Abstract A class of Lagrangian mixed finite element methods is constructed for an approximate solution of a problem of nonlinear thin elastic shell theory, namely, the problem of finding critical points of the functional of potential energy according to the Budiansky–Sanders model. The proposed numerical method is based on the use of the second derivatives of the deflection as auxiliary variables. Sufficient conditions for the solvability of the corresponding discrete problem are obtained. Accuracy estimates for approximate solutions are established. Iterative methods for solving the corresponding systems of nonlinear equations are proposed and investigated.

中文翻译：

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非线性薄壳问题的拉格朗日混合有限元方法

摘要 针对非线性薄弹性壳理论问题，即根据Budiansky-Sanders模型求势能泛函临界点的问题，构造了一类拉格朗日混合有限元方法。所提出的数值方法基于使用挠度的二阶导数作为辅助变量。获得了相应离散问题的可解性的充分条件。建立近似解的准确度估计。提出并研究了求解相应非线性方程组的迭代方法。