TY - RPRT
T1 - Rupture Analysis of Oil Tankers in a Side Collision
T2 - Global Structural Model of Bow Indentation into Ship Side
AU - Wierzbicki, Tomasz
AU - Simonsen, Bo Cerup
PY - 1996
Y1 - 1996
N2 - Since the pioneering work of Minorsky in 1958 the collision damage
of ships has been extensively studied in literature. In the past
few yearsthere has been renewed interest in this type of problem,
as exemplified by for example [4], [7]. For a complete review of
the subject, the reader is referred to the work by Jones, [4], and
subsequent reports of the International Ship Structure Committees.
Three main approachesemerged in the literature. The empirically
based methods (Minorsky, Woisin), the Finite Element Method
(DYNA-3D, PAM-CRASH, ABAQUS, ADINA, DYTRAN) and the analytical,
approach (McDermott et al. Hysing, Reckling, etc.) The present
report belongs to the latter category. The underlying philosophy
of the present approach is rooted in the First Principles of
Mechanics and is consistently based on the energy methods in
plastic structural mechanics with finite displacements and
rotations.The objective of this report is to develop a theoretical
basis for studying collision damage of the side structure of a
stricken ship. It is not our intention to predict the extent of
damage to any particular ship. Instead, a number of fundamental
problems not previously treated in the literature were formulated
and solved. The report consists of four self-contained and
independent parts.In the first part a plate strip model is
developed for a longitudinally stiffened single hull ship which
includes finite strength of transverseframes. It is shown that the
dent size is increasing with the indentation depth. The rate of
spreading of deformation to the neighbouring baysdepends on the
plastic strength of the supporting structure relative to the
longitudinal strength of the plate strip. Another interesting
result of thepresent solution is the effect of evening-out of
strains over several bays in the case of a low longitudinal
resistance of the supporting frames.In the second part of this
report two kinematically admissible solutions for a square
rigid-plastic plate under a point load are compared. One is a
2-dimensinal solution with all components of the strain tensor
retained. The other one is a simplified solution in which the
plate strength is derived from two perpendicular sets of plate
strips where the shear strength isneglected. A full equivalence of
both solutions was proved by taking on Mises yield condition in
the plate solution and a limited interaction curve in the plate
strip solution.The third part of the present report is devoted to
the derivation of an exact solution of punch indentation into a
curricular plate. A distinguished feature of the solution is a
progressive contact (wrapping) of the platearound a hemispherical
punch. It is shown that the force-deflection relationship and the
critical strain to rupture depend on the radius of theplate as
well as the punch radius. An approximate solution was also
developed which opened a way for generalizing the circular plate
solution to a rectangular plate subjected to an eccentric impact.
The solution was further extended to cover orthotropic plates.The
resistance of decks/bulkheads to in-plane indentation of a rigid
punch is treated in the fourth and last part of this report. The
analysis is similar in spirit to the earlier solution for web
crushing presented as Reports # 23 and 38 of the Phase I Tanker
Safety Project. The importantnew contribution of the present
approach is that the length of the folding wave is not assumed, as
in the previous analyses, but found as a part ofthe solution. A
simpler force-displacement relationship is obtained in the case of
both symmetric and unsymmetrical impact.The solution is valid up
to the point of first fracture. Beyond that point the plate will
fail in the central cut mode or the concertina folding mode,
depending on the geometry of the impacting bow, location of the
indentation site and direction of deck stiffeners. The central cut
failure mode is covered in a very comprehensive way in the Report
# 1 of the Collision Project. References to the concertina tearing
solutions were given earlier.It is believed that the results of
the present study (Reports # 1 and 2, together with the relevant
deliverables of Phase I Tanker Safety Project) will give important
background information for developing more detailed structural
models of collision induced damage of a broad class of ships.
AB - Since the pioneering work of Minorsky in 1958 the collision damage
of ships has been extensively studied in literature. In the past
few yearsthere has been renewed interest in this type of problem,
as exemplified by for example [4], [7]. For a complete review of
the subject, the reader is referred to the work by Jones, [4], and
subsequent reports of the International Ship Structure Committees.
Three main approachesemerged in the literature. The empirically
based methods (Minorsky, Woisin), the Finite Element Method
(DYNA-3D, PAM-CRASH, ABAQUS, ADINA, DYTRAN) and the analytical,
approach (McDermott et al. Hysing, Reckling, etc.) The present
report belongs to the latter category. The underlying philosophy
of the present approach is rooted in the First Principles of
Mechanics and is consistently based on the energy methods in
plastic structural mechanics with finite displacements and
rotations.The objective of this report is to develop a theoretical
basis for studying collision damage of the side structure of a
stricken ship. It is not our intention to predict the extent of
damage to any particular ship. Instead, a number of fundamental
problems not previously treated in the literature were formulated
and solved. The report consists of four self-contained and
independent parts.In the first part a plate strip model is
developed for a longitudinally stiffened single hull ship which
includes finite strength of transverseframes. It is shown that the
dent size is increasing with the indentation depth. The rate of
spreading of deformation to the neighbouring baysdepends on the
plastic strength of the supporting structure relative to the
longitudinal strength of the plate strip. Another interesting
result of thepresent solution is the effect of evening-out of
strains over several bays in the case of a low longitudinal
resistance of the supporting frames.In the second part of this
report two kinematically admissible solutions for a square
rigid-plastic plate under a point load are compared. One is a
2-dimensinal solution with all components of the strain tensor
retained. The other one is a simplified solution in which the
plate strength is derived from two perpendicular sets of plate
strips where the shear strength isneglected. A full equivalence of
both solutions was proved by taking on Mises yield condition in
the plate solution and a limited interaction curve in the plate
strip solution.The third part of the present report is devoted to
the derivation of an exact solution of punch indentation into a
curricular plate. A distinguished feature of the solution is a
progressive contact (wrapping) of the platearound a hemispherical
punch. It is shown that the force-deflection relationship and the
critical strain to rupture depend on the radius of theplate as
well as the punch radius. An approximate solution was also
developed which opened a way for generalizing the circular plate
solution to a rectangular plate subjected to an eccentric impact.
The solution was further extended to cover orthotropic plates.The
resistance of decks/bulkheads to in-plane indentation of a rigid
punch is treated in the fourth and last part of this report. The
analysis is similar in spirit to the earlier solution for web
crushing presented as Reports # 23 and 38 of the Phase I Tanker
Safety Project. The importantnew contribution of the present
approach is that the length of the folding wave is not assumed, as
in the previous analyses, but found as a part ofthe solution. A
simpler force-displacement relationship is obtained in the case of
both symmetric and unsymmetrical impact.The solution is valid up
to the point of first fracture. Beyond that point the plate will
fail in the central cut mode or the concertina folding mode,
depending on the geometry of the impacting bow, location of the
indentation site and direction of deck stiffeners. The central cut
failure mode is covered in a very comprehensive way in the Report
# 1 of the Collision Project. References to the concertina tearing
solutions were given earlier.It is believed that the results of
the present study (Reports # 1 and 2, together with the relevant
deliverables of Phase I Tanker Safety Project) will give important
background information for developing more detailed structural
models of collision induced damage of a broad class of ships.
M3 - Report
BT - Rupture Analysis of Oil Tankers in a Side Collision
ER -