弹性压应力波下轴向功能梯度变截面梁动力压曲稳定分析

Dynamic buckling of axially functionally-graded beams with non-uniform cross-section under elastic compression stress wave

基于微元法以及能量守恒原理,导出了轴向功能梯度变截面梁屈曲微分控制方程及应力波波前附加边界条件,研究了轴向功能梯度变截面梁屈曲与压应力波耦合动力屈曲问题。采用较为简单的数值方法,即将位移函数按Taylor级数或是Chebyshev多项式展开,从而将轴向功能梯度变截面梁屈曲问题的变系数微分控制方程转化为含参量的线性代数方程组,进而得到了含时间参量的动力屈曲问题特征方程,随后对轴向功能梯度变截面梁动力屈曲问题进行了数值研究,探讨了变截面和材料不均匀性对系统屈曲临界力参数的影响。研究表明,该数值方法具有很好的精度和收敛性。

Here,the dynamic buckling problem during the buckling of axially functionally graded beams with variant cross-section being coupled with compression stress wave was investigated. The buckling differential governing equation and the wavefront additional boundary conditions of compression stress wave for an axially functionally graded beam with variant cross-section were established based on the differential-element method and the principle of energy conservation. A simpler numerical method was introduced to transfer this varying-coefficient governing differential equation into a set of linear algebraic equations with the displacement function being expanded using Taylor series or Chebyshev polynomials. Then the eigen-equation for the axially functionally graded beam with non-uniform cross-section was obtained. Moreover, a numerical investigation for the dynamic buckling of the axially functionally graded beams was conducted to discuss the effects of variant cross-section and material inhomogeneity on the system, s critical buckling force parameters. The results showed that the proposed method has good accuracy and convergence.