Design Models in Linearized Solid Mechanics

The paper is devoted to design models in linearized solid mechanics     

压电介质平面问题的基本解

应用复变函数的方法,对于压电介质平面问题,分析导出了无限介质或半无限介质受任意 集中载荷作用时的复势函数基本解;这些结果可作为边界元法的基本解,以求解具有复杂边界压电体的平面问题。     

计算固体力学的发展及其在航空航天工程中的应用

本文讨论了计算固体力学发展的基础和背景,并以它在航空航天领域中的应用为例,说明计算力学的应用所带来的益处。还讨论了为进一步发展计算固体力学应深入研究的一些课题。最后简要展望了计算固体力学的发展前景。     

New Transforms for the Resolving Equations in Elastic Theory and New Integral Transforms, with Applications to Boundary-Value Problems of Mechanics

This paper reviews results from an analysis of exact boundary-value solutions of static and dynamic elasticity obtained by the method of integral transforms. Consideration is given to the solutions of problems for a half-space and a blunted hollow cone, the heat conduction problem for a cone, and the diffraction problem for a cone with a hole along the generatrix. Solutions of mechanics problems are analyzed and the method of integral transforms is generalized     

Pressure Distribution in a Semi-infinite Horizontal Aquifer with Steep Gradients Due to Steady Recharge and/or Drainage: The Exact Explicit Solution

Groundwater flow with steep gradients in a vertical plane of infinite horizontal extension due to arbitrary non-symmetric strip sources and/or sinks can be described by the 2D Laplace equation. Notwithstanding the strongly nonlinear character of the free surface boundary condition, the exact analytical solution to this problem is developed in a closed form by employing neither the Dupuit assumption nor any other form of linearization. The first section of the development, still including the unsteady case, leads via conformal mapping and transformation procedures to a singular integro-differential-equation for the transient groundwater table. From this point onwards we restrict ourselves to the steady case for which the exact solution of the 2D Laplace equation for the pressure head and the location of the groundwater table was achieved. The solution is expressed exclusively in algebraic terms without the need for iterative procedures. It can not only be applied to real world phenomena, including a simple solution of the inverse problem, but also provide a new transparency regarding the solution characteristics and may serve as a standard for investigating numerical solutions and the domain of validity of simplified approaches. The computer program can be downloaded from www.tu-dresden.de/fghhihm/hydrologie.html     

二维直角平面内固定圆形夹杂对稳态入射反平面剪切波的散射

利用复变函数法、多极坐标及傅立叶级数展开技术求解了二维直角平面内固定圆形夹杂对稳态入射反平面剪切（shearing horizontal, SH）波的散射问题。首先构造出介质内不存在夹杂时的入射波场和反射波场,然后建立介质内存在夹杂时由夹杂边界产生的能够自动满足直角边应力自由条件的散射波解,从而利用叠加原理写出介质内的总波场。利用夹杂边界处位移条件和傅立叶级数展开方法列出求解散射波中未知系数的无穷代数方程组,在满足计算精度的前提下通过有限项截断,得到相应有限代数方程组的解,最后通过算例具体讨论了二维直角平面水平边界点的位移幅度比和相位随量纲一波数、入射波入射角及夹杂位置的不同而变化的情况,结果表明了算法的有效实用性。