Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Mindlin-Reissner Analytical Model with Curvature for Tunnel Ventilation Shafts Analysis

Version 1 : Received: 13 March 2021 / Approved: 15 March 2021 / Online: 15 March 2021 (11:57:34 CET)

A peer-reviewed article of this Preprint also exists.

Álvarez-Pérez, J.; Peña, F. Mindlin-Reissner Analytical Model with Curvature for Tunnel Ventilation Shafts Analysis. Mathematics 2021, 9, 1096. Álvarez-Pérez, J.; Peña, F. Mindlin-Reissner Analytical Model with Curvature for Tunnel Ventilation Shafts Analysis. Mathematics 2021, 9, 1096.

## Abstract

The formulation and analytic solution of a new mathematical model with constitutive curvature for analysis of tunnel ventilation shaft wall is proposed. Based on the Mindlin-Reissner theory for thick shells, this model also takes into account the shell constitutive curvature and considers an expression of the shear correction factor variable (αn) in terms of the thickness (h) and the radius of curvature (R). The main advantage of the proposed model is that it has the possibility to analyze thin, medium and thick tunnel ventilation shafts. As a result, two comparisons were made: the first one, between the new model and the Mindlin-Reissner model without constitutive curvature with the shear correction factor (α_n=6/5) as a constant, and the other, between the new model and the tridimensional numerical models (solids and shells) obtained by finite element method for different slenderness ratios (h/R). The limitation of the proposed model is that it is to be formulated for a general linear-elastic and axial-symmetrical state with continuous distribution of the mass.

## Keywords

tunnel ventilation shafts; analytical modelling; analytic solution; bending theories; cylindrical shells

## Subject

Engineering, Automotive Engineering