Journal article
Minimal energy configurations of bilayer plates as a polynomial optimization problem
Nonlinear analysis, v 231, 113034
01 Jun 2023
Abstract
We develop a discretization method for solving the minimal energy configuration of bilayer plates based on a mathematical model developed in Schmidt (2007), Bartels et al. (2017). Our discretization method employs C1-spline functions. A highlight of the method involves a trick to handle the nonlinear isometry constraint in such a way that not only numerical integration becomes unnecessary, but also that the final optimization problems are in the form of degree 4 polynomial optimization problems (POP). We develop two different versions of the method, one resulted in a constrained degree 4 POP involving a small tolerance e, another resulted in an unconstrained degree 4 POP involving a large penalty parameter mu. We develop a mathematical analysis, based on the direct method and techniques in G-convergence, to show how e and mu can be chosen according to the grid size so that the minimizers of the discrete problems converge to that of the continuum variational problem as the grid size goes to zero. We corroborate the theory through a series of computational experiments, and also report an unexpected finding related to the asymmetry of the discretized problems.
(c) 2022 Elsevier Ltd. All rights reserved.
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Details
- Title
- Minimal energy configurations of bilayer plates as a polynomial optimization problem
- Creators
- Preetham Mohan - Michigan UnitedNung Kwan Yip - Purdue Univ, Dept Math, W Lafayette, IN 47907 USAThomas Yu - Drexel University
- Publication Details
- Nonlinear analysis, v 231, 113034
- Publisher
- Elsevier
- Number of pages
- 33
- Grant note
- DMS 0512673; DMS 0915068 / National Science Foundation; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:001041787900001
- Scopus ID
- 2-s2.0-85135908916
- Other Identifier
- 991021861192104721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics
- Mathematics, Applied