复合材料层合板振动的边界元法

本文用边界元法分析了复合材料特殊正交各向异性层合板的振动.为了克服在用边界元法求解正交各向异性层合板振动时寻求相应的基本解的困难,本文采用了傅立叶级数形式的近似基本解.算例说明了近似基本解方法的可行性和有效性.      

正交各向异性平面问题边界元素法研究

边界元素法是近年来受到国内外广泛重视并得到迅速发展的一种计算方法。本文系统地研究了正交各向异性平面问题边界元素法的有关基本问题,包括基本解,C矩阵、G_ii矩阵和域内应力的表达式等,并在此基础上建立了常值边界元素和线性边界元素的计算公式。所述理论和公式适用于各类边值问题。最后,按本文所述理论和公式计算了含孔正交各向异性板的应力,数值结果与解析解相符甚好。      

正交各向异性孔板的材料参数识别

结合优化技术和边界元分析,针对正交各向异性孔板进行了材料参数的识别。材料参数识别的问题转化为极小化目标函数的问题,其中目标函数定义为测量位移与边界元计算相应的位移之差的平方和。采用Levenberg-Marquardt方法解极小化目标函数的问题,其中灵敏度的计算是基于离散的边界元代数矩阵方程对识别材料参数的求导。数值算例中,首先把边界元计算正交各向异性圆孔方板位移的结果与解析解进行比较,两者符合良好;然后采用本文提出的方法识别正交各向异性圆孔方板的材料参数。数值算例表明本文提出的方法是有效的。     

轴向极化的层合压电圆柱壳的自由振动

从轴向极化的三维圆柱型正交各向异性压电弹性力学基本方程出发,建立了状态方程。采用细分近似方法,得到了状态变量解。分析了两端简支的层合压电圆柱壳的自由振动问题,给出了频率方程的精确形式,并作了具体计算。     

正交各向异性厚板振动分析的边界积分方程法

本文采用正交各向异性厚板静力问题的基本解作为边界积分方程的核函数,利用加权残数法建立了正交各向异性厚板振动分析的边界积分方程。文中详细地讨论了边界积分方程的数值处理过程并给出了若干数值算例以论证本文方法的正确性。      

正交各向异性板剪切屈曲载荷的近似表达式研究

利用Rayleigh-Ritz法和通用有限元程序ANSYS分析了纵向边被转动弹簧或扭转加劲肋约束的正交各向异性长板的临界屈曲问题, 引入无量纲正交各向异性参数、约束系数和临界屈曲系数, 利用曲线拟合技术, 得到了这两类约束板在均匀剪力作用下的临界屈曲载荷近似解公式;利用临界纵横比, 把求得的针对转动弹簧约束的临界屈曲解应用到扭转加劲肋约束板的临界屈曲解中, 同样得到了扭转加劲肋约束板的临界屈曲载荷。将求得的近似表达式与有限元ANSYS数值解以及文献中的结果进行对比, 结果吻合良好。     

几类薄板弯曲问题边界元迭代求解的统一格式

弹性地基板、具有初曲率板及变厚度板弯曲问题的控制微分方程较复杂,直接求解问题基本解建立边界积分方程较为困难。本文通过引入等效荷载,将此类问题的控制策分方程化为与普通板弯曲基本方程相同的形式,利用求解一般板弯曲问题的边界元法迭代求解,建立了分析这几类薄板弯曲问题的统一边界元方法。     

纤维增强复合材料层合板屈曲性态分析的边界元法

本文用边界元法分析了纤维增强复合材料正交各向异性层合板的屈曲性态。为了克服在用边界元法求解正交各向异性层合板屈曲时寻求相应的基本解的困维,本文采用了双重傅立叶级数和引用等效荷载的概念,建立了层合板屈曲临界荷载的特征方程。算例说明了本文方法的可行性和有效性。      

弹性地基上正交各向异性自由矩形板的弯曲

本文运用文所建立的方法,研究Winkler弹性地基上正交各向异性自由矩形板弯曲问题的精确解。以受集中载荷作用的板为例,给出不同弹性系数地基上板的位移和弯矩的数字计算结果。     

