We provide a justification of the Reissner-Mindlin plate theory, using linear three-dimensional elasticity as framework and Gamma-convergence as technical tool. Essential to our developments is the selection of a transversely isotropic material class whose stored energy depends on (first and) second gradients of the displacement field. Our choices of a candidate Gamma-limit and a scaling law of the basic energy functional in terms of a thinness parameter are guided by mechanical and formal arguments that our variational convergence theorem is meant to validate mathematically.
Paroni, R., PODIO GUIDUGLI, P., Tomassetti, G. (2007). A justification of the reissner-mindlin plate theory through variational convergence. ANALYSIS AND APPLICATIONS, 5(2), 165-182.
A justification of the reissner-mindlin plate theory through variational convergence
PODIO GUIDUGLI, PAOLO;TOMASSETTI, GIUSEPPE
2007-01-01
Abstract
We provide a justification of the Reissner-Mindlin plate theory, using linear three-dimensional elasticity as framework and Gamma-convergence as technical tool. Essential to our developments is the selection of a transversely isotropic material class whose stored energy depends on (first and) second gradients of the displacement field. Our choices of a candidate Gamma-limit and a scaling law of the basic energy functional in terms of a thinness parameter are guided by mechanical and formal arguments that our variational convergence theorem is meant to validate mathematically.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.