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