任意直角梯形截面梁扭转刚度的无穷级数解法(英文)  

Infinite Series Solutions for the Torsional Rigidity of a Prism with Right-Angled Trapezoid Cross-Sections

作　　者：杨纲[1,2] 郝一龙[1] 胡启方[1] 高成臣[1] 

机构地区：[1]北京大学微电子学研究所微米/纳米加工技术国家级重点实验室,100871 [2]北京大学深圳研究生院,广东深圳518055

出　　处：《传感技术学报》2012年第5期594-598,共5页Chinese Journal of Sensors and Actuators

基　　金：National High Technology Research and Development Program of China(2008AA042201)~~

摘　　要：分析研究截面为底角10°～80°直角梯形的弹性梁扭转刚度的解法,并用有限元模拟进行了检验。为解决这一弹性梁自由扭转问题(圣维南问题)的特殊情形,在本文中首次采用了基于布赛乃斯克流体力学假设的无穷级数解法。分析解法与软件模拟的结果对比显示,在所研究的范围内其误差精度不超过3%。对于底角为54.74°的特殊直角梯形截面梁,该解法的精度误差小于1.5%。The torsion rigidity of an elastic beam with right-angled trapezoid cross sections and base angles ranging from 10°to 80°is studied analytically and examined through FEM（Finite Elemente Method）simulation.To solve this special case of the free torsion problems of elastic prisms（the Saint-Venant problems）the infinite series method based on the Boussinesq’s hydromechanical assumptions is adopted and firstly reported in this work.By comparison with the FEM simulation results,the analytical ones give a precise prediction with errors less than 3% in the study range.For the torsion rigidity of trapezoid cross-sections beam with 54.74° base angle,the analytical results give a precise prediction with errors less than 1.5%.

关 键 词：圣维南问题 直角梯形截面梁 扭转刚度 流体力学假设 无穷级数法 

分 类 号：TN305[电子电信—物理电子学]