蜂窝材料的非线性剪切行为

THE NON-LINEAR SHEARING BEHAVIOR OF CELLULAR MATERIALS

将梁的弹性大挠度弯曲理论应用于蜂窝壁板,研究了大变形条件下蜂窝材料的非线性剪切变形行为.研究中将椭圆积分形式的解答应用于蜂窝胞元的壁板,并利用平衡和变形谐调条件建立了相应的非线性代数方程组,然后利用牛顿-拉夫森迭代法求解.在上述数值解法的基础上,确定了等效剪应力和剪应变间的非线性曲线,并给出了剪切模量的非线性修正因子,该因子只与蜂窝形状和变形情况有关,而与细长比无关,因而能描述一类蜂窝材料的剪切行为.与有限元数值结果的比较表明,此方法具有较好的精度.

Basing on the elastic bending theory of beams in large deflection, the non-linear shearing behavior of cellular materials under large deformation is studied in the paper. Non-linear algebra equations are established from the balance and kinematical conditions, which contain the elliptic-integral-form solutions and can be solved by using the New-Raphson method. Basing on the numerical results above,a non-linear relationship between shearing stress and strain is presented. A non-linear modified factor of shearing modulus is also given out,which is only related with the shape of the celular materials and deformation results and is independent of the ratio of t and l,and thus it can describe a kind of cellular materials＇ shearing behavior. Compared with the results of Finite Element Method （FEM） ,the results in this paper have fine precision.