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Numerical methods for structural analysis

Keywords: finite element method, time integration methods, structural dynamics, meshless method, error estimation.
Fig. 1. RCP stress recovery and adaptive mesh refinement (de Miranda).
Fig. 2. From magnetic resonance to finite ele- ment modeling (Castellazzi).
Fig. 3. Mode shapes of different shell structures (Tornabene).

This research line encompasses the development and application of new and effective numerical methods and computational techniques for the solution of structural engineering problems.

The current research activities address a wide range of structural issues, including:

  • finite element formulations for arches, plates and shells,
  • stress recovery techniques in finite element analysis,
  • a posteriori error estimation in finite element analysis,
  • time integration methods for transient analyses,
  • finite element approaches for structural dynamics,
  • discontinuous Galerkin methods,
  • flexible multi-body systems,
  • finite element formulations for the dynamic analysis of damaged structures,
  • meshless methods for the analysis of vibrations of spherical and parabolic shells,
  • nonconservative stability problems,
  • finite element and boundary element formulations for modeling bulk, guided and leaky guided waves in solids,
  • cell method formulations for crack paths analysis in brittle materials,
  • special finite elements for stress concentration problems,
  • image-based finite element modelling,
  • Differential Quadrature (DQ) and Differential Quadrature-based methods,
  • Strong Formulation Finite Element method (SFEM),
  • isogeometric analysis,
  • laminated composite plates and shells with discontinuities.

Main publications

Daghia F., de Miranda S., Ubertini F. (2013). Patch based recovery in finite element elastoplastic analysis. Computational Mechanics 52(4), 827-836.

Castellazzi G., de Miranda S., Ubertini F. (2011). Patch based stress recovery for plate structures. Computational Mechanics 47, 379-394.

Castellazzi G., de Miranda S., Ubertini F. (2010). Adaptivity based on the recovery by compatibility in patches. Finite Elements in Analysis and Design 46, 379-390.

Castellazzi G., Gentilini C., Krysl P., Elishakoff I. (2013). Static analysis of functionally graded plates using a nodal integrated finite element approach. Composite Structures 103, 197-200.

Castellazzi G., Krysl P., Bartoli I. (2013). A displacement-based finite element formulation for the analysis of laminated composite plates. Composite Structures 95, 518-527.

Castellazzi G., Krysl P. (2012). A nine-node displacement-based finite element for Reissner-Mindlin plates based on an improved formulation of the NIPE approach. Finite Elements in Analysis and Design 58, 31-43.

Tornabene F. (2009). Free Vibration Analysis of Functionally Graded Conical, Cylindrical and Annular Shell Structures with a Four-parameter Power-law Distribution. Computer Methods in Applied Mechanics and Engineering 198, 2911- 2935.

Tornabene F., Fantuzzi N., Viola E. (2016) Inter-Laminar Stress Recovery Procedure for Doubly-Curved, Singly-Curved, Revolution Shells with Variable Radii of Curvature and Plates Using Generalized Higher-Order Theories and the Local GDQ Method, Mechanics of Advanced Materials and Structures 23, 1019-1045.

Cannarozzi M., Molari L. (2013). Stress-based formulation for non-linear analysis of planar elastic curved beams. International Journal of Non-Linear Mechanics 55, 35-47.

Tornabene F., Fantuzzi N., Ubertini F., Viola E. (2015) Strong Formulation Finite Element Method Based on Differential Quadrature: A Survey, Applied Mechanics Reviews 67, 020801-1-55.

Mazzotti M, Bartoli I., Marzani A. and Viola E. (2013). A 2.5D Boundary Element formulation for modelling damped wave in arbitrary cross-section waveguides and cavities, Journal of Computational Physics, 248, 363-382.

Mazzotti M., Bartoli I., Marzani A and Viola E. (2013). A coupled SAFE-2.5D BEM approach for the dispersion analysis of damped leaky guided waves in embedded waveguides of arbitrary cross-section, Ultrasonics, 53, 1227-1241.

Castellazzi G., De Marchi L., Krysl P. and Marzani A. (2013). Quantitative simulation of wave propagation in human bones to support the ultrasonic non-invasive assessment of human bones, Proc. of SPIE, Vol. 8695, 86952G-1 86952G-10.

Mazzotti M., Marzani A., Bartoli I., Viola E. (2012). Guided Waves dispersion analysis for prestressed viscoelastic waveguides by means of the SAFE method, International Journal of Solids and Structures 49, 2359-2372.

de Miranda S., Mancuso M., Ubertini F. (2010). Time discontinuous galerkin methods with energy decaying correction for non-linear elastodynamics. International Journal for Numerical Methods in Engineering 83, 323-346.

Ferretti E. (2009). Cell method analysis of crack propagation in tensioned concrete plates. Computer Modeling in Engineering and Sciences 54, 253-281.

Ferretti E., Casadio E., Di Leo A. (2008). Masonry walls under shear test: A CM modeling. Computer Modeling in Engineering and Sciences 30, 163-189.

C. Gentilini, L. Nobile, K.A. Seffen. (2009). Numerical analysis of morphing corrugated plates. Procedia Engineering 1, 79–82.

Research projects

EU FP7-AAT-2011-RTD-1 ID. 284562 Project: SARISTU. Smart Intelligent Aircraft Structures.

Verification in computational structural mechanics, PRIN2007 – Research Unit of Bologna, coordinator: Prof. F. Ubertini.