Abstract
AbstractThe inflation of hyperelastic thin shells is a highly nonlinear problem that arises in multiple important engineering applications. It is characterised by severe kinematic and constitutive nonlinearities and is subject to various forms of instabilities. To accurately simulate this challenging problem, we present an isogeometric approach to compute the inflation and associated large deformation of hyperelastic thin shells following the Kirchhoff–Love hypothesis. Both the geometry and the deformation field are discretized using Catmull–Clark subdivision bases which provide the required$$C^1$$C1-continuous finite element approximation. To follow the complex nonlinear response exhibited by hyperelastic thin shells, inflation is simulated incrementally, and each incremental step is solved using the Newton–Raphson method enriched with arc-length control. An eigenvalue analysis of the linear system after each incremental step assesses the possibility of bifurcation to a lower energy mode upon loss of stability. The proposed method is first validated using benchmark problems and then applied to engineering applications, where the ability to simulate large deformation and associated complex instabilities is clearly demonstrated.
Funder
Engineering and Physical Sciences Research Council
Royal Society
Deutsche Forschungsgemeinschaft
National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Mechanical Engineering,Ocean Engineering,Computational Mechanics
Reference77 articles.
1. Adkins JE, Rivlin RS (1952) Large elastic deformations of isotropic materials IX. The deformation of thin shells. Philos Trans Roy Soc Lond Ser A Math Phys Sci 244(888):505–531
2. Akkas N (1978) On the dynamic snap-out instability of inflated non-linear spherical membranes. Int J Non-Linear Mech 13(3):177–183
3. Argyris JH, Fried I, Scharpf DW (1968) The TUBA family of plate elements for the matrix displacement method. Aeronaut J 72(692):701–709
4. Arndt D, Bangerth W, Davydov D et al (2021) The deal. II finite element library: design, features, and insights. Comput Math Appl 81:407–422
5. Arndt D, Bangerth W, Feder M et al (2022) The deal. II library, version 9.4. J Numer Math 30(3):231–246
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献