Reduced Order Models for geometrically parameterized beams and shells

11/28/2022

Reawakened by modern advances in structural design and modelling software, thin-shell covers certainly stand out due to their efficiency and aesthetics. The form suitability of an arbitrary thin-shell can be measured by its bending coefficient, the ratio between the bending and total strain energies. For an extensively multi-parameterized shell, classical numerical methods may invoke the curse of dimensionality, as one solution must be computed for each set of parameters. Thus, alternative methods, such as Reduced Order Methods (ROM), are relevant in this context. The present work focuses on finding antifunicular forms for geometrically parameterized shells. Proper Generalized Decomposition is used to obtain an explicit parametric solution. Thus, minimization of the structure´s bending coefficient is easily performed. The ROM relied on an accurate Full Order Model (FOM) which is taken as reference. The geometrical model is defined up to three parameters, with the Bézier Surface formulation. The mechanical model is based on the Mindlin-Reissner formulation, numerically analyzed with a triangular mesh, with quadratic approximations. The results demonstrate that the novel PGD application to parameterized shell structures is successfully allowing to find the antifunicular forms. The ROM is a fair approximation of the FOM for many practical purposes, not only for optimization, with significant gains in computational time and memory resources. A crucial issue in a multidimensional parametric setup is its visualization and, in general, the display of information. A Graphical User Interface (GUI) is specifically designed to postprocess the PGD solution, displaying the parametric responses in real-time.

Authors in the community:

• 

  L

  Luís Guilherme Simões da Silva Tão Espírito Santo

  ist190310

Supervisors of this institution:

• 

  J

  José Paulo Baptista Moitinho de Almeida

  ist11947

civil-engineering - Civil engineering

por - Portuguese

Instituto Superior Técnico