Shock waves as a main destruction factor of dynamical loading on structures

Abstract

In this work methods and algorithms for calculating gas dynamical effects on selected structures and structural elements using graphic-analytical means are to be presented. The impact of shock waves on the structures envisaged is solved under condition that either generally anisotropic elastic layers or rigid solids are considered. Mathematical apparatus is fully discussed and formulas needed for programming on computers are derived. In order to involve some selected phenomena from the scope of composite materials eigenparameters are also used in the formulations. They simulate wide range of mechanical behaviors the composite materials undertake, such as thermodynamic behavior the course of this described during the attack. First, an overview of the nowadays situation in literature, standards, recommendations and requests on protective structures and their assessment is presented. Large extent of examples is cited. The main objective of the work is concentrated on a numerical method known as Galerkin-Petrov discontinuous finite element approach, which is applied to the coupled modeling mutual influence of an impact of the line explosion and a semi-cylindrical arch is presented. Godunov simplification of equations of gas dynamics turns a non-linear problem of the gas dynamics to the linear time-spatial simultaneous system. Using an influence matrix which is created from relations describing the behavior of simple arch and link it to the formulation of the gas dynamics simultaneous system is extended for relation tractions-displacements on the arch surface. Note that because of the general non-linear gas dynamics assumption of a negligible stiffness of unmoved part of the air the external load along the arch surface not yet touched by the shock wave is put equal to zero. This is very important, but also very natural supposition, which can be generalized for the non-linear system of gas dynamics. Finally, the pictures of the pressures inside and on the shock wave are displayed in the end of the paper. It appears that till the front of the shock wave does not reach the arch a regular distribution of pressures is seen, but after attaining the surface of the arch the extreme of the pressure moves downwards along the arch and if the shock wave front moves above the arch the pressure attenuate in front of the arch because of reflected waves.

In this work methods and algorithms for calculating gas dynamical effects on selected structures and structural elements using graphic-analytical means are to be presented. The impact of shock waves on the structures envisaged is solved under condition that either generally anisotropic elastic layers or rigid solids are considered. Mathematical apparatus is fully discussed and formulas needed for programming on computers are derived. In order to involve some selected phenomena from the scope of composite materials eigenparameters are also used in the formulations. They simulate wide range of mechanical behaviors the composite materials undertake, such as thermodynamic behavior the course of this described during the attack. First, an overview of the nowadays situation in literature, standards, recommendations and requests on protective structures and their assessment is presented. Large extent of examples is cited. The main objective of the work is concentrated on a numerical method known as Galerkin-Petrov discontinuous finite element approach, which is applied to the coupled modeling mutual influence of an impact of the line explosion and a semi-cylindrical arch is presented. Godunov simplification of equations of gas dynamics turns a non-linear problem of the gas dynamics to the linear time-spatial simultaneous system. Using an influence matrix which is created from relations describing the behavior of simple arch and link it to the formulation of the gas dynamics simultaneous system is extended for relation tractions-displacements on the arch surface. Note that because of the general non-linear gas dynamics assumption of a negligible stiffness of unmoved part of the air the external load along the arch surface not yet touched by the shock wave is put equal to zero. This is very important, but also very natural supposition, which can be generalized for the non-linear system of gas dynamics. Finally, the pictures of the pressures inside and on the shock wave are displayed in the end of the paper. It appears that till the front of the shock wave does not reach the arch a regular distribution of pressures is seen, but after attaining the surface of the arch the extreme of the pressure moves downwards along the arch and if the shock wave front moves above the arch the pressure attenuate in front of the arch because of reflected waves.