Linear Pantographic Sheets: Existence and Uniqueness of Weak Solutions

Victor Eremeev; Francesco dell'Isola; Claude Boutin; David Steigmann

doi:10.1007/s10659-017-9660-3

Linear Pantographic Sheets: Existence and Uniqueness of Weak Solutions

Abstract

we address the well-posedness of the planar linearized equilibrium problem for homogenized pantographic lattices. To do so: (i) we introduce a class of subsets of anisotropic Sobolev’s space as the most suitable energy space E relative to assigned boundary conditions; (ii) we prove that the considered strain energy density is coercive and positive definite in E ; (iii) we prove that the set of placements for which the strain energy is vanishing (the so-called floppy modes) must strictly include rigid motions; (iv) we determine the restrictions on displacement boundary conditions which assure existence and uniqueness of linear static problems. The presented results represent one of the first mechanical applications of the concept of Anisotropic Sobolev space, initially introduced only on the basis of purely abstract mathematical considerations.

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Authors (4)

Victor Eremeev prof. dr hab.
Francesco dell'Isola Dr. hab. Prof.
- Università di Roma “La Sapienza”, Rome, Italy DISG
Claude Boutin Dr. hab.
- Université de Lyon, Lyon, France
David Steigmann Dr. hab.
- University of California at Berkeley, Berkeley, USA Dept. Mechanical Engineering

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Keywords

STRAIN GRADIENT ELASTICITY LINEAR PANTOGRAPHIC SHEETS EXISTENCE UNIQUENESS ANISOTROPIC SOBOLEV’S SPACE

Details

Category:: Articles
Type:: artykuł w czasopiśmie wyróżnionym w JCR
Published in:: JOURNAL OF ELASTICITY no. 132, edition 2, pages 175 - 196,
ISSN: 0374-3535
Language:: English
Publication year:: 2018
Bibliographic description:: Eremeev V., Dell'isola F., Boutin C., Steigmann D.: Linear Pantographic Sheets: Existence and Uniqueness of Weak Solutions// JOURNAL OF ELASTICITY. -Vol. 132, iss. 2 (2018), s.175-196
DOI:: Digital Object Identifier (open in new tab) 10.1007/s10659-017-9660-3
Verified by:: Gdańsk University of Technology