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Stable gradient flow discretizations for simulating bilayer plate bending with isometry and obstacle constraints
- Source :
- IMA Journal of Numerical Analysis. 42:1903-1928
- Publication Year :
- 2021
- Publisher :
- Oxford University Press (OUP), 2021.
-
Abstract
- Bilayer plates are compound materials that exhibit large bending deformations when exposed to environmental changes that lead to different mechanical responses in the involved materials. In this article a new numerical method that is suitable for simulating the isometric deformation induced by a given material mismatch in a bilayer plate is discussed. A dimensionally reduced formulation of the bending energy is discretized generically in an abstract setting and specified for discrete Kirchhoff triangles; convergence towards the continuous formulation is proved. A practical semi-implicit discrete gradient flow employing a linearization of the isometry constraint is proposed as an iterative method for the minimization of the bending energy; stability and a bound on the violation of the isometry constraint are proved. The incorporation of obstacles is discussed and the practical performance of the method is illustrated with numerical experiments involving the simulation of large bending deformations and investigation of contact phenomena.
- Subjects :
- 65N12, 65N30, 74K20
Discretization
Iterative method
Applied Mathematics
General Mathematics
Numerical analysis
010102 general mathematics
Mathematical analysis
010103 numerical & computational mathematics
Bending of plates
Bending
Isometry (Riemannian geometry)
01 natural sciences
Computational Mathematics
Linearization
Mathematics - Numerical Analysis
0101 mathematics
Balanced flow
Mathematics
Subjects
Details
- ISSN :
- 14643642 and 02724979
- Volume :
- 42
- Database :
- OpenAIRE
- Journal :
- IMA Journal of Numerical Analysis
- Accession number :
- edsair.doi.dedup.....e348076180680ed802d1024724101792