Green-Lagrange strain linearization separates the nonlinear strain measure into terms that can be used to form residual forces and tangent stiffness contributions during incremental nonlinear finite element analysis.
How It Works
The study notes use Green-Lagrange strain with second Piola-Kirchhoff stress in a reference-configuration virtual work statement. The strain expression is expanded with respect to the current displacement state and an incremental displacement. This separates terms associated with the existing strain state, terms linear in the increment, and terms nonlinear in the increment. The variation of the strain then produces internal force and tangent terms for Newton-Raphson iteration.
Why It Matters
In nonlinear shell analysis, the element stiffness is not a fixed matrix. The tangent must account for both material response and geometry-dependent stress terms. Linearizing the Green-Lagrange strain is the step that turns the nonlinear virtual work equation into a solvable incremental system.
김경종