Mixed models for the structural analysis

Introduction

In the most of Finite Element analysis performed by practitioners, displacement-based beam and plate models are used. Unfortunately, these models must often be corrected by shear factors, suffer from locking phenomena, and generally give a low accurate stress description. By the contrary, it is possible to set up mixed beam and plate finite elements (in which also stresses and strains are considered as independent variables) which are generally locking-free and give a more accurate stress description. Unfortunately these (sometimes called "exotic") models could be not compatible with classical ones, use a non-conform formulation, and stability problems lead often the methods to be extremely complicated to manage.

Goal

Our purpose is to look for a new development pathway that takes the best properties of both approaches while minimizing and controlling the disadvantages.

Methods

Starting from the 3D formulation fo the elastic problem, the aim is to be able to operate a “dimensional reduction of the problem”, obtaining the 1D beam model or the 2D plate model. As a second step, it is then possible to develop suitable 1D or 2D Finite Elements or apply other numerical techniques.

Results

• Planar beam
• 3D beam
• Plate
• Non-prismatic beam

Main Collaborations

• Dipartimento di Matematica “Felice Casorati” Università degli studi di Pavia
• Institut für Mechanik der Werkstoffe und Strukturen TU Wien

References

• S. M. Alessandrini, D. N. Arnold, R. S. Falk, and A. L. Madureira, “Derivation and justification of plate models by variational methods”, pp. 1–20 in Plates and shells (Quebec, 1996), edited by M. Fortin, CRM Proc. Lecture Notes 21, Amer. Math. Soc., Providence, RI, 1999.
• F. Auricchio and E. Sacco, “A mixed-enhanced finite-element for the analysis of laminated composite plates”, Int. J. Numer. Methods Eng. 44 (1999), 1481–1504.
• F. Auricchio, C. Lovadina, and A. L. Madureira, “An asymptotically optimal model for isotropic heterogeneous linearly elastic plates”, M2AN Math. Model. Numer. Anal. 38:5 (2004), 877–897.
• E. Reissner, “On a variational theorem and on shear deformable plate theory”, Int. J. Numer. Methods Eng. 23 (1986), 193–198.

Group publications

• F. Auricchio, G. Balduzzi, C. Lovadina. A new modeling approach for planar beams: finite-element solutions based on mixed variational derivations. Journal of Mechanics of Materials and Structures, 5 (2010), 771-794.
• F. Auricchio, G. Balduzzi, C. Lovadina. The dimensional reduction modelling approach for 3D beams: Differential equations and finite-element solutions based on Hellinger–Reissner principle. International Journal of Solids and Structures, 50 (2013), 4184–4196.
• F. Auricchio, G. Balduzzi, M.J. Khoshgoftar, G.R. Rahimi, R. Sacco. Enhanced modeling approach for multilayer anisotropic plates based on dimension reduction method and Hellinger–Reissner principle. Composite Structures, 118 (2014) 622-633.
• F. Auricchio, G. Balduzzi, C. Lovadina. The dimensional reduction approach for 2D non-prismatic beam modelling: A solution based on Hellinger–Reissner principle. International Journal of Solids and Structures, 63 (2015) 264–276.