# Plate theory as the variational limit of the complementary energy functionals of inhomogeneous anisotropic linearly elastic bodies

We consider a sequence of linear hyper-elastic, inhomogeneous and fully anisotropic bodies in a reference configuration occupying a cylindrical region of height epsilon. We then study, by means of Gamma-convergence, the asymptotic behavior as epsilon goes to zero of the sequence of complementary energies. The limit functional is then identified as a dual problem for a two-dimensional plate. Our approach gives a direct characterization of the convergence of the equilibrating stress fields.

## Similar Publications

We study and classify free actions of compact quantum groups on unital C*-algebras in terms of generalized factor systems. Moreover, we use these factor systems to show that all finite coverings of irrational rotation C*-algebras are cleft. Read More

We present a construction of cellular BF theory (in both abelian and non-abelian variants) on cobordisms equipped with cellular decompositions. Partition functions of this theory are invariant under subdivisions, satisfy a version of the quantum master equation, and satisfy Atiyah-Segal-type gluing formula with respect to composition of cobordisms. Read More

In this short note we provide a new way of constructing the subcritical and critical Gaussian multiplicative chaos (GMC) measures corresponding to the 2D Gaussian free field (GFF). The constructions are based on the theory of local sets of the Gaussian free field and are reminiscent of the constructions of multiplicative cascades using stopping lines. As a special case we recover E. Read More

We apply the nested algebraic Bethe ansatz to the models with gl(2|1) and gl}(1|2) supersymmetry. We show that form factors of local operators in these models can be expressed in terms of the universal form factors. Our derivation is based on the use of the RTT-algebra only. Read More

An accurate closed-form expression is provided to predict the bending angle of light as a function of impact parameter for equatorial orbits around Kerr black holes of arbitrary spin. This expression is constructed by assuring that the weak- and strong-deflection limits are explicitly satisfied while maintaining accuracy at intermediate values of impact parameter via the method of asymptotic approximants (Barlow et al, 2016 Q. J. Read More

We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections. A few examples where this problem is relevant are compressed sensing, sparse superposition codes, and code division multiple access. There has been a number of works considering the mutual information for this problem using the replica method from statistical physics. Read More

We study a scattering on an ultra-low potential in zigzag graphene nanoribbon. Using mathematical framework based on the continuous Dirac model and augumented scattering matrix, we derive a condition for the existence of a trapped mode. We consider the threshold energies where the continuous spectrum changes its multiplicity and show that the trapped modes may appear for energies slightly less than a threshold and its multiplicity does not exceeds one. Read More

The Eisenhart geometric formalism, which transforms an Euclidean natural Hamiltonian $H=T+V$ into a geodesic Hamiltonian ${\cal T}$ with one additional degree of freedom, is applied to the four families of quadratically superintegrable systems with multiple separability in the Euclidean plane. Firstly, the separability and superintegrability of such four geodesic Hamiltonians ${\cal T}_r$ ($r=a,b,c,d$) in a three-dimensional curved space are studied and then these four systems are modified with the addition of a potential ${\cal U}_r$ leading to ${\cal H}_r={\cal T}_r +{\cal U}_r$. Secondly, we study the superintegrability of the four Hamiltonians $\widetilde{{\cal H}}_r= {\cal H}_r/ \mu_r$, where $\mu_r$ is a certain position-dependent mass, that enjoys the same separability as the original system ${\cal H}_r$. Read More

We consider a generalization of the classical Laplace operator, which includes the Laplace-Dunkl operator defined in terms of the differential-difference operators associated with finite reflection groups called Dunkl operators. For this Laplace-like operator, we determine a set of symmetries commuting with it, which are generalized angular momentum operators, and we present the algebraic relations for the symmetry algebra. In this context, the generalized Dirac operator is then defined as a square root of our Laplace-like operator. Read More

We discuss several new bi-Hamiltonian integrable systems on the plane with integrals of motion of third, fourth and sixth order in momenta. The corresponding variables of separation, separated relations, compatible Poisson brackets and recursion operators are also presented in the framework of the Jacobi method. Read More