一种正交各向异性板的等效各向同性板计算法

上、下表面平整的正交各向异性板的有效抗扭刚度是2个主方向抗弯刚度的几何平均值. 根据这一特性、从正交各向异性板挠曲面的偏微分方程出发,保持一个主方向尺寸不变,另一主方向的尺寸做线性缩放,保持弹性模量与第一主方向相同,泊松比取2个主方向泊松比的几何平均值,将这类正交各向异性板等效为一块各向同性板;通过分析得到：各向同性板任意点的挠度就是原正交各向异性板对应点的挠度,各对应点内力之间存在简单的比例关系,该文的方法将为工程技术人员提供方便,同时可以更加直观的认识正交各向异性板的受力.     

层合厚板混合状态Hamiltonian动力元及其半解析解

文中在时间方向采用Ｌａｐｌａｃｅ变换，给出了层合厚板动力学问题混合状态Ｈａｍｉｌｔｏｎ正则方程及其半解析法．该方法在层板平面内采用通常的有限元离散，而沿板厚方向采用状态控制方程给出解析解答．在层与层之间采用迁移矩阵法，给出层合板上下表面力学量之间的关系式．利用打靶法得到响应在象空间的一般解，然后再利用拉氏逆变换的数值解求出层合板的瞬时位移场和应力场．     

LARGE AMPLITUDE FREE VIBRATIONS OF LAMINATED COMPOSITE PLATES

This paper deals with large amplitude free flexural vibrations of laminated composite plates using a 9-node Heterosis degenerated isoparametric quadrilateral element, including the effects of transverse shear and rotary inertia. The nonlinear dynamic equations of the plates are formulated in von Karman's sense. Amplitude-frequency relationships are obtained through dynamic response history using the Newmark numerical integration scheme. Detailed numerical results based on various parameters are presented for orthotropic laminated plates with different boundary conditions. The rectangular anti-symmetric cross-ply plates show the softening type of nonlinearity for initial small amplitudes. The displacement amplitudes decrease and nonlinear frequencies increase with the increment of time. Supported by the NNSFC (No. 19672033), the National Key Project on Basic Research and Applied Research (PD9521904) and the Doctoral Training Foundation of Education Commission of China(No. 98000304).     

用无网格局部径向点插值法分析非均质中厚板的弯曲问题

用无网格局部径向点插值法分析了非均质中厚板的弯曲问题.利用虚位移原理推导了中厚板的离散系统方程.采用径向基函数耦合多项式基函数来近似试函数,用四次样条函数作为加权残值公式中的权函数.所构造成的形函数具有Kronecker delta性质,可以很方便地施加本质边界条件.此方法不需要任何形式的网格划分,所有的积分都在规则形状的子域及其边界上进行,是一种真正的无网格方法.在计算过程中,取积分中的高斯点的材料参数来模拟问题域材料特性的变化.算例结果表明这种无网格方法具有效率高、精度高和易于实现等优点.     

THE MIXED STATE HAMILTONIAN DYNAMIC ELEMENT AND A SEMI-ANALYTICAL SOLUTION FOR THE ANALYSIS OF THICK LAMINATED COMPOSITE PLATES

Through introducing the Laplace transformation in the time direction,the mixed state Hamilton canonical equation and a semi-analytical solution arepresented for analyzing the dynamic response of laminated composite plates.Thismethod accounts for the separation of variables,the finite element discretization can beemployed in the plane of laminar,and the exact solution in the thickness direction isderived by the state space control method.To apply the transfer matrix method,therelational expression at the top and bottom surface is established.So the generalsolution in transformation space is deduced by the spot method.By the application ofinversion of Laplace transformation,the transient displacements and stresses can bederived.     

NUMERICAL ANALYSIS OF MINDLIN SHELL BY MESHLESS LOCAL PETROV-GALERKIN METHOD

The objectives of this study are to employ the meshless local Petrov-Galerkin method （MLPGM） to solve three-dimensional shell problems. The computational accuracy of MLPGM for shell problems is affected by many factors, including the dimension of compact support domain, the dimension of quadrture domain, the number of integral cells and the number of Gauss points. These factors＇ sensitivity analysis is to adopt the Taguchi experimental design technology and point out the dimension of the quadrature domain with the largest influence on the computational accuracy of the present MLPGM for shells and give out the optimum combination of these factors. A few examples are given to verify the reliability and good convergence of MLPGM for shell problems compared to the theoretical or the finite element results.     

h-ADAPTIVE ANALYSIS BASED ON MESHLESS LOCAL PETROV-G ALERKIN METHOD WITH B SPLINE WAVELET FOR PLATES AND SHELLS

Using the two-scale decomposition technique, the h-adaptive meshless local Petrov- Galerkin method for solving Mindlin plate and shell problems is presented. The scaling functions of B spline wavelet are employed as the basis of the moving least square method to construct the meshless interpolation function. Multi-resolution analysis is used to decompose the field variables into high and low scales and the high scale component can commonly represent the gradient of the solution according to inherent characteristics of wavelets. The high scale component in the present method can directly detect high gradient regions of the field variables. The developed adaptive refinement scheme has been applied to simulate actual examples, and the effectiveness of the present adaptive refinement scheme has been verified.     

