Nonlinear Analysis

Lecture 5: Updated Lagrangian Formulation - Incremental Analysis

Topics: Updated Lagrangian formulation for incremental general nonlinear analysis

  • Principle of virtual work in terms of 2nd Piola-Kirchhoff stresses and Green-Lagrange strains referred to the configuration at time t
  • Incremental stress and strain decompositions in the updated Lagrangian form of the principle of virtual work
  • Linear and nonlinear strain increments
  • Consistent linearization of terms in the principle of virtual work
  • The “out-of-balance” virtual work term
  • Iterative equations for modified Newton-Raphson solution
  • Flowchart of complete solution
  • Comparison to total Lagrangian formulation

Instructor: Klaus-Jürgen Bathe

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