The modeling and numerical analysis of wrinkled membranes | Zendy

Ding Hongli | Zendy; Yang Bingen | Zendy

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The modeling and numerical analysis of wrinkled membranes

Author(s) -

Ding Hongli,

Yang Bingen

Publication year - 2003

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.832

Subject(s) - membrane , discretization , finite element method , smoothing , numerical analysis , parametric statistics , mathematics , relaxation (psychology) , dynamic relaxation , constraint (computer aided design) , mathematical optimization , mathematical analysis , structural engineering , engineering , geometry , chemistry , psychology , social psychology , biochemistry , statistics

In this paper three fundamental issues regarding modeling and analysis of wrinkled membranes are addressed. First, a new membrane model with viable Young's modulus and Poisson's ratio is proposed, which physically characterizes stress relaxation phenomena in membrane wrinkling, and expresses taut, wrinkled and slack states of a membrane in a systematic manner. Second, a parametric variational principle is developed for the new membrane model. Third, by the variational principle, the original membrane problem is converted to a non‐linear complementarity problem in mathematical programming. A parametric finite element discretization and a smoothing Newton method are then used for numerical solution. The proposed membrane model and numerical method are capable of delivering convergent results for membranes with a mixture of wrinkled and slack regions, without iteration of membrane stresses. Three numerical examples are provided. Copyright © 2003 John Wiley & Sons, Ltd.

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