摘要
通过引入两个位移函数,对用位移表达的运动平衡方程作了简化.利用算子理论,严格地导出了横观各向同性非耦合热弹性动力学问题的通解.对于静力学问题,通解的形式可进一步简化成用4个准调和函数来表示.具体考察了横观各向同性体内平面裂纹上下表面有对称分布温度作用的问题,推广了势理论方法,导出了一个积分方程和一个微分-积分方程.针对币状裂纹表面受均布温度作用情形,给出了具体的解.
By the introduction of two displacement functions, the equations of motion in terms of displacement for a transversely isotropic elastic medium with thermal effect are simplified. The general solution of dynamic problem for the uncoupled thermoelastic theory is strictly derived utilizing the operator theory. It can be expressed by two functions: one satisfies a second-order wave equation and the other satisfies a sixth-order homogeneous partial differential equation. For static problem, the general solution is further simplified by virtue of the generalized Almansi's theorem, and can be expressed in terms of four quasi-harmonic functions. The problem of a flat crack located in a plane perpendicular to the symmetric axis and distributed with prescribed temperature is investigated. The potential theory method proposed by Fabrikant is generalized for thermoe-lasticity. A new potential corresponding to the temperature field is introduced, and consequently, an integral equation and an integro-differential equation are derived. For a penny-shaped crack with uniform distributing temperature, exact solutions can be obtained using Fabrikant's results. It is found that all expressions for the thermoelastic field can be expressed in terms of elementary functions. The stress intensity factor at the crack tip is derived exactly. Comparison with existent results shows a good agreement. Moreover, the proposed method can be used to analyze non-axisymmetric problems such as a penny-shaped crack subjected to a point temperature load, for which the Hankel transform method can not be utilized. Further results in this respect will be reported in other papers.
出处
《力学学报》
EI
CSCD
北大核心
2003年第5期578-583,共6页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金(10002016)
教育部留学回国人员科研启动基金