摘要
硬脑膜是一种粘弹性材料,为控制硬脑膜在脑压作用下的膨出度,对粘弹性薄膜受压膨出挠度作力学分析。以位移为未知量,从粘弹性材料的积分型本构关系出发将Fpple薄膜大挠度理论从弹性推广到粘弹性膜,得到一组非线性积分偏微分方程。先在空间域上运用Galerkin方法将积分偏微分方程组化为积分常微分方程组。然后,在时间域上运用数值积分和有限差分将方程离散为非线性代数方程组。本文对四周固定夹紧的圆形、椭圆形和矩形薄膜进行了求解,并将求解结果用于颅底缺损重建膜的膨出量计算,计算值与实验值吻合,为颅底外科提供一个理论分析方法。
In this paper, by using the integral type constitutive equation of viscoelastic, the Fopple membrane large deflection equation about the displacement was generalized. A series of nonlinear integral partial differential equations were obtained. In order to solve this series of equations, Galerkin method was employed in the spatial domain and a set of simplified equations which are only related to the time variant were presented. Then, by using the finite differential method in time domain, the equations were reduced to a set of nonlinear algebraic equations. The solutions of a circular, rectangular, and elliptic membrane were given respectively. In the example about dural reconstruction of cranial base defects, the computa-tive results are basically consistent with the experimental results. It may provide a new method of analysis for cranial base surgery.
出处
《力学季刊》
CSCD
北大核心
2001年第3期317-321,共5页
Chinese Quarterly of Mechanics
基金
国家自然科学基金(39670199)
