3 Temperature Variation Modelling of an Assembled Three-Storey Structure 29 3.6 High-Fidelity FEA Modelling The high-fidelity FEA was comprised of three types of elements, eight-node bricks (C3D8), six-node triangular prism (C3D6) and four-node tetrahedral (C3D4) elements. For this system, the steel portions were constructed using the tetrahedral elements, while the aluminium was comprised of the eight- and six-node elements. The reason for this is due to the mesh refinement of the contact area. During the initial model updating, it was found that using brick elements for the steel would result in different natural frequencies compared to using tetrahedral elements. This was found to be due to the stress propagation across the joint. To demonstrate this, Fig. 3.7 shows results from identical loadings and mesh seed but different element types. Figure 3.7a shows the case with brick elements, and Fig. 3.7b shows the tetrahedral elements. The tetrahedral elements produced natural frequencies near the experimentally found values. The main aspect to note from Fig. 3.7 is the difference in stress locations, mainly near the centre of the contact patch. In the physical system, there is no contact there since the aluminium has a T-slotted geometry. It was found that refining the brick element mesh by a factor of 4 eliminated this difference but added a large amount of computational time since the system is already large. After the initial model was created and calibrated, both temperature approaches were applied to the high-fidelity model. First, the coefficient of thermal expansion was modelled. However, this produced some anomalous results. These issues arise in the thermal trends in the natural frequencies. As mentioned in Sect. 3.3, the first three bending modes all decrease in frequency with an increase in environmental temperature. For the high-fidelity model, this trend only occurs for the fundamental frequency and is opposite for the second and third bending modes. Both of these modes increase in natural frequency with an increase in environmental temperature. There are three possible reasons for this discrepancy, with the first being that the combination of thermal elements and the tied contact make it impossible to model. This would be based on the physics associated with the mass and stiffness matrices for an element. The second possibility is that there is a trade-off between the stiffness and damping for the damped natural frequency found experimentally. It was observed in Sect. 3.3 that there is a noticeable increase in damping that is not taken into account in the modelling. If there is a large increase in the damping and a slight increase in stiffness, then it is still possible for the damped natural frequency to decrease. The third possible reason is due to the tied connection used. This constraint is predominately an enforcement of displacement of the connected nodes on the surfaces. This thermal effect Fig. 3.7 Cross-sectional stress with different steel elements. (a) Eight-node brick elements. (b) Four-node tetrahedral elements
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