具有功能梯度加强环的有限尺寸开孔板应力集中问题  

Stress Concentration in Finite Plates With Functionally Graded Rings Around Circular Holes

作　　者：杨权权[1] 朱为国[1] 刘飞[1] 

机构地区：[1]淮阴工学院江苏省先进制造技术重点实验室,江苏淮安223003

出　　处：《应用数学和力学》2016年第11期1239-1246,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金青年科学基金(11502090);江苏省高校自然科学研究面上项目(15KJB130001)~~

摘　　要：基于复变函数理论,结合最小二乘边界配点法,对具有功能梯度加强环的有限尺寸开孔板在任意均布载荷作用下的应力集中问题进行了研究.首先,采用分层均匀化方法,给出了材料参数沿径向任意变化的功能梯度加强环内的复势及孔边应力的半解析解;然后,通过几组数值算例,讨论了组分梯度、加强环厚度、板相对尺寸及偏心率的变化对孔边应力集中的影响.结果表明,通过合理选择功能梯度加强环内材料参数的递变规律及加强环的厚度,可以有效缓解有限尺寸开孔板内的应力集中.Based on the complex variable method and combined with the least squares boundary collocation technique,the problem of stress concentration in finite plates with functionally graded rings around circular holes was studied when the plates were subjected to arbitrary uniform distributed loads at the outer boundaries. With the method of piecewise homogeneous layers,the semi-analytic solutions of stresses around the hole were first given through formulation of the complex potentials in the functionally graded ring with arbitrary radial elastic properties. The numerical results of stress distributions around the holes were then obtained for plates with different material properties,ring thicknesses,plate sizes and hole eccentricities,respectively. It is found that the stress concentration in the finite plate can be significantly reduced on the condition of a proper distribution of the radial elastic property and a proper thickness of the ring.

关 键 词：功能梯度材料 复变函数 有限尺寸 圆孔 应力集中 

分 类 号：O341[理学—固体力学]