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半无限平面问题的相对位移
引用本文:雷国辉,孙华圣,吴宏伟.半无限平面问题的相对位移[J].岩土力学,2014,35(5):1224-1230.
作者姓名:雷国辉  孙华圣  吴宏伟
作者单位:1.河海大学 岩土力学与堤坝工程教育部重点实验室,南京 210098;2.河海大学 岩土工程科学研究所,南京 210098; 3.香港科技大学 土木及环境工程学系,香港
基金项目:国家自然科学基金项目资助(No. 51278171);中央高校基本科研业务费专项资金项目资助(No. 2011B02814,No. 2010B28114);2010年度江苏省高校青蓝工程培养计划资助;高等学校学科创新引智计划即“111计划”资助(No. B13024);长江学者和创新团队发展计划资助(No. IRT1125)
摘    要:通过Flamant和Melan的解析解答、Mindlin解答的积分蜕化公式以及有限元数值分析计算结果,展示了在半无限平面问题中线荷载作用方向位移解答的不确定性。线荷载作用方向没有绝对位移,只有相对位移,但相对位移会随着与位移约束参考点距离的增大而增大,或随着线荷载在垂直于半平面方向分布长度的增大而增大,不具收敛性。这意味着,在解析和数值分析中,纯粹的半平面问题的位移解答具有多值性,因此,将岩土工程问题作为半空间问题进行分析是必要的。

关 键 词:位移  半平面  半空间  解析解  数值分析  
收稿时间:2013-02-20

Relative displacements in semi-infinite plane
LEI Guo-hui,SUN Hua-sheng,NG Charles Wang Wai.Relative displacements in semi-infinite plane[J].Rock and Soil Mechanics,2014,35(5):1224-1230.
Authors:LEI Guo-hui  SUN Hua-sheng  NG Charles Wang Wai
Institution:1. Key Laboratory of Geomechanics and Embankment Engineering of Ministry of Education, Hohai University, Nanjing 210098, China; 2. Geotechnical Research Institute, Hohai University, Nanjing 210098, China; 3. Department of Civil and Environmental Engineering, the Hong Kong University of Science and Technology, Hong Kong, China
Abstract:By using the analytical Flamant and Melan solutions, the integral formulae derived from Mindlin’s equations, solutions in semi-infinite plane are derived to calculate displacements and compare with computed results from the finite element method. It is found that the calculated displacements are indeterminate in the line loading direction, where no absolute displacements but only relative displacements can be obtained. However, the calculated relative displacements increase with an increasing in the distance away from the reference point of displacement constraint; and they also increase with an increasing length of line load distribution normal to the half-plane, leading to non-convergence. This means the derived displacement solutions of pure half-plane problems are multivalued. Thus, it is necessary to analyze geotechnical problems using the half-space assumption.
Keywords:displacement  half-plane  half-space  analytical solution  numerical analysis
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