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4.2.1 Methodology

In this section different modelling techniques available to the designer are presented. Guidance is provided on the choice between global and local modelling, and on appropriate element types and geometric simplification. Some design examples are presented. The level of modelling accuracy adopted should be appropriate to the purpose of the model and relate to the scale of the glass structure. One of two

approaches may be adopted in finite element modelling of glass structures: either, a simple global model and a series of detailed local models are created which are complementary and analyses are carried out iteratively; or a single detailed global model is created which addresses all structural aspects.

In the first approach, the simple global model allows for time-efficient study of the global behaviour and for deflections and reaction forces to be established. The simple global model is complemented by detailed local models which assess stress distribution in the portion of structure modelled. In the second

approach, the single detailed global model is used to calculate all structural aspects of the glass structure which are principally reaction forces, deflections and internal stresses. Such an approach increases the computational analysis time and is less easily modified to accommodate structural alterations

during the design process. However, the whole project is stored in one analysis file, avoiding the need to create and update multiple analysis models. In the development of a glass structural model, the behaviour of the supporting primary structure needs to be considered and represented realistically. Therefore attention to contact detailing is essential. Specialised non-linear contact elements should be used as required. Of particular concern are the relative movements of the glass structure’s support points. The possible deflected shapes of the support structure can be represented by separate load cases applied to the glass structural model. These can be post-processed into advanced load combinations. 4.2.2 Simple global model

An example of a simple global model is presented in Figure 4.1. Figure 4.2 is of the actual structure. In such instances, it is appropriate to model glass members with two-dimensional shell elements. For laminated glass, the thickness of the shell elements can be calculated applying an effective thickness approach. Various calculation methods are presented

Figure 4.1 Example global model of entrance vestibule

in the Eurocodes and ASTM. Alternatively, the effective thickness can be calculated from first principles using a purpose-built finite element model. Due to the fact that effective (equivalent) thickness is always less than the overall thickness of the laminate, adjustments to the dead load need to be made to the model to allow for this. One way to do this is by increasing the partial safety factor applied to the dead load/permanent action in order to compensate for the reduction in self-weight of the global model.

It is not necessary to include holes which penetrate the glass, radii at panel corners or arrisses along panel edges. These aspects are not relevant to the global behaviour. They are captured by the detailed local models which are used to calculate the stress distribution in the structure.

Similarly, glass-glass connections and glass- substructure connections can be modelled using one-dimensional beam or link elements with appropriately assigned releases, restraints and stiffnesses. An example is shown in Figure 4.3. Where the lateral bending stiffness and torsional bending stiffness of a connection contributes to the global stability of the structure, these properties should be modelled accordingly. This approach provides an appropriate level of detail for the calculation of global behaviour, deflections and reaction forces. A more detailed approach to connection modelling can be applied to local models which are used to accurately calculate stress distribution.

4.2.3 Detailed local models

Detailed local models are created to complement a simple global model. Separate detailed local models can be created to analyse the local behaviour and stress distribution in the region of a single glass-glass or glass-substructure connection. Three-dimensional volumetric elements can be used as illustrated in Figure 4.4. The simple global design stage and detailed local design stage are not entirely independent. The two processes interact and iterations are required.

Symmetrical boundary conditions shall be used when appropriate to dimensionally reduce the model. This allows for a reduction in computational time. Furthermore, when appropriate to the problem, representing the structural components with a two- dimensional plane strain model can be beneficial. An example is shown in Figure 4.5.

4.2.4 Detailed global model

Sometimes, it is necessary to include a greater level of detail than in the approach described in

Section 4.2.3. However, some simplifications may still be incorporated without compromising the accuracy of the analysis. An example is presented in Figure 4.6 and the actual structure is shown in Figure 4.7. If one of the purposes of the model is to establish the stresses in the glass at a bolted connection, the glass holes at that connection need to be incorporated and the mesh density in that region needs to be sized appropriately. An example of the level of complexity required at the connection is shown in Figure 4.8. The connection should account for all materials in the load path. The method of load transfer should be modelled, e.g. a compression-only connection should be modelled as such. The use of two-dimensional Figure 4.3 Simplified bolted connection in global models

Figure 4.4 Bolted connection, volumetric local model

Figure 4.5 Bonded connection, two-dimensional stress-strain model

shell elements may provide adequately accurate results. However, consideration should be given to the effect of increased stress on the level of composite action through the laminated panel in the region of the connection. The effective thickness of the two-dimensional elements may be altered in the region of the connection to reflect this.