基于2种经典梁理论与高阶梁理论对比解析梁弯曲行为的研究

Comparative Analysis of Bending Behavior of Beams Based on Two Classical Beam Theories and Higher-order Beam Theory

以箱型梁为例,分析了力学课程中常用的Euler-Bernoulli和Timoshenko经典梁理论与高阶剪切变形理论求解梁弯曲行为时的处理方法。研究了在不同梁理论框架下位移场和应力场分布特点。Euler-Bernoulli梁理论使用的平截面假设导致横截面变形锁定,过高估计了弯曲刚度。Timoshenko梁理论允许梁横截面发生剪切变形,但依然限制变形后的截面为平面,忽略了截面翘曲。高阶梁理论通过引入翘曲形状函数的方式能够更加有效地描述正应力和剪应力分布特征。

Taking box beams as an example,this paper analyzed the processing methods for solving beam bending behavior using the classical Euler-Bernoulli and Timoshenko beam theories and the high-order shear deformation theory,which were commonly employed in mechanics curricula.The distribution characteristics of displacement and stress field under different beam theory frameworks were investigated.Notably,the flat section hypothesis adopted by the Euler-Bernoulli theory inherently constrains cross-sectional deformation,leading to an overestimate of bending stiffness.The Timoshenko theory acknowledges shear deformation within the beam's cross-section but maintains a planar constraint,overlooking cross-sectional warping.However,the high-order beam theory,by incorporating a warping shape function,can more effectively describe the distribution characteristics of both normal and shear stress.