MODELING OF THERMO-ELASTIC-VISCO-PLASTIC DEFORMATION OF SHALLOW METAL-COMPOSITE SHELLS USING THE REFINED THEORY OF BENDING

Abstract

The dynamic problem of thermo-elastic-viscous-plastic deformation of shallow composite shells is formulated using the refined theory of bending. In this case, tangential displacements along the thickness of constructions are approximated by polynomials of the third and higher orders, and the deflection does not depend on the transverse coordinate. Normal transverse stresses in the composition have a linear distribution over the thickness. The temperature over the thickness of the curved panels is approximated by a 7th order polynomial. The geometric nonlinearity of the problem is taken into account in the Karman approximation. The constructions are multidirectionally reinforced with continuous fibres. The composition materials are isotropic; their plastic deformation is described by the flow theory with isotropic hardening, and the loading function depends on temperature and strain rate. The numerical solution of the coupled nonlinear two-dimensional initial-boundary value problem is obtained using an explicit scheme. Elastic-viscous-plastic, thermo-elastic-plastic and thermo-elastic-viscous-plastic response of a metal-composite cylindrical shallow shell of a rectangular shape with an orthogonal 2D-reinforcement structure has been studied. The construction is frontally loaded with an air blast wave. It has been demonstrated that curved metal-composite panels under such loading must be calculated, taking into account the temperature response that occurs in them and the sensitivity of the plastic properties of the composite materials to the rate of their deformation. In this case, it is necessary to apply the refined theory of bending of shallow shells, and not its simplest version, the Ambartsumian theory. A more intense thermomechanical response of a curved panel is observed when it is dynamically loaded from the convex front surface. In this case, at individual points of the construction, the temperature can briefly increase by 200 °C. It has been found that under dynamic loading of shallow shells from the side of any face-surface, they snapping towards the concavity of thin-walled structures.