The time-dependent generalized membrane shell model and its numerical computation. (English) Zbl 1440.74212
Summary: 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.
MSC:
| 74K25 | Shells |
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 74K15 | Membranes |
Keywords:
time-dependent; generalized membrane shell; finite element method; Newmark scheme; hyperbolic shell; conical shellSoftware:
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