Premium
Analysis of 2‒D bimodular materials and wrinkled membranes based on the parametric variational principle and co‒rotational approach
Author(s) -
Zhang L.,
Gao Q.,
Zhang H. W.
Publication year - 2014
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4649
Subject(s) - discontinuity (linguistics) , parametric statistics , nonlinear system , convergence (economics) , mathematics , stiffness matrix , stiffness , mathematical optimization , dynamic relaxation , iterative method , algorithm , matrix (chemical analysis) , quadratic equation , computer science , structural engineering , mathematical analysis , materials science , engineering , geometry , composite material , statistics , physics , quantum mechanics , economics , economic growth
SUMMARY In the numerical analysis of 2‒D bimodular materials, strain discontinuity is problematic, and the traditional iterative algorithm is frequently unstable. This paper develops a stable algorithm for the large‒displacement and small‒strain analyses of 2‒D bimodular materials and structures. Geometrically nonlinear formulations are based on the co‒rotational approach. Using the parametric variational principle (PVP), a unified constitutive equation is created to resolve the problem induced by strain discontinuity in the local coordinate system. Because the traditional stress iteration is not required, the local linear stiffness matrix does not need to be updated when computing the global stiffness matrix and the nodal internal force vector. The nonlinear problem is ultimately transformed into a complementarity problem that is simply solved by combing the Newton–Raphson scheme and the mature quadratic programming algorithm. Numerical examples demonstrate that the PVP algorithm presents better convergence behavior than the traditional iterative algorithm. By incorporating the concept of material modification, the new algorithm is also be successfully extended to the wrinkling analysis of thin membranes. Copyright © 2014 John Wiley & Sons, Ltd.