OS-C501

Offshore Standard DNV-OS-C501, November 2013
Sec.9 Structural analysis – Page 156
eccentricity of loading) that results in compressive forces that are not coincident with the neutral axis of the
member may require consideration. The assumed form and amplitude of the imperfection shall be decided on
the basis of the production process used with due consideration of the relevant production tolerances. Refer to
Sec.6 [8].
11.2.4 In some cases a geometrically non-linear analysis may be avoided as follows. The elastic critical load
(without imperfections) P e is calculated. In addition an ultimate failure load P f is estimated at which the entire
cross-section would fail by compressive fibre failure, in the absence of bending stresses at the section in
question. If P e > P f the further assessment may be based on geometrically linear analysis provided geometrical
imperfections are included and the partial load effect modelling factor is increased by multiplying it by the
factor:
11.2.5 In cases where it is possible to establish the bending responses (stresses, strains or displacements)
associated with an in-plane loading separately from the in-plane (axial) responses, a first estimate of the
influence of geometrical non-linearity combined with the imperfection may be obtained by multiplying the
relevant bending response parameter obtained from a geometrically linear analysis by a factor:
1 −
1
1 − P f 4 P e
e 1 − σ σ e 1
and combining the modified bending responses with the (unmodified) in-plane responses.
11.2.6 The above procedures ([11.2.5] and [11.2.4]) may be non-conservative for some cases where the postbuckling
behaviour is unstable. Examples include cylindrical shells and cylindrical panels under axial loading.
Such cases shall be subject to special analysis and or tests.
11.3 Buckling analysis of more complex elements or entire structures
11.3.1 Buckling analysis of more complex elements or entire structures shall be carried out with the aid of
verified finite element software or equivalent.
11.3.2 Initially an 'eigenvalue' buckling analysis shall be performed assuming initial (non-degraded) elastic
properties for the laminates and, for sandwich structures, for the core. This shall be repeated with alternative,
finer meshes, until the lowest 'eigenvalues' and corresponding 'eigenmodes' are not significantly affected by
further refinement. The main purposes of this analysis are to clarify the relevant buckling mode shapes and to
establish the required mesh density for subsequent analysis.
11.3.3 Careful attention shall be paid to correct modelling of boundary conditions.
11.3.4 If the applied load exceeds, or is close to, the calculated elastic critical load, the design should be
modified to improve the buckling strength before proceeding further.
11.3.5 A step-by-step non-linear analysis shall be carried out. Geometrical non-linearity shall be included in
the model. The failure criteria shall be checked at each step. If failure such as matrix cracking or delamination
is predicted, any analysis for higher loads shall be performed with properties reduced as described in Sec.4 [9].
11.3.6 Alternatively to the requirement in [11.3.5] a geometrically non-linear analysis may be performed using
entirely degraded properties throughout the structure. This will normally provide conservative estimates of
stresses and deformations. Provided reinforcing fibres are present in sufficient directions, so that the largest
range of un-reinforced directions does not exceed 60º, such an estimate will not normally be excessively
conservative.
11.3.7 The influence of geometric imperfections should be assessed, on the basis of the production method and
production tolerances. Refer to Sec.6 [8].
11.4 Buckling analysis of stiffened plates and shells
1
P
P
,
1
11.4.1 When stiffened plate or shell structures are analysed for buckling, special attention shall be paid to the
following failure modes:
— local buckling of laminate (plate) between stiffeners
— possible local buckling of individual plate-like elements in the stiffeners themselves
— overall buckling of the stiffened plate or shell, in which case separation (debonding) of the stiffener from
the plate or shell laminate must be explicitly considered.
11.4.2 The finite element model shall be able to reproduce all the relevant failure modes as listed in [11.4.1].
Stiffener debonding shall be evaluated by the insertion of appropriate elements at the interface to monitor the
tensile and shear forces that are transmitted across the bond, together with an appropriate criterion based on
tests or relevant published data.
or
1
− ε ε
e
DET NORSKE VERITAS AS