Analytical sensitivity analysis of geometrically nonlinear structures based on the co-rotational finite element method

This paper is concerned with the parameter sensitivity analysis of structures undergoing large displacements. The authors introduce the analytical sensitivity expressions for an element independent co-rotational formulation of a geometrically nonlinear finite element method. An extension of this formulation to treat follower forces is presented. The co-rotational framework uses a pre-existing linear finite element library and does not require the development and implementation of kinematically nonlinear element formulations. This feature along with the element independence makes the co-rotational framework an attractive option for the implementation of geometrically nonlinear analysis and sensitivity analysis capabilities. The sensitivity formulations with respect to shape and material parameters are presented and their numerical treatment is discussed. The importance of a consistent tangent stiffness, including unsymmetric terms, on the accuracy of computed sensitivities is addressed. The framework is applied to shape and topology optimization examples, verifying the methodology and highlighting the importance of accounting for large displacement effects in design optimization problems.