Vol. 10, No. 1, 2015

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ISSN: 1559-3959
On the occurrence of lumped forces at corners in classical plate theories: a physically based interpretation

Laura Galuppi and Gianni Royer-Carfagni

Vol. 10 (2015), No. 1, 93–103
DOI: 10.2140/jomms.2015.10.93
Abstract

The paradigmatic example of a twisted square plate is here considered. An equivalent partition of the plate in a grid of beams à la Grashof is found such that, as the number of beams tends to infinity, the grid exhibits the same deflection of the plate. This scheme is used to interpret, through the distinction between Euler–Bernoulli and Timoshenko beam theories, the different types of natural boundary conditions that can arise in the Kirchhoff–Love and Mindlin–Reissner theories of plates. A physically based interpretation for the occurrence of lumped forces at the plate corners through the formation of a boundary layer is provided.

Keywords
Kirchhoff–Love plates, Mindlin–Reissner plates, Grashof partition, boundary conditions, boundary layer, singular shear forces
Milestones
Received: 27 October 2014
Revised: 15 January 2015
Accepted: 3 February 2015
Published: 6 May 2015
Authors
Laura Galuppi
Dipartimento di Ingegneria Industriale
Università degli Studi di Parma
Parco Area delle Scienze 181/A
I-43124 Parma
Italy
Gianni Royer-Carfagni
Dipartimento di Ingegneria Industriale
Università degli Studi di Parma
Parco Area delle Scienze 181/A
I-43124 Parma
Italy