Search results for "MSC: 49J45"

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Dimensional reduction for energies with linear growth involving the bending moment

2008

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.

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)
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