Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 92, Issue 1, Pages -Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-022-01848-1
Keywords
Generalised periodicity; Unit cell; Metamaterial; 4th order PDE; C-0 finite elements; Interior penalty method; Strain gradient elasticity; Flexoelectricity
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Funding
- European Research Council [StG-679451]
- Agencia Estatal de Investigacion [RTI2018-101662-B-I00]
- Ministerio de Economia y Competitividad [CEX2018-000797-S]
- Generalitat de Catalunya [2017-SGR-1278]
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This paper proposes a methodology to solve high-order PDE boundary value problems with generalised periodicity using the C-0 interior penalty method. The method is developed for analyzing flexoelectricity-based metamaterial unit cells, formalizing the problem statement and weak form, and providing details on the implementation of the local and macro conditions for generalised periodicity. Numerical examples demonstrate the high-order convergence of the method and its applicability in realistic problem settings.
We propose a methodology to solve high-order PDE boundary value problems with generalised periodicity, in the framework of the C-0 interior penalty method. The method is developed for the analysis of flexoelectricity-based metamaterial unit cells, formalising the corresponding problem statement and weak form, and giving details on the implementation of the local and macro conditions for generalised periodicity. Numerical examples demonstrate the high-order convergence of the method and its applicability in realistic problem settings.
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