ENCOR4050 Modelling & Simulation in Engineering
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.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
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.
The simplest approach is to rene 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.
Compare the quality of 3-node triangular, 6-node triangular, 4-node quadrilateral and 8-node quadrilateral elements. To evaluate the quality of dierent 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 dierent elements will be compared with this reference solution. Rank the performance of the elements according to their accuracy. Comment on the observations you made.
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
- This assignment contributes to 30% of the total assessment of this course
Plot of Finite Element Mesh. 5
Contour Plot of Displacement. 5
Tabulated displacements and stresses at required locations. 7
The Finite Element Analysis is the technique which has been for the finding of the solutions which are nearly approximate to the boundary value problems. There have been different methods for the variations which includes the calculus of the minimisation and the maximisation of the functional parts with the minimisation of the error functions along with producing a stable solution. The major focus of the project has been beam part through the use of the finite element method. The geometry and the loading conditions are based on the size which is mainly to mimic an environment related to the real world scenario. Hence, the analysis is mainly performed through the Abacus which includes the calculations and the theoretical calculations which are to make sure for the convergence of the structure. As per the results and analysis, there have been different variety of the loads which are there mainly due to the vehicular traffic which are for the utilising the bridge. The important part is to perform the structural analysis by properly considering the loading. The Finite Element Method has been for the analysis to get the accuracy in the results.
The Finite Element method includes the solving of the engineering and the non-engineering problems which are based on the analysis of the analytical mathematical solution. The elements are based on the respectability with the form of the Rayleigh Ritz method. Hence, this is for the handling of the situations for the stress analysis. The procedures are for the computer programming with the solving of the problems like the stress, heat transfer, fluid flow and the electromagnetics. This is the actual domain method which is for the idealised structure of the discrete elements that has been for the finite element. There has been discretization of the domain in elements with the selection of the interpolation functions and the assigning of the nodes for the elements. This also includes the properties with the assembling of the properties to obtain the equations for the system.
Description of Mesh
The project is for the handling of the Finite Element Analysis which is for the proper deigning and the fabrications of the structural configurations that have been provided. Hence, for this, there have been testing and the erection process along with the fabrication with proper designing and analysis. This is based on the culmination in the steel structure which has been to meet the performance and the economy. The computation is based on the approach of the Electromagnetics, Acoustics, Biomechanics/Biomedical, Geotechnics, Seismic analysis. With this, there is a possibility in the project to handle the matrix equation with the proper expressing of the element behaviour. (Guimaraes et al., 2016). This has been in complete combination for the system solution and the system. The work is based on the handling of the algorithm the vibrational methods that have been used for the minimisation and maximisation of the functions. These are to handle the error of the functions with the production of the stabilised solutions. Hence, the analogy is mainly about the connections with the approximations. The methods with the sub domains and the finite elements include the larger region with the well-defined output values. (Bahrebar et al., 2015). The discussion is based on analysing the view with the proper elements approach of the 3D model as show in the part of the analysis.
Analysis of the results
The analysis is based on the performance which is with the ignoring of the segments of the other parts with the assumption that it is for the element for the simplicity analysis. The Abacus analysis has been performed so as to obtain the critical loading which is important for the allowable stress along with the maximised deflection process. (Van Gaalen et al., 2016). There has been performance by the ignoring of the beam segments with the assumption of the one element with the simplicity of the analysis. This is for the performance with the proper critical loading which is important for the allowable stress and deflection which is more critical.
of the material that has been based on the model configuration and the boundary conditions with loading. The service load simulations have been for the material constants like the Young modulus and the Poisson ratio. (Msekh et al., 2015). The Abaqus has been properly equipped with the values which are for the indication of the typical concrete performance
Conclusion and Suggestion
A proper finite element method has been performed in the project where there is a possibility to easily predictions with the behaviour of the steel bridge with the maximum deflection and the stress. There have been results which are based on the convergent and the information which is important for the designing. Hence, there is a need to use the 3D element bridge for the performance to perform the elements accuracy. (Madenci et al., 2015). The methods are based on handling the representation with a proper set calculating with the increased concentrated load for the maximised deflection or the maximised stress process.
Guimarães, A. S., & Teixeira, M. J. (2016). Project Design Abacus for Wall Base Ventilation Drying Systems to Control Dampness. Drying Technology, (just-accepted).
Bahrebar, P., & Stroobandt, D. (2015, December). Design and exploration of routing methods for NoC-based multicore systems. In 2015 International Conference on ReConFigurable Computing and FPGAs (ReConFig) (pp. 1-4). IEEE.
van Gaalen, J. B., Trejos, A. L., Nikolov, H. N., Ivanov, T. G., Pollman, S. I., & Holdsworth, D. W. (2016, May). Versatile smart hip implant technology using 3D metal printing. In 2016 IEEE International Symposium on Circuits and Systems (ISCAS) (pp. 2731-2734). IEEE.
Msekh, M. A., Sargado, J. M., Jamshidian, M., Areias, P. M., & Rabczuk, T. (2015). Abaqus implementation of phase-field model for brittle fracture.Computational Materials Science, 96, 472-484.
Tornabene, F., Fantuzzi, N., Ubertini, F., & Viola, E. (2015). Strong formulation finite element method based on differential quadrature: a survey.Applied Mechanics Reviews, 67(2), 020801.
Madenci, E., & Guven, I. (2015). The finite element method and applications in engineering using ANSYS®. Springer.