6533b837fe1ef96bd12a315e

RESEARCH PRODUCT

Dimensional reduction for energies with linear growth involving the bending moment

Jean-françois BabadjianElvira ZappaleHamdi Zorgati

subject

Mathematics(all)Asymptotic analysis49J45 49Q20 74K35dimension reductionGeneral Mathematics01 natural sciencesMathematics - Analysis of PDEsTangent measures; bending moments; dimension reductionFOS: Mathematics[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]0101 mathematicsScalingFunctions of bounded variationMathematicsDeformation (mechanics)Applied Mathematics010102 general mathematicsMathematical analysisTangent measures010101 applied mathematicsNonlinear systemΓ-convergenceDimensional reductionBounded variationBending momentbending momentsVector fieldMSC: 49J45; 49Q20; 74K35Analysis of PDEs (math.AP)

description

A $\Gamma$-convergence analysis is used to perform a 3D-2D dimension reduction of variational problems with linear growth. The adopted scaling gives rise to a nonlinear membrane model which, because of the presence of higher order external loadings inducing a bending moment, may depend on the average in the transverse direction of a Cosserat vector field, as well as on the deformation of the mid-plane. The assumption of linear growth on the energy leads to an asymptotic analysis in the spaces of measures and of functions with bounded variation.

yearjournalcountryeditionlanguage
2008-12-01
10.1016/j.matpur.2008.07.003http://hdl.handle.net/11573/1458188