工程科学与技术2017，Vol.49Issue(2)：54-61,8.DOI:10.15961/j.jsuese.201501082
不同加载条件下平面应力圆盘应力和位移的全场解
Full-field Solutions to Stresses and Displacements in the Plane Stress Disk Under Different Loading Conditions
摘要
Abstract
Investigation on the stress displacement field for the plane stress disk,which is also called the Brazilian disk,has an important theoretical and practical value for elastic mechanics,rock mechanics and fracture mechanics.In order to obtain the closed-form solution to stresses and displacements in the Brazilian disk under different loading conditions,based on the theory of elasticity and a series solution of stress for the Brazilian disk subjected to a pair of compressive forces,the explicit expressions of displacements were obtained for the Brazilian disk under diametral-compression loading.The series solutions to stresses were then derived by using mathematical analysis method and the explicit expressions of displacements were obtained subjected to uniformly distributed pressure.The calculated results showed that the stressesσθ,σrand radial displacement u were symmetric to the loading line θ =0,and the stress τrθ and tangential displacement v were anti-symmetricto θ =0.At the loading point of a concentrated force and the starting point or the end point of the distributed pressure,the stress field and displacement field had a abrupt change.For the same condition,the effect of the loading types on the displacements was less than that on the stresses.On the other hand,the loading type only had an important effect on the stress or displacement distributions near the loading point (i.e.,when p was larger),and the effect on the stress or displacement distributions was very small at points away from the loading point or loading range (i.e.,when p is smaller).This conclusion agreed well with the Saint-Venant principle.In addition,the radial displacement increased with the increase ofp,and it had a maximum value nearp =0.7.The further analysis showed that the series formula obtained by other researcher can be simplified and combined,and the formula derived from the present paper is the simplest form for the Brazilian disk loaded by pressure.关键词
平面应力/巴西圆盘/应力/位移/幂级数解Key words
plane stress/Brazilian disk/stress/displacement/series solution分类
数理科学引用本文复制引用
董世明,李一凡,徐积刚..不同加载条件下平面应力圆盘应力和位移的全场解[J].工程科学与技术,2017,49(2):54-61,8.基金项目
国家自然科学基金资助项目(11172186) （11172186）
