双模量泡沫铝芯夹层梁的弯曲计算分析

Bending calculation and analysis of bimodulous aluminum foam core laminated beam

研究了双模量泡沫铝芯夹层梁的弯曲问题。本文利用双模量材料纯剪切应力状态单元体,推导出了双模量材料剪切弹性模量表达式。证明了作用在双模量梁上的横向载荷,对任意边界条件下的双模量梁中性轴位置无影响,确定了双模量泡沫铝芯夹层梁弯曲时的梁中性轴位置。在考虑剪切效应的基础上,建立了双模量泡沫铝芯夹层梁弯曲的微分方程,利用奇异函数推导出了外载荷作用下双模量泡沫铝芯夹层梁弯曲的应力及挠度表达式,并讨论分析了泡沫铝芯夹层拉压弹性模量对双模量泡沫铝芯夹层梁弯曲的影响。算例分析表明,对双模量泡沫铝芯夹层梁的弯曲挠度计算时,不但要考虑剪切变形的影响,还要考虑泡沫铝芯的双模量特性。

Bending of bimodulous aluminum foam core laminated beam is studied. Using pure shear stress state unit body of bimodulous material, expression of shear modulus of bimodulous material is derived. The fact that lateral loads have no effect on the position of the neutral axis of bimodulous beam under arbitrary boundary conditions is proved, and the position of the neutral axis of bending bimodulous aluminum foam core laminated beam is determined. On the basis of considering shear effect, the bending differential equation of bimodulous aluminum foam core laminated beam is established, expressions of bending stress and deflection of bimodulousaluminum foam core laminated beam under loads are derived by using singular function, and the influence of modulus of elasticity in tension and compression of aluminum foam core sandwich on bending of bimodulous aluminum foam core laminated beam is analyzed. Computational results indicate that the influence of modulus of elasticity in tension and compression of aluminum foam core sandwich on bending of bimodulous aluminum foam core laminated beam can not be ignored.