The time-dependent generalized membrane shell model and its numerical computation

• Published in: Computer methods in applied mechanics and engineering Vol. 344; pp. 54 - 70
• Main Authors: Shen, Xiaoqin, Jia, Junjun, Zhu, Shengfeng, Li, Haoming, Bai, Lin, Wang, Tiantian, Cao, Xiaoshan
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.02.2019; Elsevier BV
• Subjects: Conical shell; Conical shells; Convergence; Finite element method; Generalized membrane shell; Hyperbolic shell; Mathematical models; Newmark scheme; Numerical analysis; Numerical methods; Stability analysis; Time dependence; Time-dependent; Finite element method; Conical shell; Time-dependent; Generalized membrane shell; Newmark scheme; Hyperbolic shell
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2018.10.001

In this paper, we discuss the time-dependent generalized membrane shell model, which has not been addressed numerically in literature. We show that the solution of this model exists and is unique. We first provide a numerical method for the time-dependent generalized membrane shell. Concretely, we semi-discretize the space variable and fully discretize the problem using time discretization by the Newmark scheme. The corresponding numerical analyses of existence, uniqueness, stability and convergence with a priori error estimates are given. Finally, we present numerical experiments with a portion of the conical shell and a portion of the hyperbolic shell to verify theoretical convergence results and demonstrate the effectiveness of the numerical scheme. •Existence and uniqueness of the time-dependent generalized membrane shell.•Newmark scheme for the time-dependent generalized membrane shell.•Analyses of existence, uniqueness, stability, convergence and a priori error estimate for elastodynamic problem.