Nonlinear Analysis

Lecture 4: Total Lagrangian Formulation - Incremental Analysis

Topics: Total Lagrangian formulation for incremental general nonlinear analysis

  • Review of basic principle of virtual work equation, objective in incremental solution
  • Incremental stress and strain decompositions in the total Lagrangian form of the principle of virtual work
  • Linear and nonlinear strain increments
  • Initial displacement effect
  • Considerations for finite element discretization with continuum elements (isoparametric solids with translational degrees of freedom only) and structural elements (with translational and rotational degrees of freedom)
  • Consistent linearization of terms in the principle of virtual work for the incremental solution
  • The “out-of-balance” virtual work term
  • Derivation of iterative equations
  • The modified Newton-Raphson iteration, flowchart of complete solution

Instructor: Klaus-Jürgen Bathe

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