- STATIC PROBLEMS
- Notes
- Direct Differentiation Method (DDM)
- Linear Static DDM
- Adjoint Method
- Nonlinear Static DDM
- Bouc-Wen Material Derivatives
- Examples
- Sensitivity of Cantilevered Beam Displacement
- DYNAMIC PROBLEMS
- Notes
- Linear Dynamic DDM
- Nonlinear Dynamic DDM
- Rayleigh Damping Derivatives
- Modal Damping Derivatives
- Eigenvalue Derivatives
Although I love the topic of sensitivity analysis, and wish the DDM was in more widespread use, some of the notes posted above are a bit sloppy. I am currently writing a free online textbook on the topic; I will post it here as soon as it is ready in the fall of 2026. In the meantime, direct differentiation for the calculation of first- and second-order response sensitivities for linear, nonlinear, static, and dynamic analysis is comprehensively implemented in the Python code G2 posted on the Finite Elements page.