横观各向同性体非轴对称半空间问题的统一解  

United solution of asymmetric half-space problem for transversely isotropic elastic body

作　　者：张学民[1] 阳军生[1] 李婕[2] 顿志林[2] 高雪冰[2] 

机构地区：[1]中南大学土木建筑学院,长沙410075 [2]河南理工大学土木工程学院,河南焦作454000

出　　处：《哈尔滨工业大学学报》2009年第10期177-180,共4页Journal of Harbin Institute of Technology

基　　金：国家自然科学基金资助项目(50808178);河南省自然科学基金资助项目(9740900)

摘　　要：利用Hankel积分变换和Bessel函数理论,在象域中推导了任意非对称表面荷载作用下横观各向同性弹性半空间体内应力分量和位移分量的统一表达式.此解答具有一般性,包含了非对称荷载作用下各向同性弹性半无限体问题.该解答可用于求解单向水平荷载、圆形单向均布水平荷载、单向水平集中荷载、半球形单向水平荷载以及凹盆形单向水平荷载作用等多种荷载边界条件下一般空间问题的求解.Based on the three-dimensional analytical solution in the polar coordinate system obtained by displacement function method,the generalized expressions of displacement and stress component in the transversely isotropic half-space body under discretional asymmetrical loadings on the surface are derived in the image domain.The united solution is performed by using Hankel integration transform and Bessel function theory,and its universality characteristic includes the solutions for isotropic half-space elastic body under discretional asymmetrical loadings. The obtained solutions can be used to solve multiform asymmetrical problems of transversely isotropic semi-infinite elastic body under different boundary conditions, such as unilateralism level load, unilateralism level uniform load distributed on a circular area, unilateralism level point force load, halfspherical unilateralism level load and concave-basin unilateralism level load on a circular area.

关 键 词：工程力学 横观各向同性弹性体 位移法 非轴对称半空间问题 HANKEL变换 

分 类 号：TB12[理学—工程力学] TU470[理学—力学]