Cantilever I-Shape Beam Lab Report
Problem Description:
The main purpose of this report is to show how to solve a 3-D finite element model of a cantilever I-shape beam, which is subjected to two concentrated loads (P = 1600 lb.) at the flanges of the free end along z axis.
In this assignment, a convergence study will be used to determine the convergence of the solution with respect to mesh refinement. In addition, it will be used to achieve an accurate solution for problems that have sufficiently dense mesh, which cannot be solve by computer machine.
Finally, the solution obtained from the model will be used to determine the deformation of the structure, the maximum von Mises stress and the position of the largest error at the convergence point. Analysis Method: The material …show more content…
Also, to reduce the difficulty of obtaining the convergence of the results. Figure 5: Picture of mesh refinement technique. Convergence study
The convergence study was used to optimise the solution of the problem and to obtain accurate results. Initially, a coarse mesh (i.e. small number of elements) was used to determine the von Mises stress and the error percentage.
Next, a finer mesh (i.e. more elements) was used every time in order to compare the von Mises stress and the error percentage with the previous test as shown in table 3. In this assignment, the point of convergence has occurred when the number of elements were 1152 as shown in figure 6. The von Mises stress of the I-beam at the point of convergence was 15396.6 psi and it remain constant even when a finer mesh was used.
In summary, when the number of elements were 1152, the solution of the problem is accurate enough for that particular geometry, loading and constraints.
Table 3: Results obtained from the convergence study.
Number of elements Von Mises stress (psi) Error Error %
160 11414.5 0.099452 …show more content…
Shell analysis
Shell analysis technique was used in this assignment to reduce the problem of stability with the I-beam model. Also, it was used to create high quality elements, with less disk space required to solve the problem and obtaining the results.
In addition, shell elements generate a high-quality mesh, which results in reducing the error percentage of the model. Error estimation
Error estimation technique was used to evaluate the quality of the mesh that is applied to the finite element model, in order to determine the accuracy of the results obtained from the model.
In fact, if the mesh in the areas of high stress is too coarse, the stress results will not be accurate and the error percentage will be significantly high. However, if the mesh in the areas of high stress is fine, the stress results will be more accurate and the error percentage will be minimal. Results: Figure 7: Plot of maximum displacement (inches) of the structure. Figure 8: Plot of the maximum von Mises stress (psi). Figure 9: Plot of the structural energy error. Discussion and
The main purpose of this report is to show how to solve a 3-D finite element model of a cantilever I-shape beam, which is subjected to two concentrated loads (P = 1600 lb.) at the flanges of the free end along z axis.
In this assignment, a convergence study will be used to determine the convergence of the solution with respect to mesh refinement. In addition, it will be used to achieve an accurate solution for problems that have sufficiently dense mesh, which cannot be solve by computer machine.
Finally, the solution obtained from the model will be used to determine the deformation of the structure, the maximum von Mises stress and the position of the largest error at the convergence point. Analysis Method: The material …show more content…
Also, to reduce the difficulty of obtaining the convergence of the results. Figure 5: Picture of mesh refinement technique. Convergence study
The convergence study was used to optimise the solution of the problem and to obtain accurate results. Initially, a coarse mesh (i.e. small number of elements) was used to determine the von Mises stress and the error percentage.
Next, a finer mesh (i.e. more elements) was used every time in order to compare the von Mises stress and the error percentage with the previous test as shown in table 3. In this assignment, the point of convergence has occurred when the number of elements were 1152 as shown in figure 6. The von Mises stress of the I-beam at the point of convergence was 15396.6 psi and it remain constant even when a finer mesh was used.
In summary, when the number of elements were 1152, the solution of the problem is accurate enough for that particular geometry, loading and constraints.
Table 3: Results obtained from the convergence study.
Number of elements Von Mises stress (psi) Error Error %
160 11414.5 0.099452 …show more content…
Shell analysis
Shell analysis technique was used in this assignment to reduce the problem of stability with the I-beam model. Also, it was used to create high quality elements, with less disk space required to solve the problem and obtaining the results.
In addition, shell elements generate a high-quality mesh, which results in reducing the error percentage of the model. Error estimation
Error estimation technique was used to evaluate the quality of the mesh that is applied to the finite element model, in order to determine the accuracy of the results obtained from the model.
In fact, if the mesh in the areas of high stress is too coarse, the stress results will not be accurate and the error percentage will be significantly high. However, if the mesh in the areas of high stress is fine, the stress results will be more accurate and the error percentage will be minimal. Results: Figure 7: Plot of maximum displacement (inches) of the structure. Figure 8: Plot of the maximum von Mises stress (psi). Figure 9: Plot of the structural energy error. Discussion and