發(fā)布時間：2019-03-22 09:30

【摘要】：基于Ciarlet-Lods定義的廣義膜殼,首次提出了該模型的一種Galerkin協(xié)調(diào)有限元離散格式。首先,對積分區(qū)域進(jìn)行三角剖分,并在三角網(wǎng)格上對位移前兩個分量用帶泡一次Lagrange插值多項式逼近,而對第三個分量,即法向位移,用一次Lagrange插值多項式逼近。其次,討論了廣義膜殼弱解的存在性、唯一性和數(shù)值解的存在性、唯一性以及弱解與數(shù)值解的誤差估計。最后,本文對生物材料的雙曲膜殼采用該方法進(jìn)行數(shù)值模擬,得到不同網(wǎng)格下雙曲殼中性面上的位移,并通過分析數(shù)值模擬結(jié)果證明了有限元離散格式的收斂性和有效性。
[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.
【作者單位】： 西安理工大學(xué);
【基金】：國家自然科學(xué)基金(11571275;11572244) 陜西省工業(yè)科技攻關(guān)資助項目(2015GY021;2015JQ1001)
【分類號】：O302

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