厚板动力分析的混合状态Hamiltonian等参元

本文提出一种对板动力学问题Ｈａｍｉｌｔｏｎ正则方程进行正则变换的方法，并给出一种强有力的半离散半解析方法—混合状态Ｈａｍｉｌｔｏｎ动力元。这种方法滑板厚方向未作任何有关应力和位移的人为假设，而是采用状态空间法给出真解，所以可通用于薄、厚板及强厚板的动力计算问题。     

一维正方准晶椭圆孔口反平面问题的半逆解法

选取新的位移势函数,利用半逆解法及待定系数法,研究一维正方准晶平行于准周期方向的椭圆孔口问题,给出了应力场的显式解析解。在极限状态下,椭圆孔口问题可退化为Griffith裂纹问题,得到了相应裂纹问题的应力场和应力强度因子的显式解析解。     

复合材料层合梁非对称分层问题的解析解法

根据叠加原理将含有非对称分层的复合材料层合梁在横向载荷作用下的受力状态分解为对称和反对称情况,再将反对称受力状态分解为无分层梁受反对称横向载荷状态与含分层梁在分层表面承受附加剪切载荷状态。将分层问题归结为在附加载荷状态中,层合梁附加位移与附加应力的分析,并据此建立了一个简单的力学模型。最后,根据工程梁理论得到了由分层引起的附加位移与应力的解析解答,利用能量释放率方法确定了应力强度因子,计算分析了分层区长度与层板厚度对附加位移的影响。      

复合材料层合曲梁分层问题的解析解法

根据叠加原理将含有分层的复合材料层合曲梁在横向载荷作用下的受力状态分解为在面受力状态与出面受力状态,再将出面受力状态分解为无分层曲梁受横向载荷状态与含分层曲梁承受附加剪切载荷状态。将分层问题归结为在附加剪切载荷状态中,层合梁附加位移与附加应力的分析,并据此建立了一个简单的力学模型。最后得到了由分层引起的附加位移与应力的解析解答,并用能量释放率方法确定了应力强度因子。     

含金属内衬复合材料缠绕容器固化过程应力场的混合Hamilton元半解析法

基于Hellinger-Reissner广义变分原理,提出了一种分析含金属内衬复合材料缠绕壳结构过程应力场的混合状态Hamilton元半解析法。该方法在周向面内采用有限元离散,而沿径向对状态方程进行解析求解;在求解过程中,又采用了传递矩阵技术,这样,不仅保证了相邻铺层的界面上层间位移和层间法向和剪应力的连续性,同时,又得到了缠绕结构的内、外表面状态向量之间的关系式。为此,不论缠绕结构的层数有多少,最后都可归结为一个求解缠绕结构内、外表面状态向量未知量的方程组。同有限元法相比,有效地提高了应力分析精度,而且也大大地降低了求解未知量的数目。     

直角域非等腰三角形凸起对SH波的散射与地震动

本文采用复变函数及移动坐标方法给出了SH波对直角域非等腰三角形凸起散射问题的解析解答。首先,采用“分区”的思想,将求解模型划分为两个区域,区域I为含有半圆形弧底的非等腰三角形凸起,区域II为含有半圆形凹陷的直角域。求解本文问题的关键在于构造满足非等腰三角形两斜边应力为零的驻波解答和构造满足直角域边界应力为零的散射波解答。其次,根据“公共边界”上应力、位移连续性条件建立无穷代数方程组,并截断有限项求解。最后,给出了地表位移幅值的具体算例。结果表明：入射角度,入射波数以及直角域垂直边界都对地表位移幅值有影响。     

正交压电复合材料层板各类边界的解析解

压电复合材料层板由压电片与纤维层叠合而成。基于等效单层理论的位移场和电势场,针对正交铺层压电复合材料层板柱面弯曲问题,建立了力电耦合平衡方程,获得了一般边界的解析解。解析解由特解和通解两部分组成,特解对应于简支边界条件,通解由其他各类边界条件确定。平衡方程的变量仅4个,且不随层数变化。如采用相应的位移和电势分布函数,可以得到一阶理论、高阶理论、指数型理论等多种理论的解析解。算例中给出了各种边界条件下位移、应力和电势的解,讨论了各种理论的精度,观察到了固支边界的应力奇异现象。     

