Premium
A Rational Deduction of Plate Theories from the Three‐Dimensional Linear Elasticity
Author(s) -
Bisegna P.,
Sacco E.
Publication year - 1997
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19970770509
Subject(s) - elasticity (physics) , plate theory , mathematics , lagrange multiplier , conjecture , congruence (geometry) , mathematical analysis , compatibility (geochemistry) , linear elasticity , mathematical optimization , geometry , physics , finite element method , boundary value problem , structural engineering , engineering , pure mathematics , chemical engineering , thermodynamics
In this paper a general procedure for a rational derivation of plate theories is proposed. The methodology is based on the conjecture that plate theories can be carried out from the three‐dimensional elasticity by imposing suitable constraints on the strain and stress fields. The powerful Lagrange multipliers theory is adopted to derive the variational principles, based on the Hu‐Washizu functional, governing the constrained elasticity problems. Both the first‐order shear deformation plate theory, and the higher‐order Lo‐Christensen‐Wu plate theory are derived. The governing equations are recovered, and the reactive fields, arising as a consequence of the imposed constraints, are carried out. When these reactive fields are taken into account, the equilibrium, congruence, and constitutive equations turn out to be exactly satisfied.