Non linear analysis

FEM(non linear

analysis)Unit-5

S. YUVARAJASSISTANT PROFESSORK.S.R. COLLEGE OF ENGINEEINGTIRUCHENGODE

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

FE Approximation

• Temperature distribution u(x) – a single degree of freedom case

(SDOF)

• Approximation: assumption of “shape” of solution throughout element – usually polynomial – linear,quadratic,…

• More nodes & elements → greater accuracy

• Generally quadratic better than linear

Types of FEM problems

• Linear problems.(obeys hook’s law)

• Non linear problems.(hook’s law not applicable)

Linear Graph

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

Solution Algorithms for Nonlinear Problems (TH)

• Newton and Modified Newton Methods • Consistent Linearization • Line Search • Quasi-Newton Updates ("BFGS", etc.) • Arc-Length Strategies

Information

• For other algorithms refer non-linear finite element analysis by j.n reddy.