Costa K D, Hunter P J, Rogers J M, Guccione J M, Waldman L K, McCulloch A D
Department of Bioengineering, University of California San Diego, La Jolla, CA, USA.
J Biomech Eng. 1996 Nov;118(4):452-63. doi: 10.1115/1.2796031.
A three-dimensional Galerkin finite element method was developed for 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 savings 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.
针对心室心肌以及其他不可压缩、非线性弹性、各向异性材料的大变形问题，开发了一种三维伽辽金有限元方法。使用圆柱和球形单元来求解轴对称问题，均方根误差通常小于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单元（自由度节省69%，厚壁圆筒膨胀求解时间节省78%）。线性拉格朗日多项式和三次埃尔米特多项式的广义张量积允许创建性能更优的自定义单元，包括圆盘压缩时自由度节省52%，求解时间节省66%。对于诸如心脏建模这样的大规模问题，这种计算效率变得十分显著。
