Integrated form finding, simulation and optimization using the generalized force density method based on mixed functionals

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The proposed project sets itself the goal of expanding the force density method (KDM) into a universally applicable tool for solving mixed problems of form finding, optimization, structural simulation and cutting pattern analysis. The KDM is to be developed into a further, thorough tool of structural analysis, which allows to handle not only completely novel but also conventional tasks of form finding with significantly better accuracy. The methodically new aspect is to treat the force densities as equivalent variables in addition to the deformations. The classical understanding of energetically conjugated forces and displacements is complemented by the special formulation of the force density as moderator between force and geometry. As a result of the reparameterization by means of force densities, the mathematical properties of known (nonlinear) questions change significantly; simulation, form finding and cutting pattern analysis can be smart and efficiently dealt with together. It opens up new perspectives along the force densities into standard statics, including direct and adjoint simulation and sensitivity analysis. Because of its consistent integration into continuum mechanics, the method will be mathematically and numerically sound. The force densities as scalar quantities can also be easily and clearly visualized for 3D structures, which should be used for the development of interactive methods and practice-relevant implementations. Last but not least, the goal is to demonstrate the practical relevance of large, impressive examples together with cooperation partners from the relevant engineering sector, which significantly advance the current state of the art and open up new fields of application. Methods and models are implemented in own or open source software (KRATOS, Carat ++, TeDA, kiwi!3d).