TY - JOUR
T1 - A new duality approach to elasticity
AU - Ciarlet, Philippe G.
AU - Geymonat, Giuseppe
AU - Krasucki, Françoise
PY - 2012/1
Y1 - 2012/1
N2 - The displacement-traction problem of three-dimensional linearized elasticity can be posed as three different minimization problems, depending on whether the displacement vector field, or the stress tensor field, or the strain tensor field, is the unknown. The objective of this paper is to put these three different formulations of the same problem in a new perspective, by means of LegendreFenchel duality theory. More specifically, we show that both the displacement and strain formulations can be viewed as Legendre-Fenchel dual problems to the stress formulation. We also show that each corresponding Lagrangian has a saddle-point, thus fully justifying this new duality approach to elasticity.
AB - The displacement-traction problem of three-dimensional linearized elasticity can be posed as three different minimization problems, depending on whether the displacement vector field, or the stress tensor field, or the strain tensor field, is the unknown. The objective of this paper is to put these three different formulations of the same problem in a new perspective, by means of LegendreFenchel duality theory. More specifically, we show that both the displacement and strain formulations can be viewed as Legendre-Fenchel dual problems to the stress formulation. We also show that each corresponding Lagrangian has a saddle-point, thus fully justifying this new duality approach to elasticity.
KW - constrained quadratic optimization
KW - duality
KW - intrinsic elasticity
KW - Lagrangians
KW - Legendre-Fenchel transform
KW - Linearized elasticity
UR - http://www.scopus.com/inward/record.url?scp=84856102299&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84856102299&origin=recordpage
U2 - 10.1142/S0218202512005861
DO - 10.1142/S0218202512005861
M3 - RGC 21 - Publication in refereed journal
VL - 22
JO - Mathematical Models and Methods in Applied Sciences
JF - Mathematical Models and Methods in Applied Sciences
SN - 0218-2025
IS - 1
M1 - 1150003
ER -