多功能力矩分配法

提出了新的力矩分配思想,将角位移和线位移综合考虑,使力矩分配法能直接应用于有侧移结构,且在计算内力的同时还能计算结构的位移,使力矩分配法具有多功能. 实例计算表明,该方法正确、简单,有利用价值.     

力矩分配法的快速实用计算研究

对力矩分配法的计算过程进行了改进,采用Excel表格编制出了无侧移框架、连续梁的统一计算表格并给出了计算示例,使这一方法在计算多、高层框架和多跨连续梁的内力时达到快速、准确、实用的目的,对教学、科研和工程设计具有一定的实用意义.     

一次性分配的力矩分配法

提出以多跨连续梁为单元参与力矩分配法的设想,导出了任意跨连续梁的杆端转动刚度和结点处弯矩传递系数的递推计算式,使得设想能够实施．改变了传统力矩分配法的渐近解法,只需一次性分配就可求得精确解．     

力矩分配法的方程解法

在传统力矩分配法的基础上,将渐进的计算过程转化为方程组的求解,可以更好地理解力矩分配法的分析思路及计算过程,同时提高计算效率和精度。该方法所得到的方程与矩阵位移法所得方程形式相同,但未知量完全不同,方程的推导过程更简洁且易于理解,在教学中可以启发学生对矩阵位移法分析思想的思考。     

连续梁的多结点力矩分配法

计算了连续梁在结点力偶荷载作用下柔度矩阵的表达式,在此基础上,提出了多结点力矩分配法. 对于一个承受任意荷载的$N$个结点的连续梁,该方法同时松开多个结点,通过迭代获得各结点转角值,然后利用杆件的转角位移方程就可获得杆端弯矩的值.该方法综合了位移法和力矩分配法的优点,较传统力矩分配法可显著减少计算工作量.     

力矩分配法在对称结构中的应用

以力矩分配法为基础，探索了对称结构的简化计算方法．为了克服对称结构计算时通常方法所产生的不便，提出了新的力矩分配概念，找出了新的分配系数和传递系数．应用改进的力矩分配法，对对称结构进行了计算，算例表明该方法简化了计算，加快了收敛速度．     

多结点力矩分配法精确计算研究

针对多结点力矩分配法轮流放松结点只能获得渐近解的不足,提出了一种将分配结点分层并按顺序放松、相邻结点不同时放松、放松后不重新固定的放松策略,即从远端只与基础相连的结点开始将其划分为若干层,按照同层相邻分配结点逐个或间隔放松的原则由外层向内层逐层移除结点约束,引入弹性支座模拟相邻杆件的转动约束作用,通过推导远端转动弹性支承等直杆弯矩形常数,确保结点放松时转动刚度和传递系数已知或可计算,结果表明,按顺序逐层移除约束的放松约束方式一方面各分配弯矩能够直接或通过已放松结点向支座传递,其中,向放松结点传递的弯矩通过结点协调变形依次向远端传递直至支座,而不产生新的不平衡力矩,从而快速消除结点不平衡力矩,结果精确;另一方面各分配结点只经历一轮完整力矩分配与连续传递过程即恢复至最终变形位置,计算量小。

     

混合型有限元双向分配法解有侧移刚架及其微机程序

本文应用混合型有限元双向分配法得到有侧移刚架的数值解。文中给出了计算机程序,具有占用内存少、收敛快等特点。文末给出了算例。     

On the tangential stress anomaly in the displacement discontinuity method

It is shown that the anomaly associated with the incorrect evaluation of tangential stresses in the displacement discontinuity (DD) method, commonly used to solve crack problems, is related to the order of singularity of the fundamental solutions of linear elasticity. It is established here that a minimum of linear variation of the shear DD distribution is needed to obtain the correct tangential stress jump across a crack. Alternatively, a correction term (‘patch’) that improves tangential stresses is derived. It is also shown that need for higher functionality is a fundamental requirement rather than a convenient artifice for obtaining better accuracy.     

Stress distribution in a lap joint under tension-shear

This paper deals with the elastostatic load transfer of a tensile load in a model of an adhesive lap joint (tension-shear problem). The adhesive layer is regarded as infinitesimally thin and the displacement and traction vectors in the adherends are assumed to be continuous across the bond. The problem is reduced to a pair of Fredholm integral equations of the second kind which involve the mean angle between the deformed bond line and the tensile load. This angle, in turn, is determined by means of a scheme due to Goland and Reissner. Numerical results for the bond line stresses and the stress intensity factors at the ends of the bonded region are presented.     

On the complex variable displacement method in plane isotropic elasticity

A modified formulation of the complex variable displacement method in plane isotropic elasticity is presented. It makes use of two equations deduced from the planar Navier equations in terms of the complex variable, which differs from England’s original formulation based on only one equation. This formulation is more direct and complements the one by England.     

On the effect of constraint parameters on the generalized displacement control method

In this work, we investigate the generalized displacement control method (GDCM) and provide a modification (MGDCM) that results in an equivalent constraint equation as that of the linearized cylindrical arc-length control method (LCALCM). Through numerical examples, we illustrate that the MGDCM is more robust than the standard GDCM in capturing equilibrium paths in regions of high curvature. Moreover, we also provide a geometric and physical interpretation of the method, which sheds light on the general class of path following methods in structural mechanics.     

Simulation of the Brownian coagulation of nanoparticles with initial bimodal size distribution via moment method

The Brownian coagulation of nanoparticles with initial bimodal size distribution, i.e., mode i and j, is numerically studied using the moment method. Evolutions of particle number concentration, geometric average diameter and geometric standard deviation are given in the free molecular regime, the continuum regime, the free molecular regime and transition regime, the free molecular regime and continuum regime, respectively. The results show that, both in the free molecular regime and the continuum regime, the number concentration of mode i and j decreases with increasing time. The evolutions of particle geometric average diameter with different initial size distribution are quite different. Both intra-modal and inter-modal coagulation finally make the polydispersed size distribution become monodispersed. As time goes by, the size distribution with initial bimodal turns to be unimodal and shifts to a larger particle size range. In the free molecular regime and transition regime, the inter-modal coagulation becomes dominant when the number concentrations of mode i and j are of the same order. The effects of the number concentration of mode i and mode j on the evolution of geometric average diameter of mode j are negligible, while the effects of the number concentration of mode j on the evolution of geometric average diameter of mode j is distinct. In the free molecular regime and continuum regime, the higher the initial number concentration of mode j, the more obvious the variation of the number concentration of mode i.     

A realization of the moment method

The difficulties involved in solving a system of moment equations using two-sided distributions are analyzed. The properties of these distributions do not permit the realization of the moment method (in the case of a collision integral in Boltzmann form) in specific transport boundary-value problems. A method of obtaining analytic solutions of the system of moment equations for linearized transport problems is proposed. The accuracy of the method is analyzed with reference to a classical transport problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 185–188, May–June, 1991.