A Numerical Framework for Form-Finding of Gridshells Accounting for Material Uncertainties

  • Tóth, Bálint (BME, POLIMI)
  • Bruggi, Matteo (POLIMI)
  • Lógó, János (BME)

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The Force Density Method (FDM) [1] enables the form-finding of reticulated shells by exploiting the equilibrium conditions of bar structures. A FDM-based method of robust design optimization [2] is introduced in this contribution, tailored to elastic gridshells affected by material uncertainties. Assuming that imperfections and variability (likely to arise from manufacturing processes) are small relative to the truss dimensions, and that mean material properties are normally distributed with known second-order statistics, an augmented deterministic form-finding problem is implemented based on perturbation techniques, see [3]. This approach avoids the computational costs associated with probabilistic formulations and Monte Carlo-based optimization algorithms, which require multiple assemblies and inversions of the global stiffness matrix. To minimize the influence of stochastic variability, the set of force densities corresponding to the spatial geometry of minimum mean compliance that fulfills prescribed geometric constraints is sought using sequential convex programming. The dependence of the global stiffness matrix on the varying network geometry is handled in terms of the minimization unknowns by exploiting the formalism of the force density method, see e.g. [4], which is especially useful for computing sensitivities. Numerical simulations address reticulated shells subjected to gravity loads and a lightweight column-like element related to metal additive manufacturing, investigating the sensitivity of the optimal shape to material uncertainties. Extensions to other types of uncertainties are foreseen. REFERENCES [1] Schek H., The force density method for form finding and computation of general networks, Computational Methods in Applied Mechanics and Engineering, Vol. 3(1), pp. 115–134, 1974. [2] Log´ o J., ´ New type of optimality criteria method in case of probabilistic loading conditions, Mechanics Based Design of Structures and Machines, Vol. 35(2), pp. 147–162, 2007. [3] Guest J.K., Igusa T., Structural optimization under uncertain loads and nodal locations, Computer Methods in Applied Mechanics and Engineering, Vol. 198(1), pp. 116–124, 2008. [4] Bruggi M., Guerini C., Energy-based form-finding of reticulated shells accounting for eigenvalue buckling, Composite Structures, Vol. 354, pp. 118742, 2025.