Development of the mechanics of underground and special structures in Kazakhstan over the last 40 years

Some results on underground structures obtained by Kazakh mechanicians are reviewed. The review covers a period of the last forty years. Also results on the mechanics of special objects are discussed.Translated from Prikladnaya Mekhanika, Vol. 40, No. 10, pp. 3–36, October 2004.     

An unflexural refined model of deformation of multilayered plates on an undeformable foundation

The stress-strain state of multilayered plates on an undeformable foundation is investigated. The design diagram of a transversely loaded plate is formed by supplementing it with a symmetric one about the contact surface of the foundation. The double-thickness plate obtained becomes loaded bilaterally and symmetrically about its midsurface. In such a way, only unflexural deformations can be modeled, which reduces the number of unknowns and the general order of differentiation of the resolving system of equations. The refined continual model developed takes into account the deformations of transverse shear and transverse compression in high iterative approximations. The cases of a rigid contact between the foundation and the plate and frictionless slip of the plate over the foundation are considered. Calculations confirm the efficiency of such an approach, which allows one to obtain solutions qualitatively and quantitatively close to three-dimensional ones. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 643–654, September–October, 2006.     

Twin Paradox and the Logical Foundation of Relativity Theory

We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization Specrel of special relativity from the literature. Specrel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove the usual relativistic properties of accelerated motion (e.g., clocks in acceleration) in Specrel. As it turns out, this is practically equivalent to asking whether Specrel is strong enough to “handle” (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to Specrel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of Specrel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that~the Twin Paradox becomes provable in AccRel, but it is not provable without IND.     

水闸闸室结构三维样条边界元分析

用三维样边界元法分析水闸闸室结构。底板，闸墩和载水墙等为其子结构，交通桥，工作桥和胸墙等处理为内部支撑。地基和边载可以是任意的，只要能给定地表位移面力关系。在各种工况下，不论是设置平板门还是弧形门，是平底板是反拱底板，即使在稀疏剖分下也能给出高精度的位移场，应力场和地基反力场。     

某工程地基基坑支护探讨

软土地基中的支护是基础工程的关键，在节约成本的前提下，选择合理的支护结构至关重要．通过对某公司将要开发的2个基坑支护方案的项目进行的相关分析、计算和探讨，总结出了软土地基中的基坑支护方案的选择原则及其相对应的施工措施等．     

模糊神经网络在复合地基沉降量预测中的应用

复合地基后期沉降变形对于建筑物设计及安全具有重要意义,针对通过长期沉降观测以得到复合地基的最终沉降需要耗费较多资源的问题,提出了一种基于模糊神经网络的预测方法.该方法考虑沉降变化过程有较大的随机性和模糊性,直接将样本数据进行模糊化,所得的模糊数代表了样本点集与控制点集中各分量之间的相关度,并依此建立模糊BP神经网络进行学习和估算.实验结果表明了该方法对沉降进行预测是可行与有效的,且在相对误差的有效控制方面优于BP网络方法与灰色方法.     

On the free vibration response of rectangular plates,partially supported on elastic foundation

Rectangular plates on distributed elastic foundations are widely employed in footings and raft foundations of variety of structures. In particular, mounted columns and single footings may partially occupy the rectangular plate of any kind.     

Study on wave dispersion characteristics of piezoelectric sandwich nanoplates considering surface effects

In this study, the wave propagation properties of piezoelectric sandwich nanoplates deposited on an orthotropic viscoelastic foundation are analyzed by considering the surface effects (SEs). The nanoplates are composed of a composite layer reinforced by graphene and two piezoelectric surface layers. Utilizing the modified Halpin-Tsai model, the material parameters of composite layers are obtained. The displacement field is determined by the sinusoidal shear deformation theory (SSDT). The Euler-Lagrange equation is derived by employing Hamilton’s principle and the constitutive equations of piezoelectric layers considering the SEs. Subsequently, the nonlocal strain gradient theory (NSGT) is used to obtain the equations of motion. Next, the effects of scale parameters, graphene distribution, orthotropic viscoelastic foundation, and SEs on the propagation behavior are numerically examined. The results reveal that the wave frequency is a periodic function of the orthotropic angle. Furthermore, the wave frequency increases with the increase in the SEs.

     

时滞效应对弹性地基上梁主共振响应影响分析

本文研究了弹性地基上梁主共振响应的时滞效应．基于Hamilton原理,建立了时滞影响下弹性地基上梁的非线性运动微分方程,采用多尺度法,求得了时滞效应下主共振响应调制方程以及稳定性条件．通过数值算例,分析了时滞和调谐参数影响下主共振响应的峰值及幅频响应特性．结果表明,地基反力中的时滞效应对主共振响应影响较大,会导致共振域偏移,在一定区间内,响应幅值随时滞变化先减小再增大,呈现出周期性,并导致幅频曲线弯曲程度增大．     

优化MGM(1,n)模型及其应用研究

从最小二乘估计的适用条件出发,在建立MGM(1,n)模型前,先采用BoxCox变换对原始数据进行变换,以解决或缓解误差项的正态性偏离问题.首先,以模型拟合平均误差最小化为目标,建立非线性优化模型,在参数的置信区间内,应用PSO(Particle Swarm Optimization)算法求最优解.然后,应用求解得到的参数,建立优化MGM(1,n)模型.在实例分析中,将优化MGM(1,n)模型应用于深基坑围护结构变形预测,实验结果表明通过对原始数据做合适的Box-Cox变换,能够有效提高模型的拟合及预测精度,拓广多变量灰色预测模型的适用范围.