求解多层弹性半空间轴对称问题的精确刚度矩阵法

本文首先从弹性力学的基本方程出发，利用Hankel积分变换等数学手段，推导出了单层弹性半空问轴对称问题的刚度矩阵，然后按传统的有限元方法组成总体刚度矩阵。通过求解由总体刚度矩阵所构成的代数方程和Hankel积分逆变换就可解出静荷载作用下多层弹性半空间轴对称问题的精确解。由于刚度矩阵的元素中不含有正指数项，计算时不会出现溢出的现象，从而克服了传递矩阵法的缺点。由于在推导过程中摒弃了应力函数的选择，使得问题的求解更加理论化和合理化，同时也为进一步研究这类问题如温度场，动力学等方向奠定了理论基础。最后，文中还给出了计算实例来证明推导结果的准确性。     

多层弹性半空间问题解的精确刚度矩阵法

利用二维Fourier积分变换和刚度矩阵法,得到了直角坐标系下多层弹性半空间问题的精确解.在推导的过程中,直接从空间弹性力学的基本方程出发,利用积分变换等数学手段,首先推导出了单层空间弹性问题的刚度矩阵,然后按有限元法组成总体刚度矩阵.通过求解由总体刚度矩阵所构成的代数方程和积分逆变换,就可解出在任意静荷载作用下多层弹性半空间问题的精确解.由于刚度矩阵中不含有正指数项,计算时不会出现溢出现象,从而克服了传递矩阵法的缺点.由于在推导过程中摒弃了应力函数的选择,使得问题的求解更加合理化.最后还给出了计算实例来证明推导结果的准确性.     

三维粘弹性层状半空间埋置集中荷载动力格林函数求解—修正刚度矩阵法

针对三维粘弹性层状半空间埋置集中荷载作用下动力响应计算,在柱面坐标下,结合径向Hankel和周向Fourier变换,提出了一种新的求解方法修正刚度矩阵法.方法首先固定荷载所在层的上下界面,在空间波数域内,由波动方程的特解和齐解叠加得到“固端”反力.进而放松两“固端约束”,利用直接刚度法容易求得各层面位移.荷载作用层内反应另需叠加上该“固定层”内解,其中特解部分积分由全空间解析解代替,由此解决了当接收点和源点作用水平面接近时异常积分收敛问题.算例分析表明,对于低频(可退化为静力状态)和高频问题,论文方法均具有很高的计算效率和精度.     

用积分变换及边界积分方法求解多层地基的静力问题

本文利用积分变换及矩阵递推方法得到了任意n层弹性体平面应变及轴对称问题的Mindlin解。再把此解作为基本解,利用Somigliana关系式,得到计算多层弹性体内部任意点位移的简便方法。利用此法很容易编制程序,且具有较高的计算精度与速度。     

列车荷载作用下黏弹性半空间体的随机动力响应Dynamic response of viscoelastic half-space subjected to train loads

针对列车荷载作用下黏弹性半空间体响应的问题,利用虚拟激励法将系统的随机分析转化为确定性分析。根据列车荷载构造了相应的虚拟激励形式,通过傅里叶积分变换法把半空间体控制方程转入波数‐频率域,并推导获得了系统虚拟响应的积分形式解。当相速度接近或大于瑞利波速时,积分形式解中被积函数往往具有奇异性和高振荡性,使得数值计算相当困难。对此,将被积函数图形化以确定函数的积分限,并通过自适应数值积分算法解决被积函数的振荡性。数值算例中,进行了随机列车荷载作用下半空间体的响应分析,讨论了荷载移动速度及频率等参数变化对响应的影响,给出了响应的时间和空间分布规律。本文方法可进一步推广至移动矩形荷载等载荷模型,对移动荷载作用下环境振动行为预测具有很好的借鉴意义。     

A dynamic analysis of elastic circular plate on saturated poroelastic half space

In this paper the low frequency vibrations of an elastic circular plate on a saturated poroelastic half space are studied by the analytical method. First the governing equations of the dynamic problem for a saturated poroelastic medium are solved by means of Hankel transform. Then the dual integral equations of vertical forced vibration of an elastic plate on saturated poroelastic half space are established according to the mixed boundary-valued condition. By applying Abel transform the dual integral equations are reduced to a Fredholm integral equation of the second kind. Numerical examples are given at the end of the paper.     

Thermoelastic problems in the half space—An application of the general solution in elasticity

In this paper, some thermoelastic problems in the half space are studied by using the general solutions of the elastic equations. The method presented here is extremely effective for the axisymmetric problems of the half space as well as the half plane problems.     

变质量、变阻尼、变刚度结构系统的动力响应

本文首次提出了变质量、变阻尼、变刚度结构系统的动力响应问题,并根据抓斗卸船机的工作过程导出了结构系统的动力方程及解法。最后给出了工程实际算例。     

The method of solving axisymmetric problems in elastic space by complex function and some examples

This paper proves Love’s stress function of space axisymmetric problem can be represented by choosing two generalized analytic functions of complex variates reasonably^[1], and deduces the expressions of the components of stress displacements and boundary conditions in complex function. To present the feasibility of the method here and examining the truth of the formulae founded in this paper, the problem of circular shaft with globular cavity pressed on the side and pulled at the ends is solved by using power series and the result is the same as that solved by other methods. In the end, the problem of a cone sheared by uniform shear stress on the sideface is solved, and the solution of a cone acted on by gravity is given by converting constant body forces into surface forces.     

Investigation of the dynamic behavior of two collinear anti-plane shear cracks in a piezoelectric layer bonded to two half spaces by a new method

The dynamic behavior of two collinear anti-plane shear cracks in a piezoelectric layer bonded to two half spaces subjected to the harmonic waves is investigated by a new method. The cracks are parallel to the interfaces in the mid-plane of the piezoelectric layer. By using the Fourier transform, the problem can be solved with two pairs of triple integral equations. These equations are solved by using Schmidt’s method. This process is quite different from that adopted previously. Numerical examples are provided to show the effect of the geometry of cracks, the frequency of the incident wave, the thickness of the piezoelectric layer and the constants of the materials upon the dynamic stress intensity factor of cracks.