二维正交各向异性结构弹塑性问题的边界元分析

给出了二维正交各向异性结构弹塑性问题的边界元分析方法, 包括相应边界积分方程、内点应力公式、边界元求解格式以及弹塑性应力计算方法。在弹塑性分析中, 引入了Hill-Tsai 屈服准则, 采用初应力法和切向预测径向返回法确定实际应力状态。通过具体算例分析了二维正交各向异性结构的弹塑性应力和塑性区分布情况, 部分数值结果与已有结果进行了比较, 两者基本吻合。结果表明, 本文中给出的边界元法可以有效地用于求解二维正交各向异性结构的弹塑性问题。      

矩形弹性中厚板的短梁函数解法

本文给出承受均布载荷和集中载荷作用的短梁的梁函数。应用梁函数构造矩形中厚板的基函数系。应用最小势能原理可以求得承受任意载荷作用的矩形弹性中厚板弯曲问题的多项式近似解。计算结果表明精度较高。当板的剪切刚度C→∞时,本文结果与结果相一致。     

基于Kriging代理模型的拉压不同模量平面问题的近似求解

该文建议采用Kriging代理模型数值求解拉压不同模量平面问题。通过本构方程光滑化、有限元法及拉丁超立方采样技术,对拉压不同模量桁架与二维平面问题,给出了基于Kriging模型的近似数值解,以代理基于有限元的数值解,并探讨了样本点数目和问题规模对所建Kriging近似模型求解精度/效率的影响。数值算例表明:所提方法可为求解拉压不同模量平面问题提供精度合理的近似数值解。当问题规模较大且正问题需要多次求解时,该方法有望显著减少计算时间,这对于降低拉压不同模量反问题与优化问题的计算开销十分重要。     

Generalized Kelvin solution based boundary element method for crack problems in multilayered solids

This paper presents a new boundary element method (BEM) for linear elastic fracture mechanics in three-dimensional multilayered solids. The BEM is based on a generalized Kelvin solution. The generalized Kelvin solution is the fundamental singular solution for a multilayered elastic solid subject to point concentrated body-forces. For solving three-dimensional elastic crack problems in a finite region, a multi-region method is also employed in the present BEM. For crack problems in an infinite space, a large finite body is used to approximate the infinite body. In addition, eight-node traction-singular boundary elements are used in representing the displacements and tractions in the vicinity of a crack front. The incorporation of the generalized Kelvin solution into the boundary integral formulation has the advantages in elimination of the element discretization at the interfaces of different elastic layers. Three numerical examples are presented to illustrate the proposed method for the calculation of stress intensity factors for cracks in layered solids. The results obtained using the proposed method are well compared with the existing results available in the relevant literature.     

A numerical method for unilateral problems

Variational inequalities connected with Signorini's problem have appeared as a natural generalization of the minimum potential-energy theorem for bodies with unilateral constraints. In this paper, we describe numerical experience on the use of variational inequalities and Pade approximants to obtain approximate solutions to a class of unilateral boundary value problems of elasticity, like those describing the equilibrium configuration of an elastic membrane stretched over an elastic obstacle. These problems have the peculiar feature of being alternatively formulated as nonlinear boundary value problems without constraints for which the technique of Pade approximants can be successfully employed. The variational inequality formulation is used to discuss the problem of uniqueness and existence of the solution.     

Transient non-linear simulation with component mode synthesis

A method is presented to incorporate non-linear material behavior in a transient simulation with component mode synthesis reduction. This method is used in conjunction with rigid body solution techniques to expand the useful range of rigid body design tools for the development of complex mechanisms. A fixed interface component mode synthesis technique is enhanced with an algorithm to approximate the effect of plastic deformation during a dynamic simulation. The plastic strain is determined from the elastic modal response using classical plasticity theory and applied to the modal solution by projecting an effective nodal force vector on the modal coordinates to induce the necessary plastic deformation. This method can be used during the design process to approximate the non-linear dynamic response of complex mechanisms and offer significant computational savings over a full fidelity, non-linear dynamic solution.     

