致,但刚度相应折减的完善子板,运用三分区模型,根据板壳理论、复合材料力学等基本原理建立各子板的屈曲控制方程,同时结合边界条件和连续性条件求解。算例分析表明,本文所得的屈曲荷载与考虑接触效应精确模型所得的解析解及ABAQUS有限元结果高度吻合。该研究方法充分考虑了脱层带来的刚度降低以及由于分层界面处非线性抗穿透约束的影响,不仅大大简化了繁琐的推导过程和节省了计算量,而且揭示了深层次的力学机制,更为主要的是,该方法可以有效推广到含多分层损伤层合板的非线性力学性能的评估,为航空航天先进复合材料的结构设计和力学分析提供有力的技术支持。 相似文献
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关于线性和非线性系统内在的本质联系——多自由度非线性系统的定量和定性分析 总被引:2,自引:1,他引:1
多自由度非线性振动问题是历史性国际难题,其求解方法有数值解和渐近解析解或两者结合.基于近代有限元和子结构模态综合法的动力学建模方法,获得非线性系统动力学微分方程,其自由度几乎没有限制,对左端首次近似齐次方程进行模态分析,选取对响应有贡献的部分本征对,同样对右端激励和非线性伪力作模态变换,得到减缩后非线性系统耦合动力学微分方程.用数值方法求出系统非线性响应进行定量分析,也可获得在指定参数的变动中可能发生的主谐、超谐、亚谐和组合共振,极限环和分岔、混沌等各种非线性振动现象,但其缺点是不能作一般性定性分析.渐近解析解可进行分岔混沌现象的定性分析,但迄今只限于单、两自由度系统.若系统进入共振状态,系统响应相应急剧增加到大振幅振动,振动从微幅线性振动过渡到大幅非线性振动,因之系统运动主要由所涉及的各阶单一主模态所控制.这可称为"单模态共振理论".当发生共振时,单模态理论可把多自由度系统变换为解耦的多个单自由度系统,因之可采用渐近解析法逐个进行分岔混沌等定性分析,这就克服了高自由度非线性系统定性分析的困难.为了剖析线性和非线性系统内在的本质联系,论证了首次近似表征线性系统特性的主模态是沟通线性振动和非线性振动之间的桥梁,揭示了高自由度线性振动和非线性振动都是以线性主模态呈现其运动规律. 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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In the present paper the postbuckling response of symmetrically and antisymmetrically laminated composite plates subjected to a combination of uniform temperature distribution through the thickness and in-plane compressive edge loading is presented. The structural model is based on a higher-order shear deformation theory incorporating von Karman nonlinear strain displacement relations. Adopting the Galerkin procedure, the governing nonlinear partial differential equations are converted into a set of nonlinear algebraic equations, which are solved using the Newton–Raphson iterative procedure. The critical buckling temperature is obtained from the solution of the linear eigenvalue problem. Postbuckled equilibrium paths are obtained for symmetrically laminated cross-ply, quasi-isotropic and antisymmetric angle-ply composite plates with and without initial geometric imperfections. Modal participation of each mode in the postbuckling deflection is reported using a multi-term Galerkin procedure. 相似文献
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《Composites Part B》2000,31(4):345-354
Analytical solutions for the vibrations of thick symmetric angle-ply laminated composite cylindrical shells are established using the first-order shear deformation theory. The complex method is developed to deal with the partial differential governing equations of thick symmetric angle-ply laminated composite cylindrical shells. Numerical results are provided for comparison, and coincide with existing results in the literature. The frequency characteristics for thick symmetric angle-ply laminated composite cylindrical shells with different H/R and L/R ratios are studied in comparison with those of symmetric cross-ply laminates. Also, the influence of lamination angle and number of lamination layers on frequency is investigated in details. 相似文献
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该文导出了面内热载荷作用下,梁过屈曲问题的精确解。首先基于非线性一阶剪切变形梁理论,推导了控制轴向和横向变形的基本方程。然后,将3 个非线性方程化简为一个关于横向挠度的四阶非线性积分-微分方程。该方程与相应的边界条件构成了微分特征值问题。直接求解该问题,得到了热过屈曲构形的闭合解,这个解是外加热载荷的函数。利用精确解,得到了临界屈曲载荷的一阶结果与经典结果的解析关系。为考察热载荷、横向剪切变形以及边界条件的影响,根据得到的精确解给出了两端固定、两端简支以及一端固定一端简支边界条件下的具体数值算例,讨论了梁在面内热载荷作用下的过屈曲行为,并与经典结果进行了比较。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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Jalaleddin Farsa Anant R. Kukreti Charles W. Bert 《International journal for numerical methods in engineering》1993,36(14):2341-2356
In this paper a differential quadrature method is presented for computation of the fundamental frequency of a thin laminated rectangular plate. The partial differential equations of motion for free vibration are solved for the boundary conditions by approximating them by substituting weighted polynomials functions for the differential operator. By doing this, the coupled partial differential equations of motion are reduced to sets of homogeneous algebraic equations. These sets of homogeneous algebraic equations are combined to give a set of general eigenvalue equations for the problem. Three types of laminated plate problems, which include symmetric, antisymmetric cross-ply, and symmetric, balanced angle-ply laminates, are analysed by the method and the results obtained are compared with solutions reported in the literature for other numerical methods. The effects of the level of discretization on the accuracy and rate of convergence of the results are also discussed. The method presented gives accurate results and is found to use not much computer time. 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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针对复合材料悬臂板系统的非线性动力学行为进行了分析。模型考虑高阶横向剪切效应、几何大变形和横向阻尼的影响,基于Reddy的高阶剪切变形理von Karman的大变形理论,利用Hamilton原理,Galerkin离散和多尺度法得到系统横向位移的平均方程。应用广义Melnikov方法研究了复合材料悬臂板的非线性混沌动力学行为。分析了在共振带附近,复合材料悬臂板系统存在的Shilnikov类型多脉冲跳跃同宿轨道。最后结合数值模拟,进一步揭示系统存在多脉冲跳跃现象。 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