A Python implementation of the Force Density Method (FDM), introduced by Schek (1974).
- FDM is an algebraic approach for finding the shape (geometry) of structures under equilibrium of forces.
- The FDM methods requires a connectivity graph (a given topology with fixed and free nodes), external loadings on the nodes (Vectors in 3 dimensions) and force densities on the edges as the main inputs.
- The solver then simply solves a system of linear equations and provides the 3-dimensional coordinates of the nodes under equilibrium.
Implemented by: Vahid Moosavi
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Implementation is the same as described in Schek (1974).
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Schek, H. J. (1974). The force density method for form finding and computation of general networks. Computer methods in applied mechanics and engineering, 3(1), 115-134.
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Works easily with mesh-based structures or graphs (in Networkx format)
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As shown in examples, can be mixed with any machine learning algorithms, optimization methods (either gradient based or evolutionary strategies.)
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Look at the examples here
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Some sample results:
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Meshed shell structures
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Parametrizing the force densities based on network centrality measures
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A case of roof where the fixed nodes are on a circle with fixed radius.
- Clustering of 10K generated geometries based on the distribution of forces, edge length and load-paths.
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- Integrating the FDM solver with an auto-differentiation framework such as JAX or Tensorflow.
- Integrating the FDM solver with rule based subdivision systems and parametric topologies in addition to parametric force densities.
- Integrating the FDM solver into an agent-based framework and Reinforcement Learning (RL) set up, where the agent will explore the design space toward a given goal. The goal could be any from optimization concepts or based on other aspects such as maximizing the chance of finding unseen geometries!