Lecture 4: Total Lagrangian Formulation - Incremental Analysis

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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

Related Resources

Study Guide (PDF)

Readings

Sections 6.2.3, 6.2.4

References

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.