An integral equation method for non-self-adjoint eigenvalue problems and its applications to non-conservative stability problems

The aim of the work reported in this paper is to present the new formulation of the integral equation method for non-self-adjoint problems and to apply the method to stability problems of elastic continua subjected to non-conservative loadings. A general non-self-adjoint eigenvalue problem stated in terms of differential operators is transformed into a set of coupled integral equations. Our derivation of integral equations is based on an inverse formulation of a canonical form for the original problem and the corresponding fundamental solution pair. Three well-known non-conservative stability problems in elasticity are examined by this integral equation method as illustrative examples. The approximate values of the critical parameters of sample problems demonstrate a sufficient accuracy through a comparison of other values.     

Nonlinear vibration and postbuckling of orthotropic thin annular plates

This paper presents an approximate analytical solution of the geometrically nonlinear elastic axisymmetric response of polar orthotropic thin annular plates. Plates with outer edges elastically restrained against rotation and inplane displacement and with unsupported inner edges are considered. Von Kármán type equations are employed. The deflection is approximated by a one term mode shape satisfying the boundary conditions. Galerkin's method is used to obtain Duffing's equation for the deflection at the inner edge. Nonlinear frequencies, postbuckling response, static response and maximum deflection response under a step load are obtained. It is shown that good engineering accuracy is achieved by the approximate method.     

Cubic splines collocation methods for unilateral problems

Variational inequalities theory not only provides us a general unified frame work for study many unrelated moving and free boundary vary problems, but also gives more efficient numerical methods for solving them. In this paper, we describe numerical experience on the use of variational inequalities and cubic splines collocation technique to obtain approximate solution to a class of unilateral boundary value problems of elasticity, like those describing the equilbrium configuration of an elastic string stretched over an elastic obstacle. The variational inequality formulation is used to discuss the problem of uniqueness and existence of the solution of the unilateral problems.     

Design-point excitation for non-linear random vibrations

It has been shown in recent years that certain non-linear random vibration problems can be solved by well established methods of time-invariant structural reliability, such as FORM and importance sampling. A key step in this approach is finding the design-point excitation, which is that realization of the input process that is most likely to give rise to the event of interest. It is shown in this paper that for a non-linear, elastic single-degree-of-freedom oscillator subjected to white noise, the design-point excitation is identical to the excitation that generates the mirror image of the free-vibration response when the oscillator is released from a target threshold. This allows determining the design-point excitation with a single non-linear dynamic analysis. With a slight modification, this idea is extended to non-white and non-stationary excitations and to hysteretic oscillators. In these cases, an approximate solution of the design-point excitation is obtained, which, if necessary, can be used as a ‘warm’ starting point to find the exact design point using an iterative optimization algorithm. The paper also offers a simple method for computing the mean out-crossing rate of a response process. Several examples are provided to demonstrate the application and accuracy of the proposed methods. The methods proposed in this paper enhance the feasibility of approximately solving non-linear random vibration problems by use of time-invariant structural reliability techniques.     

Multi-objective optimization of skeletal structures under static and seismic loading conditions

Almost every real world problem involves simultaneous optimization of several incommensurable and often competing objectives which constitutes a multi-objective optimization problem. In multi-objective optimization problems the optimal solution is not unique as in single-objective optimization problems. This paper is concerned with large-scale structural optimization of skeletal structures such as space frames and trusses, under static and/or seismic loading conditions with multiple objectives. Combinatorial optimization methods and in particular algorithms based on evolution strategies are implemented for the solution of this type of problems. In treating seismic loading conditions a number of accelerograms are produced from the elastic design response spectrum of the region. These accelerograms constitute the multiple loading conditions under which the structures are optimally designed. This approach for treating seismic loading is compared with an approximate design approach, based on simplifications adopted by the seismic codes, in the framework of multi-objective optimization.