板结构计算模型的新发展

现代复合材料层合板具有高强和轻型的突出优点,从而在军工和民用等诸多领域发挥着重要作用。这种板结构的特点是随着纤维走向的不同,层间材料的物理-力学特性发生剧烈变化。沿板厚方向变形的梯度比较陡峭,并在层间结合面处发生强不连续,呈现zig-zag （锯齿状）现象。这导致横向剪应变在板的静态和动态响应中发生重要作用,不计横向变形的经典组合板计算模型CLPT难以适应现代多层板计算分析的需要。考虑横向剪切变形影响的板的计算模型得到重视和发展。需要指出,现有各种考虑剪切变形影响的计算模型虽然有了很大的发展,但在全面和准确性上仍然存在一定的不足,难以适应现代多层组合板横向力和物理性能多变的情况。模型预测的沿板厚方向位移和应力的变化规律难以通过严格的检验。本文提出的以比例边界有限元为基础的正交各向异性板的数值计算模型,同时可适用于各种薄板与厚板的分析,对现代复合材料层合板的分析具有特殊的优越性。所得到的板的位移、正应力和剪应力沿板厚方向的变化,与三维弹性理论的标准解高度吻合。数值算例进一步表明,随着层间纤维走向的变化,板内位移场和应力场沿板厚方向剧烈变化所呈现的锯齿现象均可以精准地进行模拟。据此,本文建议方法对现代板分析的广泛适应性和高度准确性得到了充分论证。     

横向磁场激励下铁磁梁式板的混沌运动分析

在磁体力分布的磁弹性理论模型和磁场准静态假定模式基础上，对于处在周期时变磁场 中的不可移简支铁磁梁式板非线性磁弹性动力特性进行定性与定量分析．首先利用磁场的摄 动技术和结构变形的模态法，导出了关于模态坐标的非线性动力方程；然后利用Ｍｅｌｎｉｋｏｖ方 法，从理论上给出这一磁弹性动力系统可能出现混沌运动的必要条件及参数范围；最后采用变 步长Ｒｕｎｇｅ－Ｋｕｔｔａ数值积分方法对其磁弹性相互作用的混沌现象进行了定量搜索与模拟，并 利用其轨迹的Ｐｏｉｎｃａｒｅ截面图与Ｌｉａｐｕｎｏｖ指数加以判断．结果表明磁弹性简支梁式板在横 向周期时变磁场中存在混沌吸引子，且在机械阻尼很小时其混沌吸引子表现出稠的特性．     

正交各向异性厚板的边界元解法

本文利用 Hormander 算子法和平面波分解法导出了计入剪切变形的正交各向异性厚板的基本解。建立了计入剪切变形的正交各向异性厚板的边界积分方程。文中详细地讨论了基本解的数值计算,并用边界元法分析了一些算例。     

磁驱动飞片的一维磁流体动力学数值研究

磁驱动高速飞片技术是近年来发展的一种新型实验技术,在冲击波物理领域得到应用。该过程伴随着磁场扩散,并由此引起焦耳加热,使得飞片加载面的相状态发生变化,这决定了飞片厚度的范围。基于拉格朗日坐标系,利用磁流体动力学方程组、电阻率方程和状态方程数据库,对磁驱动铝飞片进行了一维磁流体动力学数值计算,获得了不同时刻铝飞片密度、温度的剖面分布,得到了磁场扩散速率随加载电流密度的变化关系。文章所选取的电导率方程只考虑到汽化点为止,对于等离子体形成的过程无法描述,如果要精确描述更高电流密度下的驱动过程,需考虑更为普适的电导率方程。磁场扩散速率随加载电流密度的变化存在转折点,在转折点前后可分别用两个线性关系表达式加以刻画。利用这些关系和冲击波物理相关知识,对磁压加载等熵驱动飞片实验样品厚度的选择进行了研究。     

Exploring the Origin of Maximum Entropy States Relevant to Resonant Modes in Modern Chladni Plates

The resonant modes generated from the modern Chladni experiment are systematically confirmed to intimately correspond to the maximum entropy states obtained from the inhomogeneous Helmholtz equation for the square and equilateral triangle plates. To investigate the origin of maximum entropy states, the inhomogeneous Helmholtz equation is modified to consider the point interaction coming from the driving oscillator. The coupling strength associated with the point interaction is characterized by a dimensionless factor α. The δ potential of the point interaction is numerically modelled by a truncated basis with an upper index N. The asymptotic behavior for the upper index N is thoroughly explored to verify that the coupling strength of α = 1.0 can make the theoretical resonant modes agree excellently with the maximum entropy states as N→∞. It is further authenticated that nearly the same resonant modes can be obtained by using a larger coupling strength α when a smaller upper index N is exploited in the calculation.     

