GeometricTransformations

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This project implements a framework for simulating differential equations on nonlinear manifolds.

The procedure is demonstrated with the Cosserat rod model, furnishing a novel finite element formulation that rectifies the lack of objectivity exhibited by existing finite elements without violating the director constraints or compromising the symmetry of the tangent stiffness at equilibrium. The framework is element-independent, allowing its implementation as a wrapper to existing element libraries without modification of the element state determination procedures.

The foundations for this project are developed in a journal article. The findings of this project are currently being implemented in the OpenSees framework for finite element analysis. Source code for a MATLAB implementation is available at https://github.com/stairlab/GeometricTransformations. This implementation leverages the FEDEASLab toolbox for nonlinear analysis.