A three dimensional finite element method for large elastic deformations of ventricular myocardium .1. Cylindrical and spherical polar coordinates
A three dimensional finite element method for large elastic deformations of ventricular myocardium .1. Cylindrical and spherical polar coordinates
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DOI：
10.1115/1.2796031
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发表时间：
1996-11-01
影响因子：
1.7
通讯作者：
McCulloch, AD
中科院分区：
文献类型：
--
作者：
Costa, KD;Hunter, PJ;McCulloch, AD
针对心肌等不可压缩、非线性弹性、各向异性材料的大变形问题，建立了三维Galerkin有限元法。采用柱单元和球单元求解轴对称问题。误差通常小于2%。等容插值和压力边界约束方程在特殊情况下增强了低阶曲线元素（自由度节省69%，厚壁圆柱体充气的求解时间节省78%）。线性拉格朗日和三次埃尔米特多项式的广义张量积允许自定义元素具有改进的性能，包括自由度节省52%和压缩圆盘的求解时间节省66%。这样的计算效率对于诸如心脏建模的大规模问题变得重要。
A three-dimensional Galerkin finite element method was developed fro large deformations of ventricular myocardium and other incompressible, nonlinear elastic, anisotropic materials. Cylindrical and spherical elements were used to solve axisymmetric problems with r.m.s. errors typically less than 2 percent. Isochoric interpolation and pressure boundary constraint equations enhanced low-order curvilinear elements under special circumstances (69 percent savings in degrees of freedom, 78 percent saving in solution time for inflation of a thick-walled cylinder). Generalized tensor products of linear Lagrange and cubic Hermite polynomials permitted custom elements with improved performance, including 52 percent savings in degrees of freedom and 66 percent savings in solution time for compression of a circular disk. Such computational efficiencies become significant for large scale problems such as modeling the heart.