In general the ANSYS suite of FEA software was used for mesh generation. Stress analysis was then either conducted using the ANSYS solver or alternatively and in the case of the progressive damage modelling the ABAQUS solver.
Both the HSC and DLHC hybrid connections were represented using 2-dimensional 8- noded quadrilateral elements under plane stress with thickness. The elements used were Plane82 and CPS8 for ANSYS and ABAQUS respectively. A 2-D model was chosen due to computational savings and the assumption that the stress is distributed uniformly throughout the width of the joint. The computational savings become more apparent once the progressive damage modelling is implemented.
A plane stress with thickness approach was chosen against a plane strain method for a number of reasons highlighted by an analysis conducted to investigate the difference between the two theories for the geometry of the specimen examined in the present research. Firstly, a plane strain analysis was conducted to confirm the expected zero strain in the out-of plane direction. Five further plane stress analyses were conducted each having a different specimen width value, 1, 10, 100, 500, 1000 mm, where 1 mm represents a purely plane stress analysis. Figure 7.3 shows the out-of plane strain with respect to specimen width. It is known that when the specimen width is infinity, i.e. a plane strain situation, the out-of-plane strain is zero. Therefore, as the specimen width increases the curve of plane stress in Figure 7.3 will tend towards zero. The result obtained at 100 mm (equivalent to that used in the present research) shows a substantial level of out-of-plane strain. Therefore, the plane strain approximations would only be applicable if the width of the specimen was substantially larger (i.e. > 1000 mm) than that used in the present research.
With increasing specimen width, the consequences of neglecting out-of-plane stress becomes increasingly detrimental to the calculation of in-plane stresses due to Poisson effects. For example, this effect can be readily seen by substantially increasing the width of the specimen to 1000 mm. In this instance the global response is significantly affected and a plane strain analysis would be desirable. However, the current research specimen is only 100 mm wide and therefore the influence of zero out-of-plane stress on global response is felt to be insubstantial.
The specimens used in this study are divided into material areas. For the DLHC there are three areas representing the steel, GRP and glueline. The HSC has 4 areas, steel, GRP, glueline and balsawood. The material properties for the material areas were either obtained experimentally or from manufacturers data. The GRP and glueline material properties were obtained experimentally and the results were discussed in Chapter 4.
7.4.1 MESH DENSITY CONVERGENCE
A small convergence study was conducted to assess the sensitivity of joint global stiffness by changes in mesh density. Initially, a simple model was constructed with a minimum of elements in order to satisfy the element size criteria of the FEA software. The number of elements was increased to a point where the maximum number of nodes allowed by the software was exceeded. The method used to conduct this was to change the number of elements through the thickness of each of the areas of the joint. Care was taken not to exceed the element aspect ratio of 1:20 in non-critical areas and 1:5 in areas of most interest. An applied displacement of 1 mm was used for the convergence study. The results of the study are shown in Table 7.1 for a total rig deflection of 160 kN/mm. It is clear to see from the results that mesh density has little or no effect on the resultant forces on the model. There are a number of possible reasons for this result. Firstly the simple nature of the joint geometry may make its sensitivity to mesh density minimal. Alternatively the lack of apparent sensitivity to mesh density may be caused by the software’s criteria for element aspect ratio. The element size is controlled mainly by the elements in the adhesive layer. In this region two or three elements are used to represent a 0.3 mm adhesive thickness. In order to satisfy the aspect ratio criteria the resulting mesh is very dense. Therefore, it could be said that the minimum mesh density examined is beyond the sensitivity threshold and therefore suitable for this analysis in terms of providing the correct global stiffness. Conversely, by satisfying the aspect ratio criteria, taking into account that the resin
thickness is so small (0.3 mm), the number of elements in the model is very high. Historically this may have been a problem but due to the rapid increase in computing power now available, the large model still produces a solution in a matter of seconds.
Table 7.1 Mesh Convergence results Run
Number Node Count
Resultant Force (kN)
Maximum Von Mises Stress (MPa) 1 6059 -34.8 60.711 2 8071 -34.812 62.068 3 10641 -34.813 62.078 4 13501 -35.078 67.384 5 16194 -35.091 68.997 6 19417 -35.087 69.718 7 24877 -35.114 70.07 8 27351 -35.125 70.086
Although the effect of mesh density appears to have little effect on the response of the model, the progressive damage model will rely on sufficient mesh density to accurately predict the rate of growth of any damage with in the joint. A very coarse mesh will result in accelerated damage growth due to large elements failing, a fine mesh will, although more computationally expensive, allow the rate of damage growth to be represented accurately.
7.4.2 LOAD APPLICATION
Load was applied to both the DLHC and HSC in a similar manner to that in the experimental tests. A displacement was applied to the nodes located at the steel end of the specimen, in incremental steps. A total displacement of 4.5 mm was applied to the HSC joint. This value is representative of the failure displacement of the joint experimentally. The reaction force due to the displacement is output for each step. In addition, stress data for the adhesive layer was analysed to determine whether elements had exceeded their failure limits.
In order to undertake a progressive damage model (PDM) node and element data from ANSYS were output processed in a custom-written FORTRAN routine to convert the format of the node and element files into those used by the ABAQUS suite of FEA software. The loading of both the ANSYS and ABAQUS models was conducted in the same way. A comparison of the global response and the magnitude and location of the
7.4.3 SENSITIVITY ANALYSIS OF NUMERICAL MODEL TO DISPLACEMENT INCREMENT SIZE
When using a non-linear model it is required that an initial displacement step is specified to begin the analysis procedure. The ABAQUS input file provides an initial increment value; the software will examine the rate of convergence and alter the increment size correspondingly to increase the efficiency of obtaining equilibrium. Similarly, during displacement steps where poor convergence rate is observed the software will reduce the increment size in an attempt to establish equilibrium. However, it was noticed that changing the value of initial increment size had an influence on the global response of the model.
In order to investigate the influence of the initial increment size on global response the increment was decreased from 100 percent of the required global displacement to 0.001 percent systematically. The results are shown in Figure 7.4. As the displacement increment size becomes smaller there is a corresponding increase in the resultant global load on the model. The most extensive region of resultant load stability occurs between 100 percent and 0.25 percent of the total required global displacement. Therefore initial load increments less than 0.25 percent of the total load were avoided in order to reduce the artificial loading of the model.
7.5. SIMULATION OF A HYBRID STRUCTURAL CONNECTION