层状正交各向异性材料弹性波导问题的数值计算

研究复合材料弹性波导问题的数值计算方法。将问题导向哈密顿体系,在哈密顿体系中以位移向量和应力向量综合成全状态向量,在杂交体系中建立动力-部分杂交元,导出一套哈密顿体系下新的半解析法。本文中给出了该方法在分层正交各向异性材料的弹性波导问题的数值算例。计算结果展现了该方法在弹性波导问题的应用前景。     

厚板问题的位移法分析

本文从弹性体的三维 L—N方程出发,导出了平板问题的普遍形式解.作为实例,给出了半无限板、半无限长板条两个边值问题的严格解析解.用本文的方法分析平板,所得结果能反映边界位移和应力沿厚度方向的变化情况.     

覆盖层为功能梯度材料弹性半平面中的Love波

对均匀各向同性弹性半平面上覆盖一层功能梯度材料中存在的Love波的频散问题进行了研究,给出了Love波频散方程的一般形式。利用WKBJ近似理论,给出了功能梯度材料层的位移、应力近似解析解,导出了Love波WKBJ近似频散方程的一般形式。该文以功能梯度材料层的剪切弹性模量和质量密度沿厚度方向均为指数函数变化为例,进行了实例计算和分析,给出了频散曲线,讨论了Love波在功能梯度材料覆盖层弹性半平面中传播的一般性质。这些结论对无损检测和反问题分析方法的改进提供理论依据。     

The Discrete-Analytical Solution Method for Investigation Dynamics of the Sphere with Inhomogeneous Initial Stresses

The paper deals with a development of the discrete-analytical method for the solution of the dynamical problems of a hollow sphere with inhomogeneous initial stresses. The examinations are made with respect to the problem on the natural vibration of the hollow sphere the initial stresses in which is caused by internal and external uniformly distributed pressure. The initial stresses in the sphere are determined within the scope of the exact equations of elastostatics. It is assumed that after appearing this static initial stresses the sphere gets a dynamical excitation and mechanical behavior of the sphere caused by this excitation is described with the so-called three-dimensional linearized equations of elastic wave propagation in initially stressed bodies. For the solution of these equations, which have variable coefficients, the discrete analytical solution method is developed and applied. In particular, it is established that the convergence of the numerical results with respect to the number of discretization is very acceptable and applicable for the considered type dynamical problems. Numerical results on the influence of the initial stresses on the values of the natural frequencies of the hollow sphere are also presented and these results are discussed.     

复合材料层板层间应力分析的能量法

本文首先探讨了复合材料层板层间应力的问题提法,指出了轻典层板理论与层间应力的层板理论的关系;然后本文给出求解层间应力的方法,将每层的面内应力沿厚度方向以完备函数族进行单向展开,沿宽度方向设其为任意函数,利用平衡方程和余能原理可得任意函数所满足Euler方程,通过求解该方程得到层间应力。本文最后还给出了解决奇异性的方法。计算结果表明,应力分布与奇异项系数的收敛都是迅速的。      

Optimal parabolic arches

An explicit solution for the elastic stress state in a thick parabolic arch subject only to symmetric loading at its foundations is presented. This solution is found using the complex variable method of plane elasticity. The proposed stress solution has the interesting property of being isoresistent in the sense that exterior and interior boundaries of the arch convey constant hoop stresses of equal but opposite sign. Moreover, all hoop stresses are constant.     

A semi-analytical finite element for laminated composite plates

This paper presents a semi-analytical finite element solution for laminated composite plates. The method is based on a mixed variational principle that involves both displacements and stresses. Finite element meshes are only used in the plane of plate, while the through thickness distributions of displacements and stresses are obtained using the method of state equations. Numerical results show that the rate of convergence of the new method is fast and the solutions can be very close to corresponding exact three-dimensional ones. The use of a recursive formulation of the state equations leads to an algebra equation system, from which solution are sought, whose dimension is independent of the numbers of layers of the plate considered.     

