Course in. Geometric nonlinearity. Nonlinear FEM. Computational Mechanics, AAU, Esbjerg
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1 Course in Nonlinear FEM Geometric nonlinearity Nonlinear FEM
2 Outline Lecture 1 Introduction Lecture 2 Geometric nonlinearity Lecture 3 Material nonlinearity Lecture 4 Material nonlinearity it continued Lecture 5 Geometric nonlinearity revisited Lecture 6 Issues in nonlinear FEA Lecture 7 Contact nonlinearity Lecture 8 Contact nonlinearity continued Lecture 9 Dynamics Lecture 10 Dynamics continued Nonlinear FEM Introduction 2
3 Nonlinear FEM Lecture 1 Introduction, Cook [17.1]: Types of nonlinear problems Definitions Lecture 2 Geometric nonlinearity, Cook [17.10, ]: Linear buckling or eigen buckling Prestress and stress stiffening Nonlinear buckling and imperfections Solution methods Lecture 3 Material nonlinearity, Cook [17.3, 17.4]: Plasticity systems Yield criteria Lecture 4 Material nonlinearity revisited, Cook [17.6, 17.2]: Flow rules Hardening rules Tangent stiffness Nonlinear FEM Introduction 3
4 Nonlinear FEM Lecture 5 Geometric nonlinearity revisited, Cook [17.9, ]: - The incremental equation of equilibrium - The nonlinear strain-displacement matrix - The tangent-stiffness matrix - Strain measures Lecture 6 Issues in nonlinear FEA, Cook [17.2, ]: Solution methods and strategies Convergence and stop criteria Postprocessing/Results Troubleshooting Nonlinear FEM Introduction 4
5 Nonlinear FEM Lecture 7 Contact nonlinearity, Cook [17.8]: Contact applications Contact kinematics Contact algorithms Lecture 8 Contact nonlinearity continued, Cook [17.8]: Issues in FE contact analysis/troubleshooting Lecture 9 Dynamics, Cook [ ]: Solution methods Implicit methods Explicit methods Lecture 10 Dynamics continued, Cook [ ]: 18]: Dynamic problems and models Damping Issues in FE dynamic analysis/troubleshooting Nonlinear FEM Introduction 5
6 References [ANSYS] ANSYS 10.0 Documentation (installed with ANSYS): Basic Analysis Procedures Advanced Analysis Techniques Modeling and Meshing Guide Structural Analysis Guide Thermal Analysis Guide APDL Programmer s Guide ANSYS Tutorials [Cook] Cook, R. D.; Concepts and applications of finite element analysis, John Wiley & Sons Nonlinear FEM Introduction 6
7 Nonlinear FEM Geometric nonlinearity revisited 7
8 Nonlinear FEM Geometric nonlinearity revisited 8
9 Nonlinear FEM Geometric nonlinearity revisited 9
10 Nonlinear FEM Geometric nonlinearity revisited 10
11 Nonlinear FEM Geometric nonlinearity revisited 11
12 Nonlinear FEM Geometric nonlinearity revisited 12
13 Nonlinear FEM Geometric nonlinearity revisited 13
14 Nonlinear FEM Geometric nonlinearity revisited 14
15 Nonlinear FEM Geometric nonlinearity revisited 15
16 Nonlinear FEM Geometric nonlinearity revisited 16
17 Nonlinear FEM Geometric nonlinearity revisited 17
18 Nonlinear FEM Geometric nonlinearity revisited 18
19 Nonlinear FEM Geometric nonlinearity revisited 19
20 Nonlinear FEM Geometric nonlinearity revisited 20
21 Nonlinear FEM Geometric nonlinearity revisited 21
22 Nonlinear FEM Geometric nonlinearity revisited 22
23 Break Nonlinear FEM Geometric nonlinearity revisited 23
24 Example 1 Nonlinear FEM Geometric nonlinearity revisited 24
25 Example 1 Nonlinear FEM Geometric nonlinearity revisited 25
26 Example 2 Nonlinear FEM Geometric nonlinearity revisited 26
27 Example 2 Nonlinear FEM Geometric nonlinearity revisited 27
28 Example 2 Nonlinear FEM Geometric nonlinearity revisited 28
29 Example 2 Nonlinear FEM Geometric nonlinearity revisited 29
30 Example 2 Nonlinear FEM Geometric nonlinearity revisited 30
31 Example 2 Nonlinear FEM Geometric nonlinearity revisited 31
32 Example 2 Nonlinear FEM Geometric nonlinearity revisited 32
33 Example 2 Nonlinear FEM Geometric nonlinearity revisited 33
34 Example 2 Nonlinear FEM Geometric nonlinearity revisited 34
35 Example 2 Nonlinear FEM Geometric nonlinearity revisited 35
36 Example 2 Nonlinear FEM Geometric nonlinearity revisited 36
37 Example 2 Nonlinear FEM Geometric nonlinearity revisited 37
38 Example 2 Nonlinear FEM Geometric nonlinearity revisited 38
39 Nonlinear FEM Geometric nonlinearity revisited 39
40 Solution methods Nonlinear FEM Geometric nonlinearity revisited 40
41 Nonlinear FEM Geometric nonlinearity revisited 41
42 Nonlinear FEM Geometric nonlinearity revisited 42
43 Solution methods Nonlinear FEM Geometric nonlinearity revisited 43
44 Nonlinear FEM Geometric nonlinearity revisited 44
45 Nonlinear FEM Geometric nonlinearity revisited 45
46 Solution methods Nonlinear FEM Geometric nonlinearity revisited 46
47 Nonlinear FEM Geometric nonlinearity revisited 47
48 Nonlinear FEM Geometric nonlinearity revisited 48
49 Solution methods Nonlinear FEM Geometric nonlinearity revisited 49
50 Convergence criteria Nonlinear FEM Geometric nonlinearity revisited 50
51 Graphical Solution Tracking Nonlinear FEM Geometric nonlinearity revisited 51
52 Graphical Solution Tracking Title: Time value of the last calculated iteration Label x-axis: Cumulative Iteration Number In nonlinear analysis, ANSYS uses a solver that iterates to nd a solution. If a problem is relatively linear, very few iterations are required, while highly nonlinear problems necessitate many iterations. Label y-axis: Absolute Convergence Norm (non-normalized values) The quantities being plotted are always some residual versus a tolerance (residual: difference between the norms of applied load and calculated reaction load). When the residual becomes less than tolerance, a converged solution is obtained. ANSYS calculates a convergence criterion based on the norm of the applied load (the tolerance value can be adjusted by the CNVTOL command). The type of analysis determines the convergence quantities taken into account, e. g., force, moment, displacement, temperature,... Nonlinear FEM Geometric nonlinearity revisited 52
53 Convergence Provided Iteration Schemes: Newton-Raphson method (default) Newton-Raphson method with adaptive descent Arc-length method Convergence-enhancement features: Line search Automatic load stepping Bisection Nonlinear FEM Geometric nonlinearity revisited 53
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