Rational Profiling of Reinforced Rotating Disks

The problem of rational profiling of thermoelastic three-layered reinforced rotating disks of gas turbines is formulated. The conditions of equal-stressed reinforcement of the midlayer and the condition of equal-strength binder of the reinforced layer or external isotropic layers are used as criteria for rational designing. An iterative method is proposed for solving such problems. The problem of rational profiling of disks with radial and radially circumferential reinforcements, on condition that the fibers of the radial family are equally stressed, is solved analytically. The calculation results for B-Al and B-Ti disks, obtained by using both the criteria of rational design, are given for plane-parallel and 3D reinforcements. It is shown that, at an equal load-carrying capacity, the weight of such disks can be 30-60% smaller than that of reinforced disks of constant thickness, or, at an equal weight, they can have a considerably higher load-carrying capacity. The criterion of equal-stressed reinforcement, as a rule, is more efficient than the condition of equal-strength binder.     

Reissner厚板弹性弯曲的理性有限元法

本文在非协调元的修正泛函中引入满足系统微分方程的单元变形模式,提出了一种将解析方法与数值方法有机结合的理性有限元法。这种新的计算方案合乎单元的力学要求和结构的几何复杂性要求。据此所得的厚板弯曲四边形单元具有计算精度高、可对刚度矩阵精确积分等优点。     

Thermoelastoplastic Bending of Complexly Reinforced Plates

A problem on the transverse-longitudinal bending of reinforced plates of variable thickness under a thermal-force loading is formulated. A qualitative analysis of the problem is carried out, and a way of its linearization is indicated. Calculations of isotropic and metal composite plates subjected to the transverse or transverse-longitudinal bending showed that their bearing capacity in the elastoplastic bending is a number of times (occasionally, by an order of magnitude) greater than in the elastic bending. The heating of the plates sharply decreases their resistance to the bending in the case of elasticity and affects it only slightly in the case of elastoplasticity. In the elastoplastic bending, the bearing capacity of the metal composite plate a number of times exceeds that of isotropic plates made of conventional structural metal alloys. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 6, pp. 715–742, November–December, 2005.     

Reissner厚板弹性弯曲的一般解析解

针对大型工程建设中的Reisner厚板弹性弯曲问题,本文采用复级数方法求解相应的常系数偏微分方程组的边值问题,并首次得到了任意边界条件下的一般解析解.该解形式简单,计算方便、可靠.以四边简支和三边固支一边自由两种支撑条件下厚板承受均布载荷为例进行了分析验算,与已有的计算结果相比,计算结果相当满意.同时本文还着重对解的收敛速度、正确性(合理性)及边界满足情况进行了考察.     

Elasticoplastic bending of rectangular plates reinforced with fibers of constant cross section

The problem on the elastoplastic transverse bending of Kirchhoff plates of variable thickness reinforced with fibers of constant cross section is formulated and its qualitative analysis is performed. An analytical solution to the problem is constructed in the case of cylindrical bending, and, by using the Bubnov-Galerkin method, an approximate solution for a rectangular plate is obtained. Based on calculations of plates reinforced with boron fibers and steel wire, it is shown that the load-carrying capacity of the structural member in elastoplastic bending is several times (or even by an order of magnitude) higher than in purely elastic one.Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 1, pp. 17–36, January–February, 2005.     

变厚度簿板弯曲问题的任意网格差分解法

本文提出一种求解变厚度薄板弯曲问题的任意网格差分格式,可适应不同边界,各种荷载和复杂形状板.计算实例表明,该方法具有格式简单、通用性强、计算精度高,计算量少等特点.     

均布载荷下两邻边固定、一边简支、一边自由的矩形板的弯曲

用广义简支边概念和叠加法给出的均布载荷下两邻边固定、一边简支、一边自由矩形板的精确解。对正方形自由的挠度和回定边的弯矩进行了数学计算。     

Load-Carrying Capacity of Circular Plates Made of a Fiber-Reinforced Composite

The load-carrying capacity of circular plates made of a fiber-reinforced composite and loaded with axisymmetric transverse forces under axisymmetric boundary conditions is investigated. The plates can be freely supported or clamped along their contour. To the known yield condition used, in the plane of main bending moments, there correspond irregular hexagons, which depend on the mechanical properties of composite constituents and some characteristic geometrical parameters. It is shown that, depending on the ratio of ultimate radial and circumferential bending moments, in the plastic state, the circular plates (the central part of the clamped plates) take the form of a cone or a frustum of cone. For each of the cases, the limit load is found, which is a function of the above-mentioned mechanical parameters. The statically allowable fields of bending moments and the corresponding allowable fields of deflection rates are determined. The solutions found are exact. Special cases for the freely supported plates are analyzed, and the results obtained are presented in the form of graphs.__________Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 2, pp. 177–192, March–April, 2005.     

考虑高阶横向剪切正交各向异性板非线性弯曲的微分求积分析

采用微分求积方法（DQ方法）讨论了计及高阶横向剪切的正交各向异性弹性板的非线性弯曲问题．导出了非线性控制方程的DQ形式,利用推广的DQWB技巧处理了高阶矩的边界条件．进一步推广并运用新的分析技术简化了非线性方程的计算．为说明该方法的可靠性和有效性,将考虑剪切变形及不计剪切变形的薄板的数值结果与三维弹性解析解及其它数值解进行了比较,同时研究了数值结果的收敛性,并考察了不同的节点分布对收敛速度的影响A·D2还考察了几何、材料参数及横向剪切效应对正交各向异性板非线性弯曲的影响．分析结果表明横向剪切效应对正交各向异性中厚板的影响是显著的．     

一边固定及一角点支承的矩形板在均布荷载作用下的弯曲解

本文采用叠加法求出一边固定及一角点支承的矩形板在均布荷载作用下的弯曲解答,计算表明这种解法收敛速度快,计算精度高。