受均布荷载作用含加强椭圆环无限大板解析解  

Analytical solution for an infinite plate with a reinforcing elliptic ring under a remote uniform load

作　　者：李昊[1] 房世海[1] 

机构地区：[1]合肥工业大学土木与水利工程学院,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2013年第9期1106-1109,共4页Journal of Hefei University of Technology：Natural Science

摘　　要：文章基于复变函数方法,利用保角变换求解了含椭圆孔内嵌异质加强椭圆环无限大板在远端受均布荷载作用的弹性问题,并给出了加强椭圆环及无限大板的位移和应力的级数解,分析了加强椭圆环的材料属性和几何尺寸对无限大板界面处应力的影响。结果表明,选择合适的加强椭圆环的材料属性和几何尺寸可以显著降低板界面处的最大应力。研究结果为加强椭圆环的优化设计提供了理论依据。Based on the complex variable function method and the technique of conformal mapping, a general solution for the elasticity problem of a reinforced elliptic hole embedded in an infinite plate subjected to a remote uniform load is provided in this paper. The series expansion solutions for the displacement an~,stresses in the reinforcing ring and the plate are derived, and the effect of the materi- al property and geometric configurations on the interfacial stresses is investigated. The results show that the maximum stresses at the elliptic boundary of the plate drop off evidently if appropriate materi- al and geometric configurations of the reinforcing ring are chosen. The presented formulae provide a theoretical approach for the optimization design of the reinforcing elliptic ring.

关 键 词：平面弹性 加强椭圆环 均布荷载 复变函数 保角变换 

分 类 号：O343.4[理学—固体力学]