Geometric nonlinearity revisited - Aalborg...
Transcript of Geometric nonlinearity revisited - Aalborg...
Computational Mechanics, AAU, EsbjergNonlinear FEM
Course inNonlinear FEM
Geometric nonlinearity revisited
Geometric nonlinearity revisited 2Computational Mechanics, AAU, EsbjergNonlinear FEM
Outline
Lecture 1 – IntroductionLecture 2 – Geometric nonlinearityLecture 3 – Material nonlinearityLecture 4 – Material nonlinearity continuedLecture 5 – Geometric nonlinearity revisitedLecture 6 – Issues in nonlinear FEALecture 7 – Contact nonlinearityLecture 8 – Contact nonlinearity continuedLecture 9 – DynamicsLecture 10 – Dynamics continued
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Nonlinear FEMLecture 1 – Introduction, Cook [17.1]:
– Types of nonlinear problems– Definitions
Lecture 2 – Geometric nonlinearity, Cook [17.10, 18.1-18.6]:– 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
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Nonlinear FEMLecture 5 – Geometric nonlinearity revisited, Cook [17.9, 17.3-17.4]:
- 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, 17.9-17.10]:– Solution methods and strategies– Convergence and stop criteria– Postprocessing/Results– Troubleshooting
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Nonlinear FEMLecture 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 [11.1-11.5]:– Solution methods– Implicit methods– Explicit methods
Lecture 10 – Dynamics continued, Cook [11.11-11.18]:– Dynamic problems and models– Damping– Issues in FE dynamic analysis/troubleshooting
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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
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Plastic Deformation
• Permanent deformation is a result of crystallographic slip
• Slip proceeds via dislocation motion• An Isolated dislocation moves at a
particular shear stress• Interaction of dislocations impedes
progress, giving rise to strain hardening
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Plastic Deformation
• Materials have a limit of elastic strain (metals elastic strain limit ≅0,005).
• Beyond the elastic strain limit, atoms of an elastic-plastic material begin to break resulting in residual (permanent) strain once the load is removed.
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Solution methods
Geometric nonlinearity revisited 25Computational Mechanics, AAU, EsbjergNonlinear FEM
Solution methods
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Solution methods
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Solution methods