ENCOR4050 Modelling & Simulation in Engineering Project Task 1 Q L 2Q L L L L Figure 1: Bridge under load. The bridge shown in Figure 1 has the following dimension L = 10 m and is subjected to distributed load along the top and bottom brace with q = 30 kN/m. Perform a nite element analysis of the bridge using Abaqus. Your report should document the following results: 1. The deformed shape of the bridge 2. The stress contour of the bridge 3. The location of the maximum stress and maximum de ection Assume that all the members have a square cross section with sides b = 30 mm. The Young's modulus of the material used in the construction of the bridge is E = 210 GPa. In your nite element analysis, use the following: 1. Linear beam element in Abaqus 2. Perform a convergence study by increasing the number of elements along each member of the bridge. You may try to use 2, 4, 8, 16 elements per member, compare and report your observations 3. Use line load when applying the distributed load q Task 2 A concrete overpass structure is shown in the gure below. Assume plane strain condition. Let Young's modulus E = 22 GPa and Poisson's ratio = 0:25. Determine the values and locations of the maximum tensile and compressive principle stresses occurring in the part of the structure in the region 2 m above the ground. 1 Prior to analysis, note that the geometry and the boundary conditions of the problem is symmetric about the y axis. In this case, it makes sense to model only half the geometry of the problem. In order to modely the symmetric boundary condition, the displacements in the x direction on the axis of symmetry has to be constrained. Considerable amount of experience is necessary to select an optimal mesh so that the results are su ciently accurate for engineering purposes at the minimum amount of computational cost. Very often, calculations with a series of meshes starting from a coarse one need to be performed, and their results compared. In this task, you are required to follow the best-practice modelling approach. This analysis consist of two parts. Part 1 The simplest approach is to re ne the mesh uniformly. Start with a coarse mesh by specifying a global seed size hseed = 3:2 m. Use 4-node quadrilateral elements with mapped feature turned o . Perform a nite element analysis using this mesh and record the results. Then repeat the analysis by specifying a smaller global element sizes hseed = 1.6 m, 0.8 m, 0.4 m and 0.2 m. Report on the observations you make with regards to the stress contour, and the value of the maximum tensile and compressive stresses. You may need to consult the user's manual or the tutorial examples to complete the nite element analyses. A convergence study is to be performed for each of the required values. This study will lead to best estimates and error estimations to these values. The aim of this task is to exercise the best-practice approach in nite element analysis. It is unacceptable to perform the computation with one ne mesh only. Part 2 Compare the quality of 3-node triangular, 6-node triangular, 4-node quadrilateral and 8-node quadrilateral elements. To evaluate the quality of di erent types of elements, meshes with similar numbers of nodes are generated using each type of element. An element of higher quality will lead to more accurate results. In this part of the task, you will repeat the analysis in Part 1 using hseed = 0:5. Assume that the result obtained with hseed = 0:2 in Part 1 is accurate enough and will be used as a reference solution. The nite element results from the three di erent elements will be compared with this reference solution. Rank the performance of the elements according to their accuracy. Comment on the observations you made. q = 40 kN/m2 3 m 6.5 m 2 m 3 m 3 m 3 m 3 m Figure 2: Concrete overpass structure subjected to load. Report Your report should include the following key contents: Title page 2 Table of contents Brief description of objective of analysis Summary of the theoretical background of nite element method used in your calculations Description of the steps/algorithms of calculations Description of mesh Analysis results, evaluations and comments Plot of the nite element mesh Contour plot of displacements Contour plot of stresses Tabulated displacements and stresses at required locations Estimation for errors based on a convergence study Conclusions (best estimates of displacement and stresses, error estimation, etc.) and suggestion for further improvement in your analysis Additional remarks 1. This assignment contributes to 30% of the total assessment of this course 3