A Direct Approach to Membrane Reinforced Bodies

Massimiliano Lucchesi (), Miroslav Šilhavý and Nicola Zani
Additional contact information
Massimiliano Lucchesi: Università di Firenze, Dipartimento di Ingegneria Civile e Ambientale
Miroslav Šilhavý: Žitná 25, Institute of Mathematics of the AV ČR
Nicola Zani: Università di Firenze, Dipartimento di Ingegneria Civile e Ambientale

A chapter in Masonry Structures: Between Mechanics and Architecture, 2015, pp 291-312 from Springer

Abstract: Abstract The paper deals with membrane reinforced bodies with the membrane treated as a two dimensional surface with concentrated material properties. The membrane response is linearized so that it depends linearly on the surface strain tensor. The response of the matrix is treated separately in three cases: (a) as a nonlinear material, (b) as a linear material and finally (c) as a no-tension material. For the general nonlinear material, the principle of minimum energy and complementary energy are proved. For the linearly elastic matrix the surface Korn inequality is used to prove the existence of equilibrium state under general loads. Finally, for the no-tension material a theorem stating that the total energy of the system is bounded from below on the space of admissible displacements if and only if the loads are equilibrated by a statically admissible stress that is negative semidefinite. An example presenting an admissible stress solution is given for a rectangular panel with membrane occupying the main diagonal plane.

Keywords: Equilibrium of forces; Membranes in the bulk matrix; No-tension body (search for similar items in EconPapers)
Date: 2015
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-13003-3_11

Ordering information: This item can be ordered from
http://www.springer.com/9783319130033

DOI: 10.1007/978-3-319-13003-3_11

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().