OS-C501

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Offshore Standard DNV-OS-C501, November 2013 Sec.9 Structural analysis – Page 142 2 Linear and non-linear analysis of monolithic structures 2.1 General 2.1.1 Most composite structures possess linear material properties when intact. However, composites can develop various failure mechanisms, e.g. matrix cracking, at very low strains leading to reduced stiffness parameters. 2.1.2 This non-linear behaviour of the material shall be taken into account when failure analysis of composite components is performed. 2.1.3 In the present section several analysis methods will be presented. These methods may be combined with analytically [4] or numerically [5] based response calculations. Under [3] the applicability of the analysis methods will be linked to various failure criteria. 2.1.4 All response calculations shall be based on time-dependent material properties related to, for example, natural or environmental degradation during service life. 2.1.5 Regardless of the analysis method being used geometrical non-linear effects shall be taken into account when significant, see [1.7]. 2.1.6 For the choice of 2-D or 3-D analysis methods, see [1.3.4]. 2.1.7 The development of failures is most accurately described by progressive non-linear analysis methods (presented in [2.2] and [2.3] for in-plane 2-D and 3-D problems, respectively), in which degradation of material properties in case of, e.g., matrix cracking is included. However, such methods may be extremely timeconsuming in problems of practical interest. 2.1.8 In many cases the simplified analysis methods presented in [2.4], [2.5] and [2.6] may be applied. 2.1.9 When using one of the analysis methods based on locally degraded material properties, conservative results are ensured provided the element mesh is sufficiently fine. However, when one of the simple linear failure methods (non-degraded ([2.4]) or globally degraded ([2.5])) is applied, the distribution of stresses/ strains may be incorrect, in particular, near sharp corners or other kinds of geometrical or material discontinuities. The analyst shall beware of the possibility of introducing serious errors. 2.1.10 The simplified methods presented in [2.4], [2.5] and [2.6] are derived under the assumption that matrix failure occurs prior to fibre failure, which is satisfied for most fibre reinforced plastic composites. Guidance note: For certain metal matrix composites, fibre failure may occur prior to matrix failure. In such cases the simplified failure methods must be modified. ---e-n-d---of---G-u-i-d-a-n-c-e---n-o-t-e--- 2.1.11 In the sections containing simplified analysis methods the problems to be solved will be divided into three categories: — statically determinate problems, which mean problems where it is possible to determine all the forces/ moments (and laminate stresses) involved by using only the equilibrium requirements without regard to the deformations — problems where displacements (and laminate strains) are independent of material properties (and can thus be regarded as known) — general (or statically indeterminate) problems, which are problems where the forces/moments involved cannot be determined from equilibrium requirements without regard to the deformations. 2.1.12 Some of the main features of the analysis methods to be presented in the following are listed in Table 9-1. DET NORSKE VERITAS AS
Offshore Standard DNV-OS-C501, November 2013 Sec.9 Structural analysis – Page 143 Table 9-1 Analysis methods Properties Degradation of material Level of in-plane Level of through Load Method properties degradation thickness degradation In-plane 2-D progressive Step-wise degradation Local/ element level Ply level Step-wise increase 3-D progressive Step-wise degradation Local/ element level Ply/ element level Step-wise increase Linear non-degraded Non-degraded ___ ___ Extreme value (initial values) Linear degraded All degraded (except E 1 and through thickness Global (entire domain) Global (entire domain) Extreme value parameters) Two-step non-linear First step: Initial Second step: All degraded (except E 1 , see [2.6.6]) Local/ element level Ply/ element level Extreme value 2.1.13 If fibres are not oriented in the principle stress directions they want to rotate into these directions. This rotation is usually prevented by the matrix. If the matrix cracks or yields, the fibres may be free to rotate slightly. This rotation is usually not modelled. However one should check that ply stresses transverse to the fibres and ply shear stresses are low in a ply with degraded matrix. Otherwise a reanalysis with rotated fibre directions may be required. Guidance note: The rotation of fibres may, for example, be important in filament wound pipe designed for carrying just internal pressure. In this case the fibre orientation is typically about ±55 o . If the pipe experiences a strong axial load in addition to pressure, the fibres want to orient themselves more into the axial direction. 2.2 In-plane 2-D progressive failure analysis ---e-n-d---of---G-u-i-d-a-n-c-e---n-o-t-e--- 2.2.1 If all through thickness stress components can be neglected (see [1.3.4]), one may apply a 2-D (laminate based) analysis method. In-plane 2-D progressive non-linear failure analysis on the ply level provides the highest level of accuracy. 2.2.2 Initially, non-degraded ply properties (E 1 , E 2 , G 12 and ν 12 ) shall be used in the progressive non-linear failure analysis. 2.2.3 The loads on the laminate structure are imposed in a step-wise manner. In the first step a small portion, e.g. 10% of the expected ultimate load is applied. Based on this load level, laminate and ply stresses and strains are calculated and analysed by the relevant failure criterion (for each ply). If failure is detected somewhere in a ply, certain material properties of that ply shall be locally degraded, which means that the parameters shall be reduced in locations (e.g. finite elements) where the failure is detected. The properties shall be degraded according to the following sections. If no failure is observed, the load is increased to e.g. 0.2 x expected maximum load and a similar failure analysis is performed. 2.2.4 If ply stresses exceed the strength of the matrix according to the failure criteria given in Sec.6, the ply properties should be changed according to Sec.4 [9]. 2.2.5 In numerical calculations certain problems may arise, e.g. lack of inversion possibilities of the structural stiffness matrix, when degraded material properties are set equal to 0. To overcome such problems, one may apply small values, e.g. 1% of the non-degraded values instead of zero. 2.2.6 After introducing degraded parameters it is assumed that the plies behave linearly (until the next failure occurs). Laminate properties (i.e. ABD matrix) shall be recalculated based on the degraded ply parameters, and the failure analysis will be repeated (for the same load level as above). When a failure mechanism has occurred somewhere in a ply, the ply is not checked for that failure mechanism in the same region (e.g. finite elements) any more. 2.2.7 The local degradation of ply stiffness properties may induce artificial discontinuities in the stress or strain field. Using gradual change of ply stiffness properties may reduce the effects of discontinuities. 2.2.8 If fibre failure occurs in a ply and location (e.g. finite element) with matrix damage, or if matrix failure occurs in a ply and location (e.g. element) with fibre damage, all material properties of that ply shall be reduced at the location considered. Guidance note: If both fibre failure and matrix failure occur at the same location (i.e. a finite element) in a ply, all material properties of that ply are locally degraded. Thus, at that location the ply cannot carry loads any more. However, in a global sense, DET NORSKE VERITAS AS
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OS-C501

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