Hermite Isoparametric Finite Element Models for Laminated Kirchhoff Plates with Arbitrary Geometries Using Strain Gradient Theory

March 28, 2025

TIME: 3:30 PM

LOCATION: GMCS 314

SPEAKER: Michele Bacciocchi, DESD Department, University of San Marino, Republic of San Marino

ABSTRACT: The main aim of this research is the development of a finite element code based on the strain gradient theory able to deal with thin laminated plates in the framework provided by Kirchhoff hypotheses. Therefore, this numerical formulation combines the principles of a nonlocal elasticity approach with the versatility of the finite elements to model general stacking sequences, various restraints, and arbitrarily shaped domains. These studies are justified by the increasing use and analysis of micro- and nano-scaled structural elements, which highlighted the inadequacy of classical continuum approaches. For this reason, nonlocal theories are becoming more and more popular. In particular, the adopted model considers the micro/macro scale interactions within the materials and introduces an additional parameter in the constitutive laws which is related to the length-scale effect. The peculiar approach developed in this context requires higher-order continuity conditions and the use of Hermite interpolating functions due to the presence of derivatives in the primary variables. Consequently, conforming and nonconforming approximations have to be developed for both membrane and bending degrees of freedom. The proposed method is validated through the comparison with the results available in the literature. It should be remarked that most of them deals with isotropic or, in limited cased such as cross-ply and angle-ply schemes, simply supported laminated plates, all characterized by regular geometries. The current study considerably extends the applicability of this innovative approach.

HOST: Miguel Dumett

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