黏弹性层合圆柱壳的临界轴压分析

基于经典屈曲理论,研究了轴向受压黏弹性复合材料层合圆柱壳的临界屈曲载荷. 利用Boltzmann线性积分型本构关系描述铺设单层的各向异性黏弹性行为. 结合解析与数值 方法,由Donnell型屈曲控制方程以及边界条件的Laplace变换导出相空间的特征方程,根 据Laplace逆变换的极值定理,获得层合圆柱壳的瞬时弹性临界载荷与持久临界载荷. 针对 多组铺设方式,通过数值算例重点分析了临界载荷随铺设角的变化特征,两种临界载荷的峰 值点差异程度与铺设方式、几何参数以及材料类型的关系,得到了一些对黏弹性层合圆柱壳 的优化设计有参考价值的结论.     

含基体横向损伤的黏弹性板的蠕变后屈曲分析

基于Schapery三维黏弹性损伤本构关系,引入沈为和Kachanov损伤演化方程,建立了基体横向损伤的纤维单一方向铺设黏弹性板的损伤模型;应用von Karman板理论,导出了考虑损伤效应的具初始挠度的纤维单一方向铺设黏弹性矩形板的非线性压屈平衡方程. 对未知变量在空间上采用差分法离散,时间上采用增量算法和Newton-Cotes积分法离散,控制方程被迭代求解. 算例中讨论了损伤以及有关参数对黏弹性复合材料板后屈曲行为的影响,且与已有文献的结果进行了比较. 数值结果表明：随着外载荷或者初始挠度的增大,板后屈曲趋于稳定时的挠度就愈大,损伤的影响愈明显;而随着长宽比的增大,板后屈曲趋于稳定时的挠度愈小,损伤的影响却随之增大.     

基于连续丝束剪切技术的变角度复合材料层合板的热屈曲分析

连续丝束剪切(Continuous Tow Shearing, CTS)铺放技术是一种新的变角度层合板制作技术，这种新技术能显著减少丝束铺放过程中产生的丝束重叠和间隙等缺陷，然而，采用CTS技术铺设时，层合板的厚度将随着纤维角度的变化而变化．本文基于一阶剪切变形理论并应用Chebyshev-Ritz法对这种变厚度的变角度复合材料层合板的热屈曲问题进行了研究．假设纤维方向角沿板的长度方向按照线性变化，获得了均匀温度变化时变厚度层合板的临界热屈曲荷载．通过与现有文献的比较验证了本文方法的正确性，并进一步讨论了纤维铺设技术、纤维方向角的变化以及边界条件的不同对变角度复合材料层合板的临界屈曲温度的影响．研究结果表明，在体积相同的情况下，采用CTS铺设较传统的自动丝束铺放(AFP)可以进一步提升变角度层合板的临界屈曲温度．本文的研究结果可为变角度复合材料的设计提供一定的参考．     

黏弹性层合圆柱壳的蠕变分岔屈曲

采用Boltzmann积分型本构关系描述铺设单层的黏弹性力学行为,基于DMV扁壳假定和Kármán- Donnell几何非线性关系,研究了对称铺设黏弹性层合圆柱壳的前屈曲变形特征和分岔蠕变屈曲．对玻璃纤维/环氧树脂基复合材料层合圆柱壳的分析结果表明,在前屈曲阶段,挠曲变形和环向薄膜力随时间的变化趋势主要取决于圆柱壳的铺设方式,可以呈现完全相反的变化特征;层合短圆柱壳两端的边界条件对其蠕变分岔屈曲行为有决定性的影响,径厚比的增加将使分岔形式的延迟失稳现象更加明显．     

跨中集中荷载作用下弹性约束圆弧拱的稳定性分析

研究了跨中集中荷载作用下两端由不同转动刚度弹性约束的铰支圆弧拱的面内稳定性。由变形几何关系、变分原理得到了拱的非线性平衡方程,建立了外荷载、结构内力、径向位移的对应关系,通过定义拱的深浅参数和约束刚度参数进行分析,并得到了跳跃屈曲和分岔屈曲的发生条件及存在区间。通过数值分析可知本文方法所得屈曲路径和屈曲荷载与有限元法所得结论吻合良好,极值点、临界荷载相对差值在1%左右。对不同结构参数区间圆弧拱在集中荷载作用下的屈曲路径和临界荷载进行了分析,结果表明约束刚度对屈曲路径和临界荷载起决定性的作用,深浅参数决定屈曲发生条件、屈曲形式、极值点对数。     

