THE UNIVERSITY OF ADELAIDE

THE SCHOOL OF MECHANICAL ENGINEERING

MECH ENG 3108: FINITE ELEMENT ANALYSIS II LABORATORY

PART A

Introduction

Finite element analysis allows an engineering problem to be solved in a numerical method without having to produce a testing model and analyze them in real world applications. Although it remains limited in how it can model real world situations, it will enable engineers to gain a better understanding of engineering problems with the advantage of a risk free and cost effective approach. In the case of this laboratory, the use of ANSYS package will involve modeling objects and analyze them under certain specific conditions. Using ANSYS will involve defining specifically what conditions a specimen is subjected to, identifying particular constraints and limitations and interpret an analytical solution in terms of data results and diagrams that describe the behaviour of the model object. Background

The process of forming a specific solution using finite element analysis can be divided into 3 major stages of modelling. These stages being pre-processing, solution and post processing. Pre- processing is primarily defining the problem into the form of a model. This includes defining its physical parameters and its geometry. More specifically defining major keypoints that make a up areas, volumes and how they are joined together as an entire object. Additionally at this stage the material properties and characteristics also need to be identified given that its mechanical properties will influence the mechanical performance of a particular object therefore it is important to identify the type, properties and orientation of the material being used. This step is about forming a physical model that is as close as the intended form that is desired in real world. Defining the object as accurately as possible would also increase the validity of the modeled analysis using finite element analysis. The solution stage relates to applying external parameters such as loadings, constraints, limitations and possibly assumptions that relate to the intended application of the object in the real world. The ways in which these parameters are being specified are also crucial to attaining a relevant solution at the end. Identifying the types of loads, may it be pressures, point, or area loadings are important in defining the problem. Once these external parameters are applied to the system, the solution to the system can be obtained by solving the system under these loadings and constraints. Post processing refers to interpreting the solution obtained previously in a form that is useful in understanding the behavior of the object under the specific loads and constraints applied to the system. in post processing the results can be viewed in a large number of ways such as maximum stress locations, von mises stress and principal stresses to name a few. Furthermore these results can be analysed using contour plots of stress and von mises stresses, stress distribution, deflection across the object. Finally, a list of solutions can also be obtained at specific nodal points to provide a more in- depth analysis at a particular point on the object. From these 3 major steps, the finite element analysis of a model can provide a range of qualitative and quantitative representations of the behaviour of the object under the given constraints and loadings. From these results the comparison of the intended performance of the object and the model can be made to gain a measure of how the object is likely to react during its service in the real world.

Discussion The purpose of the verification model was to form a base analysis of parameters that will be tested against the verification model to ensure the most appropriate parameters are used to define the actual model correctly. This includes material properties, geometry and physical characteristics, scales and units and other parameters that define the model as accurately as possible. Therefore the verification model is developed solely for testing the most appropriate parameters before applying them to an actual object. The purpose of the verification model can also be used to verify analytical calculations as well as theoretical analysis of similar structures can assist in the actual process of fabricating a product. The use of finite element analysis ensures that an intended design of a product can be tested thoroughly under specific conditions and constraints that are easily interchangeable without the need to produce physical models for analysis. This promotes an efficient and cost effective way to analyse engineering models. Assuming that the thickness of the plate is 20mm as defined in the geometry for analytical calculations

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In calculating the maximum displacement the hole in the plate will be ignored From the material properties given E = 200GPa

( )( ) The verification model produced using ANSYS converges to the analytical calculated value as the element edge length mesh size decreases but doesn’t actually reach that particular value. Using ANSYS included some limitations such as the number of nodes that can be processed. In this case the element edge length was first taken to be 25 and decreasing to 5 by 5 incremental steps. In observing the node where maximum stress occurs being closest to the top of the circle the maximum stress converges to the calculated value of approximately 3.92MPa. Conversely, the maximum displacement values were incrementally larger in magnitude as the element edge length. It diverges away from the analytical calculations of 0.001m. In the case of the analytical calculation the assumption was made to ignore the hole in the centre of the plate. However, with the inclusion of the hole in the verification model using ANSYS it would change the nature of the flat plate and its behavior to axial loading at the hole. The verification model in terms of the maximum displacement gradually diverges to larger values of displacement as it takes into account the hole which causes a greater deflection at the end of the plate as opposed to being a regular flat plate.

The nodes on the model represent a point at which analysis has been conducted to find relevant stresses and displacements at that particular point. The above figures represent the initial mesh size element edge length of 25. The remaining figures for 20, 15, 10, and 5 element edge lengths can be referred to in the appendix. From the figures of 20 down to 5, it shows the convergence to the calculated maximum stress value from the increase in the number of nodes.

Table 1: comparison of calculated and ANSYS model mesh size behavior to maximum stress and displacement

Mesh size/calculation Max stress, σ (MPa) Max displacement, δ (mm)

25 3.5765 0.00122

20 3.6032 0.00134

15 3.7020 0.00136

10 3.7349 0.00139

5 3.8083 0.00146

calculation 3.92 0.001

Figure 1: nodes of mesh size element edge length 25

Figure 2: corresponding mesh lines of mesh size element edge length 25

From Figure 3 the largest deformation location is clearly the most right point of the hole in which the displacement values were obtained in table 1. Similarly in figure 4 below the maximum stress or Von- Mises stress is either the top and bottom point of the hole denoted by the red regions. The nodes at the furthest relative position on the hole are where the corresponding maximum stresses are obtained for each mesh size.

