Comparative Analysis of Bending Behavior of Beams Based on Two Classical Beam Theories and Higher-order Beam Theory
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 distribu-tion characteristics of displacement and stress field under different beam theory frameworks were inves-tigated.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 ac-knowledges 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.
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