curve so obtained。 Table 1 outlines the section properties that were used for the 2 ROPS models。

Boundary Conditions

The boundary conditions for each FE model were designed to simulate full base fixity and involved the implementation of translational and rotational restraints about the global X, Y and Z axes of the ROPS。 This was performed using a fixed multipoint constraint (MPC) that tied the base perimeter dependent nodes of each post to a single independent node located at the base centroid of each post。 This independent node was restrained both in translation and rotation about all global degrees of freedom。 This restraint condition was numerically identical to restraining all base perimeter nodes, however, it enabled the resultant reaction forces to be obtained at two single nodes only, which assisted greatly in developing the resulting load deflection response profiles for each loading condition。

Loading Procedure

The loading procedure involved using a displacement controlled method for the lateral loading phase and a load controlled procedure for the vertical and longitudinal loading phases。 Details of the loading procedure that simulated the requirements of the standard are as follows:

Stage 1:

Application of an arbitrary enforced displacement to the ROPS in the lateral direction and measurement of the base reactions to obtain the load deflection response

Determination of the energy absorbed by the ROPS for the applied deflection from the area under the load deflection curve and determination of the correct enforced

displacement to apply to the ROPS to obtain the energy level requirement in accordance with AS2294。2-1997

Stage 2: Six loading stages in the sequence

1。 Application of the determined enforced displacement in the lateral direction necessary to give the required amount of energy absorption

2。 Unloading of the ROPS through application of the base reactions to the model

3。 Application of the required vertical load to the ROPS using face pressures distributed over an appropriate area

4。 Unloading of the ROPS through application of the base reactions to the model

5。 Application of the longitudinal load to the ROPS using equivalent face pressures distributed over an appropriate area

6。 Unloading of the ROPS through application of the base reactions to the model

Results of Numerical Study Lateral Loading Phase

The numerical and experimental load deflection profiles of the ½ scale ROPS models are shown in Figure 5 and it is evident that there is very close agreement between the two results which provides validation of the FE model for the lateral loading phase。 As shown by the distinctive shape of this figure the FE ROPS model has exhibited a stable response with a constant load carrying capacity of approximately 190 kN。 Moreover, the ROPS has  reached a limiting peak load and sustained significant plastic deformation from about 15mm to about 65mm。 The shape of this load deflection profile is characteristic of a structure that has absorbed energy in a smooth, efficient and ductile manner。

The severity of the plastic deformation experienced by the ½ scale model ROPS is further exemplified  through  reference  to  the  Von  Mises  stress  distribution  in  Figure  10 which

indicates that plastic hinges had formed at the top and base of each post of the ROPS, which was an identical replication of the experimental findings。 The plastic hinge zones that were located at the top and base of each post underwent shape distortion during the lateral loading phase。 This was shown by the substantial distortion of the finite element mesh and was characterised by the inward folding of the elements that were located on the extreme compression face of the member。 The distortions of the mesh at two of these hinge locations are shown in Figure 11。