反对称铺设复合材料层合板非线性后屈曲分析

基于层合板壳理论,考虑反对称铺设层合板的拉弯耦合效应和后屈曲过程中的非线性几何变形,推导了由应力函数和挠度表示的复合材料层合板的后屈曲控制方程。引入无量纲参数对控制方程和边界条件进行无量纲化,以消除材料参数及几何尺寸对分析结果的影响。采用摄动法将无量纲的非线性控制方程及边界条件展开成一系列非齐次线性摄动方程组,分析各阶摄动方程的通解与特解的构造,并逐次求解,建立了反对称铺设复合材料层合板受单向均布压力作用的临界屈曲荷载及后屈曲平衡路径的理论解。进而运用ABAQUS软件对复合材料层合板在面内压缩载荷作用下的屈曲和后屈曲进行有限元分析,结果表明理论解与ABAQUS结果十分接近,验证了理论解的正确性。在此基础上进一步讨论了铺设角度、铺设层数和拉弯耦合效应等对层合板后屈曲性能的影响。研究发现层合板的屈曲载荷受铺设角度与层数的影响较为显著,而拉弯耦合效应使板的屈后强度大大降低。     

受面内双向荷载蜂窝材料的弹性屈曲模式及其影响因素

基于压弯耦合梁柱稳定理论,分析了蜂窝材料在面内双轴应力作用下的弹性屈曲行为,得到了蜂窝材料在不同应力荷载作用下发生两种屈曲模式转换的临界条件和对应的屈曲临界荷载.讨论了孔穴几何参数对此转换条件和临界荷载的影响,并用ANSYS软件进行了有限元模拟.结果表明理论分析与数值模拟吻合很好.     

含椭圆孔的变角度复合材料层合板的屈曲性能研究

本文利用变角度复合材料的纤维方向角可沿平面位置任意连续变化的特点,提出在孔附近采用与孔同心的椭圆曲线作为纤维铺设路径的层合板铺层方案,以改善含椭圆孔的层合板的孔边应力集中,进而提高层合板的抗屈曲性能．主要研究内容有：利用ABAQUS软件分析本文提出的孔边特殊铺层方式下变角度复合材料层合板的面内应力分布及屈曲性能,通过与传统直线铺层方式以及线性变角度铺层方式进行比较,说明了本文提出的新铺层方式的优越性,并详细分析了椭圆孔的离心率、开孔尺寸及开孔方位对层合板的屈曲临界荷载的影响．研究结果可为含椭圆孔的变角度复合材料层合板的结构设计和优化提供一定的参考．     

考虑制作缺陷的变角度纤维复合材料层合板的屈曲

假设纤维方向角沿层合板的长度方向线性变化,研究含丝束重叠、间隙等制作缺陷的变角度纤维复合材料层合板的屈曲问题.采用ABAQUS有限元软件建立层合板的有限元模型,选用S4壳单元计算四边简支层合板在两端压缩荷载作用下的屈曲临界荷载及屈曲模态,并进行详细的参数分析.研究结果表明:当起始角相同时,含或不含制作缺陷的层合板的屈曲...     

正交铺设层合板的蠕变屈曲分析

研究了正交铺设层合板的蠕变失稳问题。为了更好地模拟实际情况，在单层板的本构关系中，材料各主方向模量的松也时间均取不同值，并在建立控制方程时考虑了横向剪切变形的影响，通过理论分析，得到了粘弹性层合板的瞬时弹性临界载荷和持久临界载荷，并在算例中首次利用时间增量方法得到了有初始度层合板在长期受地的蠕变变表，计算结果表明了持久临界载荷对于粘弹性层合板的具体含义，从而使粘弹性层合板的为屈曲问题有了较为完整的     

Non-linear analysis of functionally graded fiber reinforced composite laminated plates,Part I: Theory and solutions

This paper deals with the large amplitude vibration, non-linear bending and postbuckling of fiber reinforced composite laminated plates resting on an elastic foundation in hygrothermal environments. Two kinds of fiber reinforced laminated plates, namely, uniformly distributed and functionally graded reinforcements, are considered. The material properties of fiber reinforced laminated plates are estimated through a micromechanical model and are assumed to be temperature-dependent and moisture-dependent. The motion equations are based on a higher order shear deformation plate theory that includes plate-foundation interaction and the hygrothermal effect. A two-step perturbation technique is employed to determine the non-linear to linear frequency ratios of plate vibration, the load-deflection and load-bending moment curves of plate bending, and postbuckling equilibrium paths of laminated plates.     

层合析参固支边界条件下的不稳定后屈曲分析

为了深入地研究复合材料层板所独具的后屈曲特性,利用能量变分原理和非线性几何方程建立了具有弹性约束的复合材料层板在面内载荷作用下的非线性稳定性控制方程组,并运用广义傅立叶级数法对其进行求解。重点分析了非对称层板在固支边界条件下的稳定性问题,发现层板在此条件下有可能存在非对称的失稳临界点和不稳定的后屈曲路径,进而构造了简化的物理模型进行解释,指出后屈曲的非对称性是由于结构关于Z轴不对称,而不稳定性是由于固支边界条件阻碍了前屈曲的发生。     

Kármán-type equations for a higher-order shear deformation plate theory and its use in the thermal postbuckling analysis

Kármán-type nonlinear large deflection equations are derived occnrding to the Reddy’s higher-order shear deformation plate theory and used in the thermal postbuckling analysis The effects of initial geometric imperfections of the plate areincluded in the present study which also includes th thermal effects.Simply supported,symmetric cross-ply laminated plates subjected to uniform or nomuniform parabolictemperature distribution are considered. The analysis uses a mixed GalerkinGolerkinperlurbation technique to determine thermal buckling louds and postbucklingequilibrium paths.The effects played by transverse shear deformation plate aspeclraio, total number of plies thermal load ratio and initial geometric imperfections arealso studied.     

