Lecture 5: Updated Lagrangian Formulation - Incremental Analysis

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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

Related Resources

Study Guide (PDF)


Sections 6.2.3, 6.2.4


Bathe, K. J., E. Ramm, and E. L. Wilson. “Finite Element Formulations for Large Deformation Dynamic Analysis.International Journal for Numerical Methods in Engineering 9 (1975): 353-386.

Bathe, K. J., and H. Ozdemir. “Elastic-Plastic Large Deformation Static and Dynamic Analysis.Computers & Structures 6 (April 1976): 81-92.

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