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A Direct Approach to Membrane Reinforced Bodies

In: Masonry Structures: Between Mechanics and Architecture

Author

Listed:
  • 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)

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.

Suggested Citation

  • Massimiliano Lucchesi & Miroslav Šilhavý & Nicola Zani, 2015. "A Direct Approach to Membrane Reinforced Bodies," Springer Books, in: Danila Aita & Orietta Pedemonte & Kim Williams (ed.), Masonry Structures: Between Mechanics and Architecture, edition 1, pages 291-312, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-13003-3_11
    DOI: 10.1007/978-3-319-13003-3_11
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