CAJ | 학술논문

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％.
분석연구절면위저각10°～ 80°직각제형적탄성량뉴전강도적해법,병용유한원모의진행료검험.위해결저일탄성량자유뉴전문제(골유남문제)적특수정형,재본문중수차채용료기우포새내사극류체역학가설적무궁급수해법.분석해법여연건모의적결과대비현시,재소연구적범위내기오차정도불초과3％.대우저각위54.74°적특수직각제형절면량,해해법적정도오차소우1.5％.
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％.