THE UNIVERSITY OF ADELAIDEFACULTY OF MECHANICAL ENGINEERING

Mechanical Engineering 2002

STRESS ANALYSIS AND DESIGN

Finite Element Analysis Practical

Date of Practical 22nd and 29th of August, 2008

Liew Joong-Yuen 1148770

Introduction

Finite element analysis (FEA) is a numerical method to solve a variety of mechanical engineering problems, e.g., static/dynamic structural analysis, heat transfer and fluid problems, as well as acoustic and electro-magnetic problems. Using ANSYS, a finite element software, it is possible to model such engineering problems so that accurate solutions can be obtained more efficiently and effectively. In this report, a two dimensional plane problem of a bridge truss and a three dimensional space problem of a bicycle frame are analysed and then solved numerically using ANSYS 11.0.

1. Two Dimensional Plane Truss

Analytical Hand Calculations

A simplified model of the West Gate Bride in Melbourne is as shown in Figure 1.0 below. Two forces act vertically downwards on Node 3 and Node 5. The reaction force at Node 2 and stresses in Elements 1 and 6 are determined with hand calculation method and then in the next section, they are compared with FEA.

Figure 1.0 West Gate Bride Model

The reaction force at Node 2 is as follows:

The free body diagram of the left side of the bride is shown in Figure 1.1 below.

Figure 1.1: Free body diagram of the left side of the bridge

The angle theta is obtained as follows:

The area for Links 1 and 2 is A1 whereas the area for Link 5, 6 and 7 is A2.

Taking sum of forces in the y direction, the force in Link 1, T1, is obtained.

Taking sum of forces in the x direction, the force in Links 6 and 7, T6, is obtained.

Therefore, ultimately, the stresses in Link 1 and Link6 are as follows:

Comparison with FEA

X

Y

76

180m

θ

168m

R2 = 25kN

T1

T6

52

The results (refer to Appendices A and B) obtained from ANSYS are as follows:

Reaction force at Node 2 = 25000 NStress in Element 1 = Stress in Element 6 =

They are exactly the same as that obtained with the hand calculation method and therefore, reliable to obtain further solutions for other analysis.

Discussion of Results and Assumptions

Plots providing stress analysis information were obtained from ANSYS to analysis the structural integrity of the bridge (refer to Appendices C, D and E). These plots ease the process of determining regions of high stress and large deformation so that failures can be determined and prevented. ANSYS allows users to make large volumes of calculations more efficiently and provides graphic depiction of stresses experience in materials.

The hand calculations for the reaction force at Node 2 and the stresses in Elements 1 and 6 were expected to be the same as the solution obtained from ANSYS because a more accurate angle was used in the hand calculations (as oppose to the rounded 25°) thus significantly reducing the final error.

Several assumptions were made to obtain these results. Firstly, it was assumed that the trusses were made of steel with a modulus of elasticity of 200GPa and that it was homogeneous. Secondly, Elements 1-4 were assumed to have a cross sectional areas of 5000mm2 whereas Elements 5-9 were assumed to have a cross sectional areas of 17000mm2.

Conclusion

The solutions to the effects of loads on a bridge were obtainable using ANSYS and through comparing with hand calculations, it was proven to be accurate and reliable. Furthermore, graphical plots including maximum stress and displacement regions were obtained for more comprehensive analysis of the bridge structure; they ease the processes of determining the most likely points of failure thus significantly improving the efficiency of the analysis.2. Beams: Bicycle Space Fame

Verification Model

Figure 2.0: Free body diagram of the beam

Safety Coefficient Calculations

The yield stress,

Taking into account the frame’s body weight and the load at the pedals, the force at Node 3 = 735.75 N and the force at Node 4 = 270 N.

Figure 2.1: Free body diagram of bicycle frame

The maximum stress obtained from ANSYS is as follows:

Therefore, the safety coefficient is as follows:

1N

100mm

6

5

4

3

2

270N

735.75N1

Discussion

The verification model was useful in helping provide an insight as to how beams are treated in the ANSYS program where a 3D coordinate system is used here instead of a 2D system as the bridge truss above. It also showed how bending moments may be calculated when beams are used. This model made the analysis of the bicycle frame later much simpler since the basics were provided. In addition, it allows for comparison of results to be made to make sure that the correct analysis type, units and scale factors were obtained.

Assumptions were made to simplify analysis. The assumptions made are that the joints and materials were perfect, no external forces were acting on the frame, forces act in one direction only, the frame was static, the pedalling force was in the downward direction at node 4 without taking into account the actual pedal, and the pedalling force was constant throughout.

Conclusion

It is undoubtedly more efficient to gain accurate results to complex problems using FEA method.

From the calculation of the safety coefficient, this returns a more than acceptable value for the bicycle frame. However, due to the many assumptions made, this bicycle model might not be ideal should all the other forces be taken into account. To provide a more reliable frame design, the calculations should be made for forces at node 3 that may not be in the downward direction, which will impart more bending moments and also stresses in the structure around node 3. Also, the pedalling force can be made into a time function with a pedal included. The implementation of a pedal will increase the load at node 4 at certain times. This will give a more accurate answer for the safety coefficient and ensure that the bicycle frame is able to successfully withstand the load it is subjected to. Also, this provides the chance to reduce materials use or change the design for economical benefits and a more artistic approach without going below the accepted safety factor since there are fewer assumptions made in this case. However, it is not known yet if ANSYS supports loads as a function of time.

From Appendix B-3, it is seen that the maximum stress occurs at node 1. A different material or a larger cross-sectional area may be used here to improve the

static strength. Also, it is noted that the maximum bending moment occurs at nodes 1, 3, 4, 5 and 6. Strengthening the material or adjusting the dimensions of the frame may be done to prevent failure at these points and hence improve overall static strength.

Appendix A: Reaction Solution

PRINT F REACTION SOLUTIONS PER NODE ***** POST1 TOTAL REACTION SOLUTION LISTING *****

LOAD STEP= 1 SUBSTEP= 1 TIME= 1.0000 LOAD CASE= 0 THE FOLLOWING X,Y,Z SOLUTIONS ARE IN THE GLOBAL COORDINATE SYSTEM NODE FX FY 2 25000. 4 -0.14175E+06 0.56500E+06 6 0.14175E+06

TOTAL VALUES VALUE 0.0000 0.59000E+06

Appendix B: Axial Stress Solution

PRINT ELEMENT TABLE ITEMS PER ELEMENT ***** POST1 ELEMENT TABLE LISTING ***** STAT CURRENT ELEM SAXL

1 -0.11630E+08 2 0.92800E+08 3 -0.33235E+08 4 0.78300E+08 5 0.16023E-09 6 0.30882E+07 7 -0.16676E+08 8 -0.83382E+07 9 0.83382E+07

MINIMUM VALUES ELEM 3 VALUE -0.33235E+08

MAXIMUM VALUES ELEM 2 VALUE 0.92800E+08

Appendix C: Deformation/Displacement

Appendix D: Deflection (Nodal Solution)

Appendix E: Axial Stress (Element Solution)

Appendix F: Deformed Frame

Appendix G: Deflection (Nodal Solution)

Appendix H: Stress in Frame (Element Solution)

Appendix I: Bending Moment (Line Stress)