Quantification of midazolam,morphine and metabolites in plasma using 96‐well solid‐phase extraction and ultra‐performance liquid chromatography–tandem mass spectrometry

Currently, pharmacokinetic–pharmacodynamic studies of sedatives and analgesics are performed in neonates and children to find suitable dose regimens. As a result, sensitive assays using only small volumes of blood are necessary to determine drug and metabolite concentrations. We developed an ultra‐performance liquid chromatographic method with tandem mass spectrometry detection for quantification of midazolam, 1‐hydroxymidazolam, hydroxymidazolamglucuronide, morphine, morphine‐3‐glucuronide and morphine‐6‐glucuronide in 100 μL of plasma. Cleanup consisted of 96 wells micro‐solid phase extraction, before reversed‐phase chromatographic separation (ultra‐performance liquid chromatography) and selective detection using electrospray ionization tandem mass spectrometry. Separate solid‐phase extraction methods were necessary to quantify morphine, midazolam and their metabolites because of each group's physicochemical properties. Standard curves were linear over a large dynamic range with adequate limits of quantitation. Intra‐ and interrun accuracy and precision were within 85–115% (of nominal concentration using a fresh calibration curve) and 15% (coefficient of variation, CV) respectively. Recoveries were >80% for all analytes, with interbatch CVs (as a measure of matrix effects) of less than 15% over six batches of plasma. Stability in plasma and extracts was sufficient, allowing large autosampler loads. Runtime was 3.00 min per sample for each method. The combination of 96‐well micro‐SPE and UPLC‐MS/MS allows reliable quantification of morphine, midazolam and their major metabolites in 100 μL of plasma. Copyright © 2010 John Wiley & Sons, Ltd.     

An asymptotic Reissner–Mindlin plate model

A mathematical study via variational convergence of a periodic distribution of classical linearly elastic thin plates softly abutted together shows that it is not necessary to use a different continuum model nor to make constitutive symmetry hypothesis as starting points to deduce the Reissner–Mindlin plate model.     

Three-dimensional analytical solution for a transversely isotropic functionally graded piezoelectric circular plate subject to a uniform electric potential difference

This paper studies the problem of a functionally graded piezoelectric circular plate subjected to a uniform electric potential difference between the upper and lower surfaces. By assuming the generalized displacements in appropriate forms, five differential equations governing the generalized displacement functions are derived from the equilibrium equations. These displacement functions are then obtained in an explicit form, which still involve four undetermined integral constants, through a step-by-step integration which properly incorporates the boundary conditions at the upper and lower surfaces. The boundary conditions at the cylindrical surface are then used to determine the integral constants. Hence, three-dimensional analytical solutions for electrically loaded functionally graded piezoelectric circular plates with free or simply-supported edge are completely determined. These solutions can account for an arbitrary material variation along the thickness, and thus can be readily degenerated into those for a homogenous plate. A numerical example is finally given to show the validity of the analysis, and the effect of material inhomogeneity on the elastic and electric fields is discussed. Supported by the National Natural Science Foundation of China (Grant Nos. 10472102 and 10432030) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20060335107)     

Nonaxisymmetric thermal stress state of laminated rotational bodies of orthotropic materials under nonisothermic loading

A procedure for numerical investigation of nonaxisymmetric temperature fields and the elastic stress-strain state of laminated rotational bodies of cylindrically and rectilinearly orthotropic materials under nonisothermal loading is proposed. The deformation of orthotropic materials is described by the equations of anisotropic elasticity theory. The equations of state are written in the form of Hookes law for homogeneous materials, with additional terms which take into account the thermal deformation, changes in the mechanical properties of materials in the circumferential direction, and their dependence on temperature. A semianalytic finite-element method in combination with the method of successive approximations is used. An algorithm for numerical solution of the corresponding nonlinear boundary problem is elaborated, which is realized as a package of applied FORTRAN programs. Some numerical results are presented.Translated from Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 731–752, November–December, 2004.     

Dynamic Behavior of Rigid–Plastic Sector Plates

The paper studies the dynamic behavior of perfect rigid-plastic plates in the form of a sector with hinged or clamped sides under short-term intensive loads. Two dynamic deformation mechanisms are demonstrated. The dynamic equation is derived for each of the mechanisms. The realization conditions for the mechanisms are analyzed. Analytical expressions are derived for the ultimate (high) loads and the maximum residual deflection. Numerical examples are given