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  BDA 31003 Task Report No.1 Analysis of Axial Problem  NADIA BALQIS BINTI ISMAIL Matrix No: CD120171 October 7, 2014 1.   Model/Problem Description In this task students should demonstrate their comprehension in doing analysis of axial problem in complex problem, including initial constraint set in point  F  . While applying the load at C  , at the same time point  F is displaced 1 cm and maintained. The illustration of Task 1 is depicted in figure 1 below. Figure 1: The axial problem 2.   Finite Element Model 2.1   Element Model The cantilever beam is modeled as two dimensional rectangular bar with three different of area which is A 1 = 5cm 2 , A 2 =2cm 2  and A 3 =5cm 2  The  x  plane surface has 6 nodes with 6 elements.  After refined the mesh will be 8 nodes the illustration of the meshing is as shown in Figure 2. The unit used in this model is consistent SI unit: Length: m E: N  /  m 2 , therefore the Young’s Modulus is  E 1 = 69000000000 N  /  m 2 , E 2 =101000000000 N  /  m 2  ,E 3 =7300000000 N  /  m 2  Poisson Ratio for this case 0.3 Force: N, the applied force for this case is 1KN but we need to change it to 1171N Figure 2: FEM Model 2.2   Constraints To represent a fixed end of the cantilever beam, all nodes in the left end are constrained in  x axis. They are not allowed to move in  x axis, using displx=0. To make sure that the cantilever beam is not moving in  y direction, one of the node is also restrained in  y -axis, using disply=0. However in end of the right node put disply=1cm because there is gap shown between free end and fix end. The constraints can be seen in Figure 2 2.3   Loadings A concentrated load is represented by indicating as a negative direction in  y direction, forcex=−1171  N.Negative value here indicates that the direction is the opposite of the  y -axis. 3.   Results and short discussion The displacement magnitude and tensile stress at user define point results are illustrated in Figure 3 and Figure 4, respectively. By looking at the magnitude (total) displacement of the deformed  beam, it is clearly shown that the free end will be mostly deformed. However the largest displacement is not at the tip where a concentrated load is applied. The displacement is 0.01m at free end compared to where load applied, the displacement at the load applied 0.004m. During  the tension deformation as indicated by deformation plot (Figure 3) this region is highly compressed, as a consequence the tensile stress shows higher at the load applied compared to other region. In this corner a tensile stress concentration is the highest (6.173+E08). Besides this area, the area around the concentrated load is also high stressed. It can be understood since the load is applied in this point. Figure 3: Displacement magnitude Figure 4: Tensile Stress at User Defined Point   Figure 5: Result for this task 4.   Conclusion Based on this simulation result, there are some results can be derived: 1)   The cantilever will be deformed in a tension mode with the largest displacement of 0.01m 2)   High concentration stresses occur at middle region of the rectangular bar where a concentrated load applied. The damage can start from this region because of this high stress concentration, as high as (6.173+E08). 3)   The area around the middle region has developed high tensile stress concentration although the concentration level is not as high as the middle region. This right region, however is  purely in tension stress, so crack can be initiated from this region if the tensile stress level reaches the fracture stress of the material.
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