四点支承单层开孔玻璃承载性能的有限差分法分析

基于小挠度薄板的近似理论,采用有限差分法分析了4 点支承带孔玻璃板位移和应力的分布规律,并通过对点支承处进行特殊处理,建立了奇点模型,同时提供了孔边应力的计算公式。该计算模型描绘了点支玻璃板中应力分布的特点,直观、理论性强且操作简便,且计算结果与现行规程、有限元计算的结果较好的吻合。孔边应力的计算方法可为规程的补充提供必要理论依据。     

Analytical solutions of heterogeneous rectangular plates with transverse small periodicity

We consider the cylindrical bending of a simply-supported orthotropic rectangular plate, which is small-periodically heterogeneous in the thickness direction. A homogenized plate model is first established by using the two-scale asymptotic expansion method. The state-space method is then adopted to analyze the homogenized plate exactly. Analytical expressions for two sets of approximate stresses, i.e. the homogenized model stresses and the zeroth-order two-scale model stresses, are presented. To check the accuracy of the approximate stresses, the state-space method is also applied to the original laminate plate or the approximate laminate model of the original heterogeneous plate with continuously varying material properties to obtain an analytical solution. In the latter case, the analytical solution is approximate but approaches the exact solution gradually when the number of layers increases. In order to avoid numerical instability, the joint coupling matrix is utilized. Numerical results illustrate that the two-scale model can predict accurately the realistic stress field in the original plate if it contains enough repeated units along the thickness.     

Elastic problem of an adhesion crack in T-junction of two orthotropic thin plates

In this study, the general solution is derived for stresses in a T-junction of two thin plates with an adhesion crack. The plates are orthotropic, and shear force is applied to the crack surface. The analysis is based on the supposition that the stresses in each plate can be approximated by the condition of plane stress. The results obtained are verified through numerical calculation using the finite element method. A singular stress field is obtained from the solution in the vicinity of a crack tip.     

Interaction between a point heat source and a nonuniformly coated circular inclusion

This paper investigates the interaction between a point heat source and a nonuniformly coated circular inclusion under plane deformation. Based on the complex variable theory and conformal mapping in conjunction with the analytical continuation method, the general expressions of the temperature, displacements, and stresses for three dissimilar media are derived explicitly in a series form. Numerical results are provided for some particular examples to investigate the effect of material combinations on the interfacial stresses. The derived analytical solution can also be used as a fundamental solution for the boundary element method as well as for other physical models, including welding and cutting.     

弹性介质模糊有限元控制方程的快速解法

线弹性模糊有限元方法是分析弹性介质体模糊特性对结构响应产生不确定性影响的有效方法。即使对弹性介质体而言,模糊有限元控制方程的求解时间问题也是困扰其推广应用的主要障碍。为获得可靠可行的模糊有限元控制方程的快速求解方法,在深入研究弹性介质体的模糊源特点基础上,提出当引起结构模糊特性的力学参数为单源模糊数时,可以利用单源模糊数的运算特点来求解模糊有限元的控制方程,进而利用合成运算求解结构的模糊位移和模糊应力的分布。推导了基于单源模糊数运算的弹性介质模糊应力和模糊位移的计算表达式。应用模糊有限元求解的区间解法和快速解法对算例进行比较分析,结果表明了快速解法的正确性。     

Investigation of the stress-strain state of a finite cylinder under the action of compressive forces

We determine the stresses and displacements formed in a finite cylinder under the action of an elastic ring simulated by uniformly distributed normal forces. For the analysis of the stress-strain state, we use the numerical-analytic least-squares method. It is shown that this method guarantees high accuracy of the solution. The changes in the stresses and displacements are analyzed depending on the radius of the cylinder, its length, and the width of the ring. We obtain two qualitatively different distributions of stresses and displacements.