非线性本构关系下两端固定多孔梁的大挠度弯曲变形

Large-Deflection Bending Deformation of Fixed Porous Beams at Both Ends under Non-linear Constitutive Relations

摘要: 本文以经典梁理论和非线性本构关系为基础，研究了两端固定多孔梁在不同的孔隙分布类型下受到外部均匀荷载作用的大挠度弯曲问题。首先设多孔梁的弹性模量与应变是线性函数关系，对非线性本构关系下多孔梁弯曲问题的基本方程进行了推导。采用打靶法计算出该边界条件下的多孔梁弯曲问题的数值解，分析非线性本构参数、载荷、孔隙率、孔隙分布类型对弯曲变形行为的影响。

Abstract: Based on classical beam theory and nonlinear constitutive relationships, the large deflection bending problem of a fixed porous beam under different pore distribution types under external uniform loads was studied. Firstly, the elastic modulus and strain of porous beams are assumed to be a linear function relationship, and the basic equations for the bending problem of porous beams under nonlinear constitutive relationships are derived. The numerical solution of the bending problem of porous beam under this boundary condition is calculated by shooting method, and the effects of nonlinear constitutive parameters, load, porosity and pore distribution type on bending deformation behavior are analyzed.