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