62
A. V. Demareva et al.
the stabilization stage. In this position, the shell inner surface is almost closed. The
third stage of the shell deformation begins, and it is characterized by a sharp increase
in the contact force.
As it is shown in Fig. 4.1, the behavior of spherical shells reaction force on
the plates movement is nonlinear. Due to this, spherical shells have good energyabsorbing properties and can be used for shock damping in protective elements. The
effective damper development is very relevant for the design of modern containers
for the transport of radioactive materials and other potentially dangerous cargo.
According to the IAEA regulations, in case of an emergency drop of a container
on a rigid plate, the acceleration experienced by the cargo shall not exceed the limit
value. In this regard, numerical studies of the damping properties of a titanium alloy
spherical shell under shock loading were carried out. The shell is located on a fixed
plate, and on top of it falls plate, simulating the transported cargo. The mass of the
falling plate is 0.889 t, the initial speed of its fall is 13 m/s.
To verify the above computational model of MHS filler, calculations were carried
out in which the shell was replaced by an equivalent in size, weight, and stiffness
prototype (cylinder R = 9 cm, height H = 18 cm) of MHS filler. The problem
was solved in three-dimensional formulation. Taking into account the symmetry of
geometry, initial, and boundary conditions, one-fourth part of the shell prototype and
plate was considered in the calculations.
The porous material stress–strain diagram (Fig. 4.2) was determined on the basis
of a smoothed graph of the change in the contact force acting on the plate (dotted line
in Fig. 4.1) at quasi-static compression of the shell. For comparison, we considered
the problem of the fall plate on four shells, which are arranged vertically one above
the other.
Figures 4.3, 4.4 and 4.5 shows time dependence graphs of the contact force on
the plate, the displacement, and the displacement velocity of the plate. Solid lines
in Figs. 4.3, 4.4, and 4.5 correspond to the solution of the problem with the finite
elements shell discretization, and dashed lines correspond to the calculation with
simulation of the MHS filler shell prototype. Numbers 1 and 2 are used to mark the
Fig. 4.2 The porous
material stress-strain
diagram
A. V. Demareva et al.
the stabilization stage. In this position, the shell inner surface is almost closed. The
third stage of the shell deformation begins, and it is characterized by a sharp increase
in the contact force.
As it is shown in Fig. 4.1, the behavior of spherical shells reaction force on
the plates movement is nonlinear. Due to this, spherical shells have good energyabsorbing properties and can be used for shock damping in protective elements. The
effective damper development is very relevant for the design of modern containers
for the transport of radioactive materials and other potentially dangerous cargo.
According to the IAEA regulations, in case of an emergency drop of a container
on a rigid plate, the acceleration experienced by the cargo shall not exceed the limit
value. In this regard, numerical studies of the damping properties of a titanium alloy
spherical shell under shock loading were carried out. The shell is located on a fixed
plate, and on top of it falls plate, simulating the transported cargo. The mass of the
falling plate is 0.889 t, the initial speed of its fall is 13 m/s.
To verify the above computational model of MHS filler, calculations were carried
out in which the shell was replaced by an equivalent in size, weight, and stiffness
prototype (cylinder R = 9 cm, height H = 18 cm) of MHS filler. The problem
was solved in three-dimensional formulation. Taking into account the symmetry of
geometry, initial, and boundary conditions, one-fourth part of the shell prototype and
plate was considered in the calculations.
The porous material stress–strain diagram (Fig. 4.2) was determined on the basis
of a smoothed graph of the change in the contact force acting on the plate (dotted line
in Fig. 4.1) at quasi-static compression of the shell. For comparison, we considered
the problem of the fall plate on four shells, which are arranged vertically one above
the other.
Figures 4.3, 4.4 and 4.5 shows time dependence graphs of the contact force on
the plate, the displacement, and the displacement velocity of the plate. Solid lines
in Figs. 4.3, 4.4, and 4.5 correspond to the solution of the problem with the finite
elements shell discretization, and dashed lines correspond to the calculation with
simulation of the MHS filler shell prototype. Numbers 1 and 2 are used to mark the
Fig. 4.2 The porous
material stress-strain
diagram