Finite Element Analysis
Stressed skin structures are used prominently in aircraft design. These are placed under load on a daily basis, and thus must be monitored for safety reasons. When a metal or plate is placed under a load, the stress is usually never uniformly distributed throughout the part. Instead, it is concentrated in certain areas. Naturally, these areas of stress concentration are subject to fatigue and cracking more so than other elements on the metal. Furthermore, stress concentrations occur mostly, and are magnified by any discontinuities on the part, such as holes or cracks. The stress concentration factor is a measure of how localised these stresses are. This factor can be easily obtained through the use of specialised software offering finite element analysis. Modelling Approach & Assumptions
Assumptions and Simplifications
The type of analysis conducted was a linear static analysis. This involves applying static loads to a model and using these to analyse the stresses formed. This particular type of analysis was used to simplify the model. Furthermore, in a static analysis, the loads are applied gradually. This eliminates any additional displacements and stresses otherwise caused by suddenly applied loads. There are three main assumptions made when conducting a linear static analysis:
Linearity Assumption: The induced response is directly proportional to the applied loads. This means that if you double the magnitude of the loads, the response of the material (Stresses, Displacements, etc.) will also double.
Elasticity Assumption: The part is not stressed beyond its yield point. This means that there is no permanent deformation and the part will return to its original shape if the loads are removed.
Static Assumption: Loads are applied slowly and gradually until they reach their full magnitudes. Symmetry
Since all of the cut-outs in the assessment task are symmetrical in 2 planes, symmetry was used in solving the finite element model to simplify the analysis and enable for a more efficient mesh. This was also tested in Patran. A basic full plate model of the circular hole was constructed in Patran, with 40 mesh seeds on the base and 80 mesh seeds around the hole. The simulation yielded a maximum principal stress of 0.854 MPa, almost identical to that of the relevantly converged quarter plate (0.855 MPa – Refer to Table 1). Loads
A uniform distributed load of 1 N/mm was applied to the top of the plate. This particular type of load was chosen to eliminate any ‘false’ stress concentrations. If a non-uniformly distributed load was chosen, or even a point load, stress concentrations would arise in locations purely because of the load, and not due to the discontinuities within the part such as holes or cracks. Neglected loads include applying an equal but opposite uniformly distributed load to the bottom of the panel. Instead, the movement bottom of the panel was simply fixed in the y-direction. Conducting a simple calculation for reaction forces will show that the reaction force that results on the bottom is a uniformly distributed load in the opposite direction. Focus for Analysis
The focus of the linear static analysis that was conducted was to obtain the stress concentration factor of each case, and validate it with published data. In order to calculate this, we first need to obtain the maximum principal stress and remote stress. Stress concentrations occur at sections where the cross sectional area changes. The more severe the change, the larger the stress concentration. For this analysis, it is only necessary to determine the maximum stress acting on the smallest cross sectional area. This is done using a stress concentration factor, K, which is determined by: K=σ_maxprincipal /σ_remote
The maximum principal stress was used as opposed to the Von Mises stress since the failure criterion chosen was the maximum principle stress theory. According to this theory,...
Patran Tutorials: http://www.mscsoftware.com/training_videos/patran/Reverb_help/index.html#page/Finite%20Element%20Modeling/mesh_forms.03.4.html
Modelling Errors and Accuracy Notes: http://www.me.mtu.edu/~bettig/MEEM4405/Lecture10.pdf
Linear Static Analysis Notes: http://www.kxcad.net/SolidWorks/COSMOSXpress_Tutorial/topics_general/Assumptions_of_Linear_Static_Analysis.htm
“Finite Element Modeling for Stress Analysis”, R D Cook, Wiley 1995
“Mechanics of Materials”, R C Hibbeler, Pearson Prentice Hall
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