固支加筋方板的大挠度塑性动力响应

本文详细分析了爆炸载荷作用下固支回筋方板的大挠度塑性动力响应，给出了各种可能的运动模拟以及相应的差别条件，导出了最大残余变形的计算式，与文献［３］的试验结果比较表明，在多数情况下符合良好。     

Large deflection dynamic plastic response of clamped square plates with stiffeners

The large deflection dynamic plastic response of fully clamped square plates with stiffeners under blast load is analyzed in detail in this paper. Various relevant motion patterns and criterions are presented. The formulas of maximum permanent deformation of the plates with stiffeners are derived. The results of. calculation are compared with those of experiment in [3], with good agreement shown in most cases.     

Free vibration analysis of stiffened laminated plates

Based on the semi-analytical solution of the state-vector equation theory, a novel mathematical model for free vibration analysis of stiffened laminated plates is developed by separate consideration of plate and stiffeners. The method accounts for the compatibility of displacements and stresses on the interface between the plate and stiffeners, the transverse shear deformation, and naturally the rotary inertia of the plate and stiffeners. Meanwhile, there is no restriction on the thickness of plate and the height of stiffeners. To demonstrate the excellent predictive capability of the model, several examples are analyzed numerically. The model presented in this paper can also be easily modified to solve the problems of stiffened piezolaminated plates and shells, or plates and shells with piezoelectric material patches.     

剪切载荷下肋板的屈曲分析与优化

利用ANSYS有限元方法分析了一系列的肋板,研究了加强肋的作用,提出了 优化肋设计的限制条件. 结果表明,由横向肋板产生的栅格数目不能小于肋板的长宽比. 换 句话说,横向加强肋必须把平板的长度划分为小于等于宽度的段. 结果还显示,加强肋的优 化几何特性与板的屈曲从整体模态到局部模态转变点相应. 而且,所有具有相似长宽比和肋 数的肋板,具有一个特定的比值$EI_{s}/aD$, 此时抗剪应力最佳.     

复合材料正交加筋板在横向载荷下挠度计算的半解析法

本文采用一种新的半解析法,即独特利用Heaviside函数建立与加筋板等效的变刚度模型来开展复合材料双向正交加筋板在横向载荷下的弯曲挠度分析．此模型可以准确地描述筋条在板面上的分布,以及由于筋条的存在而导致的板面刚度不均匀分布．使用Galerkin加权残值法求解该模型的控制方程,得到不同边界条件和载荷情况下的级数解．对于双向正交加筋板,将此半解析法的结果与传统均匀化方法和使用商业有限元软件ABAQUS建立的有限元模型所得到的弯曲挠度结果比较,验证了此方法的准确性和优越性．不同于传统均匀化方法,本双向正交加筋板的弯曲挠度半解析法可精确、有效地获取加筋间的局部弯曲挠度,可以促进复合材料结构的设计分析与优化的研究进展．     

Design of a Structure Composed of a Plate Strengthened by Equidistant Stiffeners

ABSTRACT

An alternative method to the orthotropic plate analogy for analysis of plates strengthened by longitudinal equidistant stiffeners is introduced and is shown to give accurate results, compared with the finite element method. The alternative method uses the concept of undetermined multipliers. Its capabilities in the study of plates strengthened by stiffeners is demonstrated, and design criteria are obtained.     

弹性体的正则方程和加筋板的固有频率分析

应用弹性力学的Hamilton正则方程理论和其半解析法，为整体加筋板的固有频率分析提出了一种新颖的数学模型. 采用同一种平面元素离散板和加强筋，并分别建立板和加强筋的线性方程组. 考虑到板和加强筋连接界面上应力和位移的连续性，联立板和加强筋的方程得到全结构的方程组和求解固有频率的特征方程. 主要优越性表现为：结构的旋转惯性、剪切变形等都得到了考虑，且不限制结构的板厚度和加强筋的高度. 多个数值实例的收敛分析和结果证明了方法是可靠的. 该方法很容易被修改用来分析加筋壳、加筋压电材料层合板或带有压电材料传感器和驱动器块的板壳问题.     

对实心弹性薄板优化的进一步讨论

回顾了实心弹性薄板优化研究的发展历程。给出了由无限密和无限细的肋骨加强的环板在常肋骨密度时的解析解；采用精确刚度阵的有限元法计算了具有有限根肋骨加强的板的柔顺性，它低于光滑优化解的柔顺性。这些结果进一步说明近期文献中出现的枕头形的光滑解并不是几何受约束实心弹性薄板优化问题的全局最优解。     

具有分层损伤的不同加筋形式复合材料层合板的后屈曲性态研究

基于板的一阶剪切理论和V on-K arm an大挠度理论,分别推导了复合材料层合板和层合梁的几何非线性有限元列式,提出了含嵌入分层的复合材料加筋层合板在受压缩载荷作用下的后屈曲有限元分析方法,对在板厚方向具有不同分层位置的加筋板结构进行了有限元数值分析,研究了不同的加筋方式及筋的分布对具有分层损伤的复合材料加筋层合板的后屈曲性态的影响,所得结果对确定在压缩载荷作用下含损伤复合材料加筋层合板的剩余承载能力具有参考价值。     

加筋板弹性大挠度的冲击响应分析

用半解析的方法分析了横向冲击载荷下加筋板的非线性瞬态响应。考虑膜力的存在 ,忽略筋截面上的剪切应力 ,引入板的应力函数 ,采用离散加筋板模型 ,运用能量原理建立加筋板的动响应控制方程。假设挠度为双级数形式 ,运用迦辽金法 ,将加筋板的动响应方程转化为一个多自由度的动力系统 ,采用数值方法来求解。最后给出了几个模型的计算结果。     

