24-650 Applied Finite Element Analysis
24-650 Applied Finite Element AnalysisHomework No 11Ignacio Cordova24-650 Applied Finite Element AnalysisHomework No 11Elastic-Plastic, Large Deformation Analysis of a Belleville WasherIgnacio CordovaThe objective of this assignment was to perform an elastic-plastic, large deformation analysisof a Belleville Washer (inside diameter 12 mm, outside diameter 24.32 mm, thickness 1 mm,uncompressed height H0 2.01 mm).Figure 1: Belleville Washer1. SetupThe first step was to import the model to Ansys Mechanical in a Static Structural module asa 2D geometry. The 2D behavior was selected as axisymmetric and a default mesh (shown inFigure A.1) was used (227 nodes and 60 elements). The material used was Aluminum Alloy andthe properties for plasticity are shown below: Bilinear Kinematic with a yield stress of 2.8e8 Pa and a tangent modulus of 6.0e10Pa.Figure 2: Bilinear Isotropic Hardening, Aluminum Alloy1 Page
24-650 Applied Finite Element AnalysisHomework No 11Ignacio Cordova3 cases were studied applying a load (F) that was enough to close the gap g (1 mm) Linear elastic analysis:o Loading (Step 1): From 0 s to 1 s. 20 substeps.o Unloading (Step 2): From 1 s to 2 s. 2 substeps. Large-deformation, elastic analysis:o Loading (Step 1): From 0 s to 1 s. 20 substeps.o Unloading (Step 2): From 1 s to 2 s. 5 substeps. Large-deformation elastic-plastic analysiso Loading (Step 1): From 0 s to 1 s. 20 substeps.o Unloading (Step 2): From 1 s to 2 s. 5 substeps.2. Results and AnalysisThe results are shown in Figure loadingForce (N)1000elastic loading400elasticunloading20000.00E 00-2002.00E-014.00E-016.00E-018.00E-011.00E 001.20E 00Max Deformation (mm)Figure 3: Load-deflection curvesAs can be seen in Figure 3, the force needed to close the gap for each analysis is different: Linear elastic analysis: F1 1450 N (Figure A.3) Large-deformation, elastic analysis: F2 709 N (Figure A.5) Large-deformation elastic-plastic analysis: F3 657 N (Figure A.7)2 Page
24-650 Applied Finite Element AnalysisHomework No 11Ignacio CordovaThe explanation of this is that the curve stress-strain and the way the solver works aredifferent for all the cases. For the linear elastic analysis, the curve is always linear and thegeometry is always considered the same, so the stiffness of the part doesn’t change while isbeing deformed. For the large-deformation, elastic analysis, the solver treats every substep asa new geometry, so the stiffness changes while is being deformed. In that case, the part is lessstiff when the gap is smaller, so for the same deformation a lower force is needed. Finally, forthe large-deformation, elastic –plastic analysis, a smaller force is needed. The reason of this isthat the stresses are above the yield stress of the Aluminum Allow, so a plastic deformation isoccurring.Because of the plastic deformation, after the unloading process, there is a remainingdeformation. This is shown in Figure A.8 and has a value of 0.058 mm. The final height (H0)is 0.942 mm. A contour plot of the equivalent plastic strain is shown in Figure A.9 confirmingthat a plastic deformation occurred.3. AppendixFigure A.1: Default Mesh3 Page
24-650 Applied Finite Element AnalysisHomework No 11Ignacio CordovaFigure A.2: Boundary ConditionsFigure A.3: Linear-elastic- Total Deformation (t 1 s)4 Page
24-650 Applied Finite Element AnalysisHomework No 11Ignacio CordovaFigure A.4: Linear-elastic- Total Deformation (t 2 s)Figure A.5: Large Deformation, Linear-elastic- Total Deformation (t 1 s)5 Page
24-650 Applied Finite Element AnalysisHomework No 11Ignacio CordovaFigure A.6: Large Deformation, Linear-elastic- Total Deformation (t 2 s)Figure A.7: Large Deformation, elastic-plastic- Total Deformation (t 1 s)6 Page
24-650 Applied Finite Element AnalysisHomework No 11Ignacio CordovaFigure A.8: Large Deformation, elastic-plastic- Total Deformation (t 2 s)Figure A.9: Large Deformation, elastic-plastic- Equivalent Plastic Strain (t 2 s)7 Page
24-650 Applied Finite Element Analysis . Homework No 11 . Elastic-Plastic, Large Deformation Analysis of a Belleville Washer . Ignacio Cordova . The objective of this assignment was to perform a n elastic-plastic, large deformation a nalysis of a Belleville Washer (inside diameter 12 mm, ou
Kaplan, Aaron V. MD Kiessling, Mark H. PA-C, MS King, Amanda J. APRN, MSN Kono, Alan T. MD Kwaku, Kevin F. PhD, MD Laflamme, Kelly H. PA-C 603-650-5724 603-650-5724 603-650-5724 603-650-5724 603-650-5724 603-650-5724 603-650-5724 603-650-5724 603-650-2929 603-650
Finite element analysis DNV GL AS 1.7 Finite element types All calculation methods described in this class guideline are based on linear finite element analysis of three dimensional structural models. The general types of finite elements to be used in the finite element analysis are given in Table 2. Table 2 Types of finite element Type of .
1 Overview of Finite Element Method 3 1.1 Basic Concept 3 1.2 Historical Background 3 1.3 General Applicability of the Method 7 1.4 Engineering Applications of the Finite Element Method 10 1.5 General Description of the Finite Element Method 10 1.6 Comparison of Finite Element Method with Other Methods of Analysis
Finite Element Method Partial Differential Equations arise in the mathematical modelling of many engineering problems Analytical solution or exact solution is very complicated Alternative: Numerical Solution – Finite element method, finite difference method, finite volume method, boundary element method, discrete element method, etc. 9
3.2 Finite Element Equations 23 3.3 Stiffness Matrix of a Triangular Element 26 3.4 Assembly of the Global Equation System 27 3.5 Example of the Global Matrix Assembly 29 Problems 30 4 Finite Element Program 33 4.1 Object-oriented Approach to Finite Element Programming 33 4.2 Requirements for the Finite Element Application 34 4.2.1 Overall .
2.7 The solution of the finite element equation 35 2.8 Time for solution 37 2.9 The finite element software systems 37 2.9.1 Selection of the finite element softwaresystem 38 2.9.2 Training 38 2.9.3 LUSAS finite element system 39 CHAPTER 3: THEORETICAL PREDICTION OF THE DESIGN ANALYSIS OF THE HYDRAULIC PRESS MACHINE 3.1 Introduction 52
Figure 3.5. Baseline finite element mesh for C-141 analysis 3-8 Figure 3.6. Baseline finite element mesh for B-727 analysis 3-9 Figure 3.7. Baseline finite element mesh for F-15 analysis 3-9 Figure 3.8. Uniform bias finite element mesh for C-141 analysis 3-14 Figure 3.9. Uniform bias finite element mesh for B-727 analysis 3-15 Figure 3.10.
The Finite Element Method: Linear Static and Dynamic Finite Element Analysis by T. J. R. Hughes, Dover Publications, 2000 The Finite Element Method Vol. 2 Solid Mechanics by O.C. Zienkiewicz and R.L. Taylor, Oxford : Butterworth Heinemann, 2000 Institute of Structural Engineering Method of Finite Elements II 2
