Abstract
When space structures are placed in low-Earth orbit the exposed structure
is subjected to hypervelocity collision with meteoroids and man-made orbital
debris. Prediction of damage to orbiting space structures due to collisions
with such hypervelocity space debris, which could gain speed up to 10 km/sec,
is an important issue. However, generally used finite element code needs
some extra complicated processes to be applied in dynamic collapse problems
which contain strong non-linearity and discontinuity, such as member fracture.
In this paper, the Adaptively Shifted Integration (ASI) technique with
the linear Timoshenko beam element, which can be easily implemented with
a minimum effort into the existing finite element codes, is applied to
the space debris impact analysis of a framed structure in space. In this
technique, the numerical integration point in an elastically deformed element
is firstly placed at the optimal point for linear analysis. Then the integration
point is shifted immediately after the occurrence of a fully plastic section
in the element, using the previously established relations between the
location of numerical integration point and that of plastic hinge, to form
a plastic hinge exactly at the position of that section. The technique
produces higher computational accuracy with fewer elements than the conventional
finite element code. By expressing member fracture by a plastic hinge located
at the exact position with a simultaneous release of resultant forces in
the element, discontinuous problems could be easily analyzed even by the
finite element code with displacemental form.
Explicit time integration code uses a lumped mass matrix, which is simplified
by concentrating each element's mass on each corresponding node point,
and numerical error tends to increase in response analyses. It is evident
especially if the ASI technique is used, as only few elements per member
are needed in the technique, which causes the numerical error due to mass
matrices increase. Therefore, in order to maintain higher computational
efficiency, an implicit code with the CG method, which can implement a
distributed mass matrix, is chosen for the time integration scheme. As
the occurrence of extremely large rotations and strains is anticipated
in debris impact analyses, the updated Lagrangian formulation (U.L.F.)
is used as the incremental theory. Contact between members, and the distribution
of element mass before and after member fracture has occurred, are also
examined.