双参数弹性地基上圆底扁球壳的非线性弯曲

本文从Krmn型非线性基本微分方程出发,提出了将修正迭代法和伽辽金法联合应用,分析了Pasternak弹性地基上周边固定凹圆底扁球壳在均匀压力作用下的非线性弯曲问题,给出了荷载与挠度间的数学表达式,其所得结果与已有文献结果吻合较好,且简明、计算量小.     

矩形网格扁壳结构的非线性弹性理论

本文在基本假设的前题下,分析了矩形网格离散结构的变形以及变形量与内力之间的本构关系.在此基础上,通过建立等级模型,运用虚功原理推导出网格扁壳的作线性基本控制方程与边界条件.     

弹性薄板和薄扁壳及其在半空间上接触问题解的唯一性证明

用Laplace方程的第一种内边界问题不可能有两个不同的解这一定理,证明了弹性薄板和薄扁壳及其在半空间上接触问题解的唯一性问题。第二类内边界问题唯一性也得到证明。     

弹性扁壳由移动质量引起的强迫振动

本文用变分法讨论在弹性扁壳上有移动的质量所引起的壳体的强迫振动.文中讨论了关于强迫振动、共振条件及临界速度等一系列问题.     

扁薄球壳非对称大变形问题

本文用修正选代法研究了扁球壳非对称大变形问题，求得了在线性液体载荷作用下的扁球壳变形的二次近似解析解并绘出了摄动点的挠度与载荷的特征曲线族．应用本文方法还可对其他板壳的非轴对称大变形问题进行讨论．本文通过算例对平板及不同初挠度的扁球壳大挠度变形进行了讨论．     

弹性地基上的自由矩形板

在弹性地基上的自由矩形板的弯曲,在弹性薄板理论中也是个难题.本文以叠加法提供一个精确解.它满足微分方程,自由边界的条件以及自由角点条件.这样将导致一系列无穷联立方程.所解的问题为在板的中点作用一集中力这问题.我们并以地基反力应与这集中力相平衡.校核所作的计算是否正确.     

弹性基上锥壳一般弯曲问题的精确解

本文应用Donnell的简化假定,从弹性基上锥壳位移型微分方程组出发,通过引入一个位移函数U(s,θ)(在极限情况下就退化成V.S.Vlasov对于圆柱壳所引的位移函数[5]),将基本微分方程组化成为一个八阶可解偏微分方程.这个方程的一般解用级数形式给出.对于在实际中有广泛应用价值的Winkler弹性基上锥壳的轴对称弯曲问题,本文给出了详细的数值结果,并求出了边缘荷载作用下的影响系数,这对计算弹性基上锥壳组合结构有着重要的意义.     

弹性圆底扁球壳在边缘均布力矩作用下的非线性稳定问题

本文对边缘简单支承在边缘均布力矩作用下的弹性圆底扁薄球壳的非线性问题进行了研究.用我们提出的修正迭代法求出决定上下临界载荷的二次和三次近似方程.结果画成曲线以供工程应用.并将此结果和胡海昌的结果进行了比较,我们还研究了临界点,即上下临界载荷相重点附近的情况,并指出二次近似的适用范围.文末还附带得出本问题的特殊情况:相同边缘支承和载荷下的圆平板大挠度问题的刚度设计公式及p=0.3的相应曲线,并与黄择言用摄动法得到的结果进行了比较.     

扁薄锥壳非对称大变形问题

本文用双参数摄动法研究了扁锥壳非对称大变形问题，求得了在线性载荷作用下的扁锥壳变形的三次近似解析解并绘出了摄动点的挠度与载荷的特征曲线·应用本文方法还可对其它板壳的非轴对称大变形问题进行讨论·本文通过算例对平板及不同初挠度的扁锥壳大挠度变形进行了讨论·     

