V型波纹夹层板弯曲问题的高阶剪切变形理论计算方法

Calculation method for bending of V-type corrugated core sandwich panels employing high-order shear deformation theory

为了求解V型波纹夹层板的弯曲变形与应力,本文应用能量等效法求解芯层的等效弹性模量,将波纹夹层板中间芯层等效成正交异性板,夹层板整体则等效成层合板。依据高阶剪切变形理论和最小势能原理,推导波纹夹层板的弯曲微分方程,并采用双傅立叶级数法求解该方程。通过薄夹层板算例验证,在夹层板的变形计算结果中,本文方法与有限元法吻合良好;在夹层板的应力计算结果中,有限元法计算的弯曲应力沿波纹方向分布表现出振荡现象,本文方法的应力分布是其振荡峰值的光滑插值曲线。集中载荷作用下的厚夹层板算例表明,在平行于矩形板边缘的横剖面上,本文方法计算的位移最大值和应力最大值普遍大于有限元法结果。

In order to solve bending deflection and stress of corrugated core sandwich panels, the middle core of a sandwich panel was considered as an orthotropic panel, and the whole sandwich panel was equivalent to laminated panel. Equivalent elastic moduli were solved by energy equivalence method. Bending differential equations solved by double Fourier series method were derived according to high-order shear deformation theory and minimum potential energy principle. It is validated that the deformation results of this proposed method agree well with those of FEM in case of thin sandwich plate calculation. As to calculation results of stress, the bending stress calculated by FEM shows fluctuation along corrugation direction, whose peak value interpolation smooth curve is the stress distribution curve of this proposed method. When the thick sandwich panel acts as a concentrated load, it is indicated that the maximum deformation value and the maximum stress value computed by the present method are generally greater than the results of FEM in the cross section in parallel with the rectangular panel edges.