Numerical simulations for the dynamics of flexural shells

Xiaoqin Shen (1) , Luisa Piersanti (2) , Paolo Piersanti (3)

1 Xjtu - Xi'an Jiaotong University
2 Department of Mathematics and Computer Science, University of Perugia
3 Karl-Franzens-Universität Graz

In this paper we study a model describing the displacement of a linearly elastic flexural shell subjected to given dynamic loads from the computational point of view. As expected, this model takes the form of a set of hyperbolic variational equations posed over the space of admissible linearized inextensional displacements, and a set of initial conditions. Since the original model is defined over spaces that are not amenable for the implementation of a finite element method, we conduct the experiments on the corresponding penalised model. It was recently shown that the solution to such a penalised model is a good approximation of the solution to the original model. The numerical tests are therefore conducted on the the penalised model; the approximation of the solution to the penalised model is obtained via Newmark's scheme, which is then implemented and tested for shells having the following middle surfaces: a portion of a cylinder, and a portion of a cone. For sake of completeness, we also present the results of the numerical tests related to a model describing the displacement of a linearly elastic elliptic membrane shell under the action of given dynamic loads.

Mots clés: Flexural shells; Elliptic membrane shells; finite element method; Newmark's scheme; cylindrical shell; conical shell; spherical shell

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Physique mathématique [math-ph]

Xiaoqin Shen, Luisa Piersanti, Paolo Piersanti. Numerical simulations for the dynamics of flexural shells. 2019. ⟨hal-02275020v2⟩