In this paper, an analysis of free vibration in functionally graded nanoplate is presented. Third-order shear deformation plate theory is used to reach more accuracy in results. Small-scale effects are investigated using Eringen`s nonlocal theory. The governing equations of motion are obtained by Hamilton`s principle. It is assumed that the properties of nanoplates vary through their thicknesse...

We consider a variational principle suitable for tracking boundaries of gas bubbles in liquids and its consequences. The principle is derived from a generalization of the Principle of Stationary Action applied to a Riemannian manifold of volume preserving flow maps. The dual variational principle for the markers tracking the free surfaces is induced by the Wasserstein-Kantorovich metric. This l...

This paper analyses Rawls’s celebrated di¤erence principle, and its lexicographic extension, in societies with a …nite and an in…nite number of agents. A uni…ed framework of analysis is set up, which allows one to characterise Rawlsian egalitarian principles by means of a weaker version of a new axiom the Harm Principle recently proposed by [13]. This is quite surprising, because the Harm princ...

In the present study, the buckling analysis of the rectangular nanoplate under biaxial non-uniform compression using the modified couple stress continuum theory with various boundary conditions has been considered. The simplified first order shear deformation theory (S-FSDT) has been employed and the governing differential equations have been obtained using the Hamilton’s principle. An analytic...

We prove a variational principle in reflexive Banach spaces X with KadecKlee norm, which asserts that any Lipschitz (or any proper lower semicontinuous bounded from below extended real-valued) function in X can be perturbed with a parabola in such a way that the perturbed function attains its infimum (even more can be said — the infimum is well-posed). In addition, we have genericity of the poi...