Variational formulations on thin elastic plates with constraints

We derive variational formulations for thin elastic plates from bulk energies by dimensional reduction. The main feature is to consider a family of problems with internal constraints on normal deformations. Our approach consists of two stages. First we obtain an abstract variational convergence result. Then we study the integral representation of the limit functional

Numerical analysis of microstructures: the influence of incompatibility

We are concerned with the appearance of microstructures in some problems of Calculus of Variations experiencing ‘wells’ or minimum of energy. Using piecewise linear finite elements, we give energy estimates and analyze their dependence on the incompatibility of the wells

Relaxation of second order geometric integrals and non-local effects

We are concerned with the relaxation of second-order geometric integrals, i.e., functionals of the type: C c ∞ (ℝ N )∋u↦F μ (u):=∫ ℝ N f∇ 2 u (x)dμ(x), where ∇ 2 u is the Hessian of u, f:MsymN→[0,+∞] is a continuous function, and μ is a finite positive Radon measure on ℝ N . A relaxation problem of this type was studied for the first time by G. Bouchitté and I. Fragala , where they pointed out a new phenomenon: the functional relaxed of F μ has, in general, a 'non-local' representation. Working on a more formal level than in, we develop an alternative method making clear this 'strange phenomenon'

Necessary and sufficient conditions for the interchange between infimum and the symbol of integration

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