non linear analysis
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FEM(non linear
analysis)Unit-5
S. YUVARAJASSISTANT PROFESSORK.S.R. COLLEGE OF ENGINEEINGTIRUCHENGODE
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FEM(Finite Element Method)
• The finite element method is a means of obtaining approximate numerical solutions to field problems”.
• Replace solution variable distribution with approximate distribution based on:
– fixed solution “shapes” over elements– solution variable values at nodes• Continuous → Discrete
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FE Approximation
• Temperature distribution u(x) – a single degree of freedom case
(SDOF)
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• Approximation: assumption of “shape” of solution throughout element – usually polynomial – linear,quadratic,…
• More nodes & elements → greater accuracy
• Generally quadratic better than linear
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Types of FEM problems
• Linear problems.(obeys hook’s law)
• Non linear problems.(hook’s law not applicable)
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Linear Graph
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FE Methods of Nonlinear Mechanics (TB) • Semidiscretization of Continuum Equations • Static and Dynamic Discrete Equations • Lagrangian, Eulerian, and Arbitrary Lagrangian
Eulerian (ALE) meshes • Frame Invariant Stress Rates • Total and Updated Lagrangian Formulations • Material and Geometric Stiffness
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Solution Algorithms for Nonlinear Problems (TH)
• Newton and Modified Newton Methods • Consistent Linearization • Line Search • Quasi-Newton Updates ("BFGS", etc.) • Arc-Length Strategies
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Information
• For other algorithms refer non-linear finite element analysis by j.n reddy.