Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Semi-Analytical Lower-Bound Limit Analysis of Domes and Vaults

Version 1 : Received: 2 August 2022 / Approved: 3 August 2022 / Online: 3 August 2022 (07:20:00 CEST)

A peer-reviewed article of this Preprint also exists.

Zona, R.; Esposito, L.; Palladino, S.; Totaro, E.; Minutolo, V. Semianalytical Lower-Bound Limit Analysis of Domes and Vaults. Appl. Sci. 2022, 12, 9155. Zona, R.; Esposito, L.; Palladino, S.; Totaro, E.; Minutolo, V. Semianalytical Lower-Bound Limit Analysis of Domes and Vaults. Appl. Sci. 2022, 12, 9155.

Abstract

The calculation of the collapse load of spherical domes is addressed using a semi-analytical approach under the hypotheses of small displacements and perfect plasticity. The procedure is based on the numerical approximation of the self-stress that represents the projection of the balance equilibrium null space on a finite dimensional manifold. The so obtained self-equilibrated stress span is superimposed to a finite element linear elastic solution to the prescribed loads yielding to the statically admissible set accordingly to Melan’s theorem. The compatibility of the stress with the constitutive law of the material has been enforced using linearized limit domain in terms of generalized stress, namely axial force and bending moment along the local spherical curvilinear coordinates. The procedure has been tested with reference to numerical and experimental data from the literature confirming the accuracy of the proposed method. The comparison with the literature confirms that the buckling load is much greater than the plastic collapse loads both calculated through the proposed procedure and reported in the quoted literature.

Keywords

Limit analysis of domes; Concrete caps; experiment comparison; Not Tensile Resistant Materials; Finite element

Subject

Engineering, Civil Engineering

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