Thermomagnetoelastic Deformation of Flexible Orthotropic Shells of Revolution of Variable Stiffness with Joule Heat Take
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International Applied Mechanics, Vol. 56, No. 4, July, 2020
THERMOMAGNETOELASTIC DEFORMATION OF FLEXIBLE ORTHOTROPIC SHELLS OF REVOLUTION OF VARIABLE STIFFNESS WITH JOULE HEAT TAKEN INTO ACCOUNT L. V. Mol’chenko*, I. I. Loos**, and V. N. Darmosyuk
The equations of thermomagnetoelasticity for flexible orthotropic shells of revolution are derived taking into account orthotropic electrical conductivity and Joule heat. The thermomagnetoelasticity of a truncated orthotropic conical shell is analyzed using the axisymmetric problem formulation and taking into account the orthotropy of electrical conductivity and Joule heating in comparison with a flexible isotropic shell. Keywords: magnetic field, Joule heat, Lorentz force, orthotropic conical shell, variable stiffness, orthotropic electrical conductivity Introduction. The theoretical and applied studies of nonstationary thermomechanical deformation of conductive bodies in magnetic fields have received a significant development effort [8, 9, 17, 20]. The physics behind these effects are discussed in detail in several courses on classical electrodynamics and physics [12, 13, 16]. The effect of a magnetic field on conductive bodies is the occurrence of an unsteady electric field and induction currents, which, interacting with the magnetic field, cause volumetric electromagnetic (ponderomotive) forces and give rise to sources of Joule heat. Electromagnetic forces and heat sources cause waves of stresses and strains and change the thermodynamic state of the body, and, therefore, change the electromagnetic field and electrophysical properties of the body. Thus, mechanical, temperature, and electromagnetic fields are interrelated and must be determined simultaneously solving the dynamic equations of thermomechanics and Maxwell electrodynamics [1, 6]. In specific situations, this problem be simplified. In particular, if the distribution and time-dependence of the magnetic field on the surfaces of the shell are known (for example, obtained experimentally), we can restrict ourselves to the internal problem alone. However, even in this, simplest case, it is still necessary to derive approximate equations of electrodynamics and expressions for the internal electromagnetic forces, consistent with the accepted shell hypotheses on the distribution of displacements and strains over the thickness of the shell. Here, we describe a two-dimensional theory of flexible finite-conducting orthotropic shells in the microsecond range in nonstationary magnetic fields. The equations of motion of the shell in the presence of ponderomotive forces are obtained using the principle of virtual displacements and the Kirchhoff–Love hypotheses. Approximate equations of electrodynamics and the appropriate boundary conditions are obtained by introducing certain hypotheses on the distribution of the electromagnetic field over the thickness of a flexible shell, similar to the hypotheses of magnetoelasticity of thin bodies [1, 4, 6, 7]. Such complex problems can only be solved numerically. It is from these pos
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