Numerical simulations for the dynamics of flexural shells. (April 2020)

• Record Type: Journal Article
• Authors: Shen, Xiaoqin; Piersanti, Luisa; Piersanti, Paolo
• Is Part Of: Mathematics and mechanics of solids. Volume 25:Number 4(2020)
• Page Start: 887
• Page End: 912
• Publication Date: 2020-04
• Subjects: Flexural shells -- elliptic membrane shells -- finite-element method -- Newmark's scheme -- cylindrical shell -- conical shell -- spherical shell; Materials -- Mechanical properties -- Periodicals; Solids -- Periodicals; Materials science -- Mathematics -- Periodicals; 620.11205
• DOI: 10.1177/1081286519891230
• Languages: English
• ISSNs: 1081-2865

Abstract

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. The model under consideration takes the form of a set of hyperbolic variational equations posed over the space of admissible linearised inextensional displacements, and a set of initial conditions. Since the original model is not suitable 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. 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 the 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.