基于水平集法的薄板加强筋分布优化理论研究

基于水平集方法,提出薄板加强筋分布的拓扑优化理论。采用Kirchhoff板单元,通过刚度等效,分别使用不同的抗弯刚度表征薄板与加强筋,继而通过水平集方法描述加强筋的布局并进行加强筋分布拓扑优化。以最小柔顺度为设计目标,进行了几种典型载荷下加筋板结构的加筋分布优化设计,通过与变密度方法（SIMP）结果以及现有文献设计结果进行对比,验证了本文提出的加强筋分布拓扑优化理论。结果显示,本文方法能够避免灰度单元,获得清晰的加强筋优化布局和尺寸。     

正交各向异性加筋板屈曲分析方法研究

为简化正交各向异性加筋板屈曲分析,本文将筋条位移场用其所在位置的板的位移表达,建立加筋板总势能,通过离散位移场,利用最小势能原理,推导出基于里兹法的正交各向异性加筋板屈曲分析控制方程,采用Matlab进行求解.基于本文推导的方程对单筋和三筋加筋板在不同压剪比下的屈曲荷载和模态进行分析,得到与Abaqus基本一致的结果....     

四边固定加劲板的非线性自由振动

针对工程中常用的加劲板, 研究了非线性振动的求解方法与振动特性. 将加劲板分为板与加劲肋两个部分考虑, 其中板视为考虑几何非线性的大挠度板, 加劲肋视为Euler梁. 假定加劲板的位移, 利用Lagrange方程结合系统能量和振型叠加推导了加劲板的动力平衡方程. 运用椭圆函数及摄动法计算加劲板非线性振动的单模态解, 多模态解则通过增量迭代法进行求解. 最后, 结合有限元软件ANSYS对一个四边固定且不可移动的加劲板进行分析, 讨论解的收敛性, 并分析两个方向设置不同数量加劲肋的情况下非线性自振频率与振幅的关系, 得到了一些加劲板非线性振动特性.      

Linear and nonlinear analysis of stiffened plates

An analysis is presented for the large deflection of clamped laterally loaded skew plates with stiffeners parallel to the skew directions. The governing nonlinear differential equations are derived taking into account the eccentricity of the stiffeners. A numerical procedure involving the use of integral equations of beams and the Newton-Raphson method is employed to get the solution. Numerical work has been done. The effect of variation of skew angle and size of stiffener on the behaviour of the stiffened skew plate has been studied.     

Constructal design method dealing with stiffened plates and symmetry boundaries

A new computational procedure for modelling the structural behavior of stiffened plates with symmetry boundary conditions is here presented. It uses two-dimensional finite elements as a way to decrease computational time without losing precision thanks to a relatively small number of elements applied for analyzing out-of-plane displacements (deflections) and stresses. Adding, the constructal design method was included in the procedure, together with the exhaustive search technique, with the scope to optimize the stress/strain status of stiffened plates by design changes. For the purpose, a reference plate without stiffeners was initially design and used as starting point. Part of the volume was reshaped into stiffeners: thickness was reduced maintaining unchanged weight, length and width. The main goal was to minimize strains and stresses by geometric changes. Results demonstrated that, thanks to this design procedure, it is always possible to find an adequate geometry transformation from reference plate into stiffeners, allowing significant improvements in mechanical behavior.     

Concurrent topology optimization design of stiffener layout and cross-section for thin-walled structures

Acta Mechanica Sinica - Stiffened plates or shells are widely used in engineering structures as primary or secondary load-bearing components. How to design the layout and sizes of the stiffeners is...     

复合材料层合加肋板中的瞬态波传播

研究复合材料加肋层合板结构受冲击载荷作用下的瞬态波传播.加肋层合板模型被处理成层合板的弯曲运动与层合梁的扭转与弯曲运动的耦合连续模型.通过Laplace变换,并采用回传射线矩阵法(MRRM),基于一阶剪切变形层合板理论,确定复合材料加肋层合板结构中传播的各条射线群.采用FFT变换,计算各种冲击载荷作用下加肋层合板结构的短时瞬态响应,并分析讨论脉冲类型对加肋层合板结构短时瞬态响应的影响.     

Dynamic buckling of stiffened plates under fluid-solid impact load

A simple solution of the dynamic buckling of stiffened plates under fluid-solid impact loading is presented. Based on large deflection theory, a discretely stiffened plate model has been used. The tangential stresses of stiffeners and in-plane displacement are neglected. Applying the Hamilton‘ s principle, the motion equations of stiffened plates are obtained. The deflection of the plate is taken as Fourier series, and using Galerkin method, the discrete equations can be deduced, which can be solved easily by Runge-Kutta method. The dynamic buckling loads of the stiffened plates are obtained from Budiansky-Roth ( B-R ) curves.     

受面内冲击载荷下加筋板的非线性动态屈曲

分析了受面内冲击载荷下加筋板的非线性弹性动态屈曲．考虑板与筋的膜力，忽略面内位移，运用Hamilton变分原理，得出非线性控制方程，采用双级数形式的挠度假设，由Galerkin方法得到离散方程组，根据B-R准则，判断加筋板的动态屈曲．     

Study on failure process of delaminated stiffened composite plates under compression

Failure behavior of the delaminated stiffened composite plates under compression is studied by the finite element method, based on a Global-Local variational model. A virtual crack closure technique and a self-adaptive grid moving scheme are proposed to predict the delamination growth process. The contact effect along the delamination front is considered. The numerical results show that the influences of the distribution and location of the stiffeners, the configuration and size of the delamination, the boundary condition and the contact upon the failure behavior of the plates are significant. The project supported by the National Natural Science Foundation of China (59975014)