非线性弹性地基上的圆薄板的分岔与混沌问题

根据非线性弹性地基上圆薄板大幅度方程,弹性抗力有线性项,三次非线性项和抗弯曲弹性项。在周边固定的条件下,利用Galerkin法得到了一个非线性振动方程。在无外激励情况下,求出在平衡点处的Floquet指数。分析了其稳定性与可能发生的分岔条件。在外激励条件下,用Melnikov方法分析研究了可能发生的混沌振动。通过数字仿真给出了各种地基参数下混沌区域的临界曲线和相平面图。     

Optimal Control of an Axisymmetric Conical Shell with a Unilateral Elastic Foundation and Rigid Supports

We study an optimal control problem for an elastic conical shell. The displacement vector u =(u,v) is then a function of one variable s∈(a,b), 0<a<b<∞. Here u is the meridional and v the normal displacement. The shell is assumed to be simply supported. Moreover, we consider several unilateral obstacles and an unilateral elastic foundation of Winkler type i.e. the reaction force is proportional of the positive part of the normal displacement. The state problem is formulated in a form of variational inequality for u . The design parameter e =(t,z,F) includes the variable thickness of the shell, the stiffness characteristics of the foundation and the friction coefficient. The existence of the optimal control will be explained. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

梁的弹性最优设计*

本文根据最小余能原理建立了弹性梁最优强度设计问题的数学形式,它为一个具有等式和不等式约束的泛函极值问题。进而应用拉格朗日乘子法得到了极值的必要条件,并由此导出最优解所必须满足的一组关系式,这组关系式可以用来检验等强度设计或任一可行弹性设计的最优性。当等强度设计不是最优设计时文中还建议了一个迭代寻优的数值解法。     

Investigation of the Thermoelastoplastic State of Locally Heated Shallow Shells of Double Curvature

We develop a numerical-analytic method for calculating the thermoelastoplastic state of shallow shells of arbitrary curvature under conditions of heating by localized heat sources. For solving auxiliary problems that arise in applying the method of additional deformations, we use the Fourier integral transformation and integral representations of a solution. Detailed investigations were performed for shells of cylindrical, spherical, and ellipsoidal shapes. We establish the dependence of the distribution of thermal and residual stresses on the curvatures of a shell and on the mode of heating. We consider the limiting case where the construction has the shape of a plate.     

On the Equations of Linear Shallow Shell Theory

The paper presents a formulation of the two-dimensional theory of shallow shells, including the effects of transverse shear deformation and of moments turning about the normal to the middle surface. The present formulation includes, as it must, Marguerre's theory. At the same time it is consistent with recent formulations of general linear shell theory, in particular in regard to the preservation of the static-geometric duality. Various reductions of the equation of the theory are considered. Of particular significance and effectiveness among these are reductions for the special cases of (1) shells without moments about the middle surface normal, (where an earlier result of Naghdi is extended) (2) the shell without transverse shear deformability, (the static-geometrical dual of case (1)). As an application of the general equations an explicit solution is obtained for the problem of stretching, twisting and bending of pretwisted rectangular plates.     

On Unique Solutions of Multiple-State Optimal Design Problems on an Annulus

We study the uniqueness and explicit derivation of the relaxed optimal solutions, corresponding to the minimization of weighted sum of potential energies for a mixture of two isotropic conductive materials on an annulus. Recently, it has been shown by Burazin and Vrdoljak that even for multiple-state problems, if the domain is spherically symmetric, then the proper relaxation of the problem by the homogenization method is equivalent to a simpler relaxed problem, stated only in terms of local proportions of given materials. This enabled explicit calculation of a solution on a ball, while problems on an annulus appeared to be more tedious. In this paper, we discuss the uniqueness of a solution of this simpler relaxed problem, when the domain is an annulus and we use the necessary and sufficient conditions of optimality to present a method for explicit calculation of the unique solution of this simpler proper relaxation, which is demonstrated on an example.     

On Some Contact Problems for Bodies with Elastic Inclusions

The paper deals with the contact problems of the theory of elasticity. The problems are reduced to Prandtl-type integral differential equations with a coefficient at the singular operator which has higher-order zeros at the ends of the integration interval. In some concrete cases the solution is constructed efficiently. Asymptotic representations are obtained.