A refined dynamic finite-strain shell theory for incompressible hyperelastic materials: equations and two-dimensional shell virtual work principle

06/09/2020
by   Xiang Yu, et al.
0

Based on previous work for the static problem, in this paper we first derive one form of dynamic finite-strain shell equations for incompressible hyperelastic materials that involve three shell constitutive relations. In order to single out the bending effect as well as to reduce the number of shell constitutive relations, a further refinement is performed, which leads to a refined dynamic finite-strain shell theory with only two shell constitutive relations (deducible from the given three-dimensional (3D) strain energy function) and some new insights are also deduced. By using the weak formulation of the shell equations and the variation of the 3D Lagrange functional, boundary conditions and the two-dimensional (2D) shell virtual work principle are derived. As a benchmark problem, we consider the extension and inflation of an arterial segment. The good agreement between the asymptotic solution based on the shell equations and that from the 3D exact one gives verification of the former. The refined shell theory is also applied to study the plane-strain vibrations of a pressurized artery, and the effects of the axial pre-stretch, pressure and fibre angle on the vibration frequencies are investigated in detail.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

02/19/2020

Fractional-Order Models for the Static and Dynamic Analysis of Nonlocal Plates

This study presents the analytical formulation and the finite element so...
09/06/2019

Computational analysis of transport in three-dimensional heterogeneous materials

Porous and heterogeneous materials are found in many applications from c...
12/23/2020

A general theory for anisotropic Kirchhoff-Love shells with embedded fibers and in-plane bending

In this work we present a generalized Kirchhoff-Love shell theory that c...
02/05/2021

Sharp stability for finite difference approximations of hyperbolic equations with boundary conditions

In this article, we consider a class of finite rank perturbations of Toe...
05/06/2021

Vibration Analysis of Piezoelectric Kirchhoff-Love Shells based on Catmull-Clark Subdivision Surfaces

An isogeometric Galerkin approach for analysing the free vibrations of p...
02/19/2020

Split representation of adaptively compressed polarizability operator

The polarizability operator plays a central role in density functional p...
01/26/2022

A well-posed First Order System Least Squares formulation of the instationary Stokes equations

In this paper, a well-posed simultaneous space-time First Order System L...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.