Existence theorems in the geometrically non-linear 6-parametric theory of elastic plates

In this paper we show the existence of global minimizers for the geometrically exact, non-linear equations of elastic plates, in the framework of the general 6-parametric shell theory. A characteristic feature of this model for shells is the appearance of two independent kinematic fields: the translation vector field and the rotation tensor field (representing in total 6 independent scalar kinematic variables). For isotropic plates, we prove the existence theorem by applying the direct methods of the calculus of variations. Then, we generalize our existence result to the case of anisotropic plates. We also present a detailed comparison with a previously established Cosserat plate model.Comment: 19 pages, 1 figur

Comparison of pressure, magnetic field and excess manganese effects on transport properties of film and bulk ceramic La–Ca manganites

The pressure, magnetic field and excess manganese effects on transport and magnetoresistance effect (MRE) have been studied in both the epitaxial films and bulk ceramics of manganites (La₀.₇Ca₀.₃)₁₋xMn₁₊xO₃₋y (x = 0–0.2). A comparison of electrical behavior in both kinds of samples of similar composition at hydrostatic pressures of up to 1.8 GPa and in a magnetic fields of up to 8 kOe has been performed. The pressure and magnetic field effects are shown to increase with increasing manganese content. Experimental data show that the pressure and magnetic field effects on temperatures of both metal–insulator transition (TMD) and MRE peak (TMR) are considerably stronger in the films than in ceramics. The hydrostatic pressure increases TMD and TMR. Magnetoresistance effect for both types of samples was shown to be favored by the pressure and magnetic field in an opposite way. A direct correlation is established between TMD and conductivity bandwidth as well as between MRE and concentration of charge carriers at applied pressure. The differences in the values of pressure effect on resistance, MRE and TMD temperature in the films and ceramics are connected with both granular structure of ceramics and the oxygen nonstoichiometry in ceramic and film samples of the same content as well as with the film strain induced by lattice mismatch between the film and the substrate. The origin of pressure–magnetic field effects is analyzed in the framework of double exchange interaction and small polaron hopping, and variable range hopping models