Non-linear design and control optimization of composite laminated plates with buckling and postbuckling objectives

Multiobjective design and control optimization of composite laminated plates is presented to minimize the postbuckling dynamic response and maximize the buckling load. The control objective aims at dissipating the postbuckling elastic energy of the laminate with the minimum possible expenditure of control energy using a closed-loop distributed force. The layer thicknesses and fiber orientations are taken as design variables. The objectives of the optimization problem are formulated based on a shear deformation theory including the von-Karman non-linear effect for various cases of boundary conditions. The non-linear control problem is solved iteratively until an appropriate convergence criterion is satisfied based on Liapunov–Bellman theory. Liapunov function is taken as a sum of positive definite functions with different degrees. Comparative examples for three-layer symmetric and four-layer antisymmetric laminates are given for various cases of edges conditions. Graphical study is carried out to assess the accuracy of results obtained due to the successive iterations. The influences of the boundary conditions, orthotropy ratio, shear deformation, aspect ratio on the laminate optimal design are elucidated.     

Thermomechanical postbuckling of unilaterally constrained shear deformable laminated plates with temperature-dependent properties

This paper presents a study on the postbuckling responses of shear deformable laminated plates resting on a tensionless foundation of the Pasternak-type and subjected to combined axial and thermal loads. Two different postbuckling cases are considered, namely (1) the compressive postbuckling of initially heated plates and (2) the thermal postbuckling of initially compressed plates. The postbuckling analysis of laminated plates is based on the higher order shear deformation plate theory with a von Kármán-type of kinematic non-linearity. It is assumed that the foundation reacts in compression only. The thermal effects are also included and the material properties are assumed to be temperature dependent. The initial geometric imperfection of the plates is taken into account. The analysis uses a two-step perturbation technique to determine the postbuckling response of the plates. An iterative scheme is developed to obtain numerical results without using any assumption on the shape of the contact region. Numerical solutions are presented in tabular and graphical forms to study the postbuckling behavior of antisymmetric angle-ply and symmetric cross-ply laminated plates resting on tensionless elastic foundations of the Pasternak-type, from which results for conventional elastic foundations are obtained as comparators. The results reveal that the unilateral constraint has a significant effect on the postbuckling response of the plates subjected to combined axial and thermal loads when the foundation stiffness is sufficiently large. The results also confirm that the postbuckling responses are significantly influenced by temperature dependency and initial membrane stress as well as initial thermal stress.     

Postbuckling of imperfect rectangular composite plates under inplane shear closed-form approximate solutions

In this paper, the postbuckling behavior of rectangular orthotropic laminated composite plates with initial imperfections under inplane shear load is investigated in a closed-form analytical manner. The plates under consideration are assumed to be infinitely long in the longitudinal direction. At the longitudinal edges, two different sets of boundary conditions are considered, specifically 1) simply supported edges and 2) fully clamped edges. Using Timoshenko-type shape functions for both the initial bifurcational buckling analysis and the subsequent Marguerre-type postbuckling studies, closed-form analytical solutions for the buckling loads and for the postbuckling state variables are derived. A comparison with geometrically non-linear finite element computations shows that the derived analysis approaches are suitable for postbuckling studies in load ranges not too far beyond bifurcational buckling as they are currently relevant for e.g., composite airframe structural analysis and design. Due to their strictly closed-form analytical nature, the presented analysis methods can be used conveniently in engineering practice for all application purposes where computational time is a crucial factor, especially for preliminary analysis and design or optimization procedures.     

Influence of corner stresses on the stability characteristics of composite skew plates

Stability characteristics of composite skew plates subjected to in-plane compressive load are investigated here using the shear deformable finite element approach. The influences of high prebuckling stresses at the corner regions of isotropic and composite skew plates on their stability characteristics are emphasized for different load direction, boundary condition and laminate stacking sequence. The non-linear governing equations based on von Kármán's assumptions are solved by Newton-Raphson technique to get the hitherto unreported postbuckling equilibrium paths of composite skew plates loaded between two rigid flat platens. The variation of out-of-plane deformation and end-shortening with compressive in-plane load are examined for simply supported and clamped skew plates made of isotropic, symmetric and unsymmetric laminates. Marguerre's shallow shell theory is employed to study the effect of sinusoidal imperfection on the non-linear behavior of composite skew plates.     

黏弹性结构蠕变屈曲特性的分析

分析了线黏弹性正交铺设层合板的蠕变失稳问题，由相空间的特征方程解出临界载荷，经Laplace数值反演得到屈曲载荷与时间的关系；然后，通过建立扰动模型和分析变形的有界与无界增长，讨论了黏弹性结构延迟失稳的特性，解释了临界载荷与失稳时间的具体含义．