OS-C501

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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
Offshore Standard DNV-OS-C501, November 2013 Sec.9 Structural analysis – Page 157 11.5 Buckling analysis for sandwich structures 11.5.1 Sandwich structures may be exposed to highly localised buckling modes such as wrinkling and dimpling, in addition to more global modes. For simple stress states these local modes may often be checked using standard formulae. 11.5.2 The wave-lengths for wrinkling are normally very short (often of the order of the sandwich thickness). If a direct FE analysis of wrinkling is carried out it is essential that a sufficiently fine mesh be used in the skin laminates, such that the mode shape is well represented. If each skin laminate is modelled using shell elements, the element size should not normally be greater than λ/12, where λ is the buckling wavelength. The core shall be modelled with solid elements of similar size. The required element size shall be established using iterative calculations. 11.5.3 In performing FE analysis of wrinkling it is not normally necessary to model a large area of the structure, provided the in-plane stress state in the skin is well represented. A portion of the panel extending over a few wavelengths is normally sufficient. The result is not normally sensitive to the size of the panel selected for modelling. 11.5.4 In the absence of detailed information about geometrical imperfections and their consequences, these may be allowed for by reducing the critical wrinkling stress by 40%. The face wrinkling stress in some text book formulas may already includes such allowance. 11.5.5 Wrinkling of skin laminates may be accompanied by yielding of the core if the core is made of a ductile material. This may in turn lead to a reduction in the tangent stiffness of the core and a lowering of the critical stress for wrinkling. This is mainly a problem at points of load application and at joints, where the core experiences local loading, and may be avoided by adequate thickening of the skin laminate, insertion of higher strength core material locally or by other local design features. The adequacy shall be proved by testing or analysis unless previous experience shows the solution is adequate. 12 Partial load-model factor 12.1 General 12.1.1 A deterministic factor shall be assigned to each structural analysis method. It is designated in this standard as the partial load-model factor γ Sd (see Sec.3, Sec.2 [3.6] and Sec.8 [2.2]). 12.1.2 The load-model factor accounts for uncertainties of the structural analysis method being used to accurately describe and quantify the response of the structure. 12.1.3 Model factors for the main structural analysis methods are given in the following sub-sections. 12.1.4 In some cases a structure is only evaluated by testing, and such an approach evaluates only the particular conditions tested. A procedure for this approach is given in Sec.10. 12.2 Connection between partial load-model factor and analytical analysis 12.2.1 When analytical methods are used within their assumptions and limitations a model factor of 1.0 should be used. 12.2.2 If analytical methods are used outside their assumptions and limitations, it shall be documented that the magnitude of the model factor ensures that all predicted stresses and strains are higher than in reality. If the choice of model factor cannot be documented, the analytical method shall not be used. 12.3 Connection between partial load-model factor and finite element analysis 12.3.1 The accuracy of FE methods is generally very good when the structure is properly modelled. The use of these methods with unsatisfactory models is much more uncertain. 12.3.2 When FE methods are used within their assumptions and limitations (and according to [5]) a model factor of 1.0 may be used. 12.3.3 If FE methods are used outside their assumptions and limitations, it shall be documented that the magnitude of the model factor ensures that all predicted stresses and strains are higher than in reality. If the model factor cannot be documented, the analysis method shall not be used. 12.3.4 If the boundary conditions do not exactly represent the real conditions the effect on the load model factor shall be evaluated. As a minimum a factor of 1.1 shall be used. 12.3.5 If the load-model factor cannot be determined for calculations in a critical region, e.g. a critical joint or region of stress concentrations, experimental qualification should be done (see Sec.10). DET NORSKE VERITAS AS
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OS-C501

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