生物骨圆柱壳的蠕变屈曲分析

Creep Buckling Analysis of Biologic Bone in the Form of Cylindrical Shell

将生物胫骨考虑为纤维增强的粘弹性复合材料圆柱壳,并进行了蠕变屈曲分析.采用广义Maxwell模型,提出了胫骨的粘弹性复合材料圆柱壳力学模型,得到了受轴向载荷作用粘弹性圆柱壳的蠕变屈曲控制方程.通过Laplace变换,将控制方程转换到相空间,在相空间中得到临界荷载的表达式;经过Laplace逆变换,得到了随时间变化的屈曲荷载曲线.最后依据具体的人胫骨粘性系数,对人胫骨轴压屈曲压力进行计算和分析比较,得到了蠕变屈曲临界载荷曲线,给出了蠕变屈曲荷载随胫骨长度及时间的变化曲线.研究结果表明:将胫骨考虑为纤维增强的粘弹性复合材料圆柱壳其瞬时临界荷载值、持久临界荷载值均小于将该胫骨考虑为功能梯度圆柱壳的屈曲荷载.

Based on the analysis to macroscopic structure and microscopic structure of the bone,the shinbone was considered as cylindrical shell with viscoelastic and anisotropical character and the creep buckling analysis had been done.By introducing Maxwell model,the mechanical model of cylindrical shell on viscoelastic composite material was established.The creep buckling control equation of viscoelastic composite cylindrical shell under axially load was given.Based on Laplace-transform,the control equation was transformed into phase space,in which the critical load expression was obtained.Followed by inverse Laplace-transform,the time-dependent creep load curve was obtained.Finally,according to the viscosity coefficient of human shinbone,the axial buckling load was calculated and analyzed,the creep buckling critical load curve obtained.The variation curves of creep buckling load to the length of the shinbone and the time were figured.The results show that the shinbone is considered for fiber-reinforced viscoelastic composite cylindrical shell,its instantaneous critical load value and lasting critical load value are less than the buckling critical load values considering the shinbone as functionally graded cylindrical shell load.