非线性本构关系下两端固定铰支梁的弯曲变形

Bending Deformation of Hinged-Fixed Beams at Both Ends under Nonlinear Constitutive Relations

摘要: 本文基于经典梁理论，假设弹性模量与应变成线性关系(本构关系非线性)，推导了受铅垂均布载荷作用的两端固定铰支梁弯曲的基本方程。并对基本方程及边界条件无量纲化，以使其具有一般性。然后采用数值法求解该问题无量纲基本方程的数值结果。分析了大挠度和小挠度两种情况下本构关系非线性和铅垂分布载荷对梁弯曲变形以及中性轴位置的影响并进行比较。

Abstract: Based on the classical beam theory, this paper assumes that the elastic modulus and the strain become a linear relationship (non-linear constitutive relationship), and derives the basic equation for the bending of a fixed hinge beam at both ends under a vertical uniform load. And the basic equations and boundary conditions are dimensionless to make them general. Then, the numerical method is used to solve the numerical results of the non-dimensional basic equation of the problem. The influence of the nonlinear constitutive relationship and the vertical distributed load on the bending deformation of the beam and the position of the neutral layer in the two cases of large deflection and small deflection are analyzed and compared.