复合曲梁中剪应力和径向应力的研究

文献［郾］讨论了复合曲梁在弯曲时的正应力问题，在此基础上，本文进一步导出了其剪应力和径向应力的计算公式，从而使复合曲梁的应力问题全部得到解决，作为特例，也可以从上述公式得到单层匀质曲梁的的相应公式，最后给出计算实例。     

复合材料非对称层板的横向变形特性分析

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．通过运用广义傅立叶级数法对控制方程组进行求解，得到了相应的载荷 中心挠度曲线，并重点分析了非对称层板在面内载荷作用下的变形特性．     

基于减基法的层合板瞬态响应快速分析方法

用混合数值法分析复合材料层合板结构的瞬态响应时,在波数域中引入减基法、构造减基空间,把原大型特征值问题映射到减基空间进行降阶,在保证精度的前提下快速近似求解原大型特征值问题,从而快速得到结构的时域响应. 算例表明,引入减基法后的混合数值法能更有效地解决结构瞬态响应问题. 该方法可以推广用于快速解决大型结构动力优化设计和结构动力反问题等结构动力分析问题.      

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.     

复合材料加筋板连接剪切性能试验模拟

建立了带泡沫加筋的复合材料层合板连接件及试验夹具模型,用MSC.Nastran进行非线性有限元分析,模拟加筋层合板剪切性能试验,分析试验件过渡段和夹具刚度参数对剪切试验结果的影响,结果表明,考核区的应力随着夹具刚度及过渡段铺层的增加而减小,当夹具钢片厚度增大到15mm,过渡段铺层增加到考核区铺层的7倍时,考核区应力值较为稳定,可以作为工程试验夹具及过渡段设计的参考.     

FREE VIBRATION ANALYSIS OF ARBITRARY SHAPED PLATES BY BOUNDARY KNOT METHOD

The boundary knot method （BKM） is a truly meshless boundary-type radial basis function （RBF） collocation scheme, where the general solution is employed instead of the fundamental solution to avoid the fictitious outside boundary of the physical domain of interest. In this study, the BKM is first used to calculate the free vibration of free and simply-upported thin plates. Compared with the analytical solution and ANSYS （a commercial FEM code） results, the present BKM is highly accurate and fast convergent.     

预应力条件下轴对称圆板的响应解

本文研究预应力条件下轴对称简支和固支圆板的瞬态响应,利用振型展开和Laplace变换给出解析表达式,提出简化型圆板的边界条件,利用Hankel变换和Laplace变换给出简捷的解,针对几种边界状态,比较了其频率和响应,同时讨论了几种常见的瞬态载荷的结构响应形式。     

含分层损伤复合材料层合板的压缩强度研究

给出了基于一阶剪切变形理论的含分层损伤层合板有限元分析模型,将含分层损伤层合板在压缩载荷作用下的强度破坏分析和屈曲破坏分析统一起来,先区分其破坏形式,然后再进行具体破坏分析.在屈曲特性分析中考虑了铺层强度破坏引起的刚度折减的影响.数值结果表明, 该文给出的方法和结论对含分层损伤复合材料层合板的设计更具参考价值.     

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基于形状记忆合金Brinson一维热力学本构关系和von K\'{a}rm\'{a}n几何非线性薄板理论,研究了径向嵌入SMA丝复合材料加热圆板在横向均布 机械载荷作用下的弯曲响应, 获得了周边不可移简支和夹紧圆板的中心最大挠度与升温之间的关系曲线. 结果表明,形状 记忆合金丝在从马氏体向奥氏体的逆相变过程中所产生的相变回复力对板的弯曲变形具有明 显的调整作用. 通过嵌入SMA纤维丝和施加升温载荷可以主动而有效地调节受机 械载荷作用圆板的弯曲变形.     

薄板弯曲问题的复合傅里叶级数方法

解析方法与数值方法有效融合是提高计算效能的重要途径．提出薄板弯曲问题的复合傅里叶级数方法．它以解析方法为融合基体,数值方法为融合增强相,是一种新的融合模式．在这种新的融合模式中,傅里叶级数解析解作为变形场的连续表现形式,摆脱了载荷形式和边界条件的强烈依赖性,表现出良好的收敛性态．     

Winkler地基上厚板分析的自然单元法

以自然单元法中自然邻接点的Laplace插值形函数为基础,基于Mindlin厚板理论,建立了Winkler地基上厚板弯曲挠度的自然单元法求解控制方程,并进行了相应的程序实现,最后通过算例分析,表明了该文方法的可行性和有效性.     

中厚板的耦合多项式基径向点插值无网格法

采用Mindlin平板理论,通过最小位能原理建立了各向同性中厚板的伽辽金整体弱式方程,形函数采用耦合多项式基的径向点插值法构造,可以直接施加本质边界条件. 算例表明,用耦合多项式基的径向点插值无网格法分析中厚板问题,具有效率高、精度高和易于实现等优点,可以避免薄板弯曲时的剪切自锁现象.     

TRANSIENT RESPONSE OF A BI-LAYERED MULTIFERROIC COMPOSITE PLATE

In this paper,a three-dimensional finite-element formulation for the multiferroic composite is developed and implemented into the commercial software ABAQUS for its transient analysis.First,a special three-dimensional eight-node solid element is designed to handle the multiferroic composite made of elastic,piezoelectric,and piezomagnetic materials.Second,a userdefined subroutine for this newly developed element is implemented into ABAQUS.Finally,the transient responses of a bi-layered multiferroic composite are calculated by using the direct time integration method.Two typical magnetic potential signals,Gauss and Ricker pulses,are applied to the composite with various time durations of excitation.The induced electric field shows that the transient response can be substantially influenced by the input signal,which could be tuned for the strongest electric output.