Form finding of continua shells with lattice spring models: Fid-Bau Portal

Form finding of continua shells with lattice spring models

Sá Marques, Tatiana / Dias da Silva, Vítor / N.B.S. Júlio, Eduardo

Highlights • Lattice models are proven to be very accurate for form finding of continua shells. • The mesh type has a different degree of influence depending on the approach considered. • The accuracy of the results is demonstrated for both one-step and incremental loading. • Lattice models are much simpler and faster to program than the FEM.

Abstract The use of spring cells as an alternative to finite element method (FEM) analysis of deformable continua has numerous advantages, such as its discrete representation and unidimensional stress states. This paper presents an innovative alternative approach to the continua FEM analysis, based on a new discrete model algorithm of bar elements framing a triangulated grid - lattice spring model. A non-uniform optimized thickness distribution, in both continua and discrete models, was implemented. This novel feature is a vital aspect to the optimization of the final shape. Two discrete models were developed, the classic/stiffness model and the innovative/flexibility model, that differ by the calculatory cross-section areas assigned to the bars of the cell. Results demonstrate that the latter performs better, not only for the independency of the mesh quality, but also for the approximation of the results (when compared to the continua model). An incremental shape definition algorithm is also applied to keep the horizontal coordinates unchanged. This new discrete approach led to a structural model that is easier and faster to program than FE method. It is also very accurate, since the final shapes obtained by the continuum method and the discrete methods are practically coincident.