一种生物类材料广义双曲膜壳计算模型
发布时间：2019-03-22 09:30
【摘要】：基于Ciarlet-Lods定义的广义膜壳,首次提出了该模型的一种Galerkin协调有限元离散格式。首先,对积分区域进行三角剖分,并在三角网格上对位移前两个分量用带泡一次Lagrange插值多项式逼近,而对第三个分量,即法向位移,用一次Lagrange插值多项式逼近。其次,讨论了广义膜壳弱解的存在性、唯一性和数值解的存在性、唯一性以及弱解与数值解的误差估计。最后,本文对生物材料的双曲膜壳采用该方法进行数值模拟,得到不同网格下双曲壳中性面上的位移,并通过分析数值模拟结果证明了有限元离散格式的收敛性和有效性。
[Abstract]:Based on the generalized membrane shell defined by Ciarlet-Lods, a Galerkin conforming finite element discrete scheme for the model is proposed for the first time. Firstly, the integral domain is triangulated, and the first two components of the displacement are approximated by the Lagrange interpolation polynomial with bubbles on the triangular mesh, while for the third component, the normal displacement, the first order Lagrange interpolation polynomial is used to approximate the first two components of the displacement. Secondly, the existence and uniqueness of weak solutions and the existence and uniqueness of numerical solutions for generalized membrane shells are discussed. The error estimates of weak solutions and numerical solutions are also discussed. Finally, the numerical simulation of the hyperbolic membrane shell of biomaterial is carried out, and the displacement of the neutral surface of the hyperbolic shell under different meshes is obtained. The convergence and effectiveness of the finite element discrete scheme are proved by the analysis of the numerical simulation results.
【作者单位】： 西安理工大学;
【基金】：国家自然科学基金(11571275;11572244) 陕西省工业科技攻关资助项目(2015GY021;2015JQ1001)
【分类号】：O302
本文编号：2445473
[Abstract]:Based on the generalized membrane shell defined by Ciarlet-Lods, a Galerkin conforming finite element discrete scheme for the model is proposed for the first time. Firstly, the integral domain is triangulated, and the first two components of the displacement are approximated by the Lagrange interpolation polynomial with bubbles on the triangular mesh, while for the third component, the normal displacement, the first order Lagrange interpolation polynomial is used to approximate the first two components of the displacement. Secondly, the existence and uniqueness of weak solutions and the existence and uniqueness of numerical solutions for generalized membrane shells are discussed. The error estimates of weak solutions and numerical solutions are also discussed. Finally, the numerical simulation of the hyperbolic membrane shell of biomaterial is carried out, and the displacement of the neutral surface of the hyperbolic shell under different meshes is obtained. The convergence and effectiveness of the finite element discrete scheme are proved by the analysis of the numerical simulation results.
【作者单位】： 西安理工大学;
【基金】：国家自然科学基金(11571275;11572244) 陕西省工业科技攻关资助项目(2015GY021;2015JQ1001)
【分类号】：O302
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