Figure 3: deformed and undeformed changes to the flat plate under loading

Figure 4: Maximum(Von- Mises) stress contour plot

Table 1 suggests that the relationship between the mesh size and the maximum stress is converging to the calculated value as the mesh size element edge length decreases. As for displacement, it increases away from the calculated value of maximum displacement as the mesh size decreases as the hole in the centre of the plat was ignored during the calculation. From the analysis of both methods being the analytical calculations and the verification model using ANSYS poses some limitations and discrepancies that are associated in using such methods. In relation to the analytical calculations, ignoring the hole in the centre of the plate makes a significant difference in both the stress and displacement. If the centre of the hole was to be included, analysis would be made much harder although it would provide a better measure of the stress and displacement. Furthermore the calculations included some assumptions that the thickness of the plate was per unit length for easier analysis which is different from the model of 20mm. For the verification model using ANSYS, the limitations of reducing the mesh size much below 5 will cause the stresses to be larger than the calculation value. Although increasing the amount of nodes for analysis would produce more accurate results it contradicted the calculations of the maximum stress. The assumption in ANSYS was also made that the material properties of the flat plate remained linear, isotropic and elastic which may not be such the case in real world testing. Although these assumptions model the flat plate reasonably well there still remains a degree of error due to such assumptions. Although both the modeled stress and displacement values were off compared to the calculated values they provide a verification that both forms of analysis verify the behavior of the model and are appropriate as part of engineering design of this center hole flat plate. However, the absence of considering the hole in the analytical calculations causes the largest discrepancy between the calculation and the model values of maximum displacement. Figure 5: transitional degrees of freedom throughout the plate

Figure 5 illustrates the transitional degrees of freedom throughout the plate showing that the maximum occurs at the right end where the force was applied compared to a zero value at the left end. This would mostly what is expected however it is dependent on how the stress applied at the right end transitions to the left end of the plate. If the stress is not large enough then the zero value would hold true. Conversely, if the stress is large enough to affect the nature of the left end then it would at least produce a small degree of freedom at that region. The plots suggest that physically the plate will not fail but have the largest elongation horizontally through the centre of the plate. The plate will lengthen axially creating an ellipse with the center hole and compressed in the vertical direction along the center line through the hole. The largest degree of freedom varies from a zero value at the left end to its maximum at the right end where the load is applied. The maximum stress occurs at the top and bottom end of the hole and the maximum displacement occurs at the right end of the hole through its horizontal center line. In general the integrity of the plate under the specific loadings and constraints holds up well. However it will ultimately depends on the service life of the object in the real world.

Figure 6: deformed and undeformed changes to the bracket under loading

Figure 7: Maximum(Von- Mises) stress contour plot of the bracket

In terms of the bracket, the geometrical changes would occur primarily at the bottom of the hole where the load was applied, at that point the greatest displacement occurs. Similarly the maximum stress occurs at the same point where the load was applied causing the largest transitional degrees of freedom to occur at the right end of the bracket. Similar to the plate, the left region of the bracket remains unchanged from the existing forces applied on the bracket. Comparing the plate and the bracket, the bracket is much more susceptible to deformations given its larger hole which minimizes material but maximizes displacement at the point of applied load. In general the plots suggest that the bracket will not fail but its capabilities will be dependent on purpose of the bracket in its actual application in the real world. Conclusion In conclusion the analysis of the plate and the bracket using ANSYS can provide a good measure of how they react to the given load under the specific constraints. The primary purpose of using ANSYS is the ability to easily alter the constraints of the model to verify maximum stress and displacement values from analytical calculations. ANSYS can be used as a tool to model its real world application and testing the model with similar methods to obtain a gauge of how it performs under idealized conditions. From the results obtained from the ANSYS model and analytical calculations the appropriate conclusions can then be made on the integrity of the object based on its purpose for real world applications.

Figure 8: transitional degrees of freedom throughout the bracket

PART B This part is involved in creating solid models that involves filleting, extrusion, copying and changing working planes to form solids modeled in 3 dimensions. 2 solid models were created in this section being the pulley and a spindle base. From these two models the general processes consists of forming a 2 dimensional foundations of its basic geometry and then extruding into volume regions. From these basic volumes of the object other aspects of the model can then be formed such as creating bolt holes, ribs, shaft holes and other external components. Pulley solid model The first aspect in forming the pulley was to create a cross sectional area of the pulley which included rounded edges and fillets through the inner edge of the pulley. Once these features were added to the 2 dimensional are then it was extruded or sweeping the cross sectional area around 360°. Now the general 3 dimensional shape is formed the bolt holes can be made. This involved creating a single bolt hole at the relative 0° position at the centre of the hole and removing the volume through the entire solid. Once this single hole is formed, the remaining holes can be copied around the pulley at 45° intervals. The final model is shown below. Spindle Base Similarly, the first step was to create the base rectangle and the associated bolt holes in the base. Once this 2 dimensional model is formed then it can be extruded into a volume. Next requires the forming of the back rectangle. Now the 2 areas of the base and back rectangle are merged and added together. Next the upper cylinder is formed with a volume subtracted to form the hole through the center. Finally the rib was created between the 2 inner faces and adding the areas together. The final model is shown below.

Figure 9: final solid model of the pulley

Appendix

Figure 10: final solid model of the spindle base

Figure A1: corresponding mesh lines of mesh size element edge length 20

Figure A2: corresponding mesh lines of mesh size element edge length 15

Figure A3: corresponding mesh lines of mesh size element edge length 10

Figure A4: corresponding mesh lines of mesh size element edge length 5