轴对称任意梯度圆筒的弹性动力学解

基于轴对称平面应变问题的运动方程及弹性梯度材料的应力和位移关系,通过将圆筒分层使材料性质离散为分段常数函数,同时在时域内应用有限差分格式,求得了材料性质沿径向梯度变化的圆筒弹性动力学解。本文解不仅适合任意梯度的弹性圆筒,而且容易满足多种形式的初始条件和边界条件。通过对材料性质沿径向为连续函数分布和分段函数分布的梯度圆筒数值分析,并与已有文献结果比较,得出本文解与已有文献的解吻合较好,验证了本文解的正确性和有效性。对材料性质为分段函数的三层组合圆筒分析发现,中间功能梯度层的指数分布因子对圆筒的径向位移和应力随时间变化都会产生显著影响。

An elasto-dynamic solution to hollow cylinders with arbitrarily graded materials under axisymmetric condition

Based on the motion equations of the axisymmetric plane-strain problem and the stress-displacement relations of elastic graded materials,an elasto-dynamic solution to hollow cylinders with material properties varying in the radial direction is acquired by dividing the cylinder into subshells,with material properties discretized as piecewise constant functions,and using the finite difference scheme in time domain.The present solution may not only be applied to arbitrarily graded elastic hollow cylinders,but also readily satisfy a variety of initial conditions and boundary conditions.According to the numerical analyses for the graded cylinders with material properties varying as a continuous function and a piecewise function,the correctness and validity of the present solution are verified.From the analysis of the combined cylinder with three layers possessing the material property as a piecewise function,it is found that the exponential distribution factor of the middle layer as a functionally graded one has significant influence on radial displacements and stresses varying with time.