应用数学和力学2025，Vol.46Issue(12)：1584-1597,14.DOI:10.21656/1000-0887.450256
DQM研究双相功能梯度材料中厚度扇形板V形切口的应力奇性
Study on V-Notch Stress Singularity in Functionally Graded Bi-Material Medium-Thickness Sector Plates With the DQM
摘要
Abstract
A practical method for analyzing stress singularity indexes was proposed for the problem of notch tips in bi-material functionally graded medium-thickness plates:the differential quadrature method(DQM).Firstly,according to the equilibrium equations in the cylindrical coordinate system and based on the series as-ymptotic expansion assumption about the displacement field at the tip of the notch,the eigenvalue problem of the ordinary differential equations(ODEs)with respect to the singularity exponent at the notch tip of function-ally graded bi-material medium-thickness plates was derived,and the radial boundary condition of the notch was expressed as a combination of the singularity exponent and the characteristic angular function.Then,under the DQM theory,the eigenvalue problem of ODEs was transformed into a standard-type eigenvalue problem of generalized algebraic equations,and the stress singularity index at the notch tip under the corresponding bound-ary condition was calculated for only one time,and was verified to be valid by a numerical example.Finally,the stress singularity index of functionally graded and pure metal/pure ceramic hybrid plates was calculated with the DQM.The research indicates that,the mixing of pure ceramic plates and pure metal plates with func-tional gradient plates has different effects on the stress singularity index,respectively,with the change of the notch angle.关键词
应力奇性指数/微分求积法/功能梯度板/切口/渐近展开Key words
stress singularity index/differential quadrature method/functionally graded plate/V-notch/as-ymptotic expansion分类
数理科学引用本文复制引用
曹玖银,李思燃,葛仁余..DQM研究双相功能梯度材料中厚度扇形板V形切口的应力奇性[J].应用数学和力学,2025,46(12):1584-1597,14.基金项目
安徽省自然科学基金(1808085ME147)本文作者衷心感谢安徽工程大学自然科学研究重点项目(xjky2022166)对本文的资助. （1808085ME147）
