Mindlin-Reissner Analytical Model with Curvature for Tunnel Ventilation Shafts Analysis - José Álvarez-Pérez; Fernando Peña (Mathematics, 2021)
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 <semantics>(αn)</semantics> in terms of the thickness <semantics>(h)</semantics> and the radius of curvature <semantics>(R)</semantics>. 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 <semantics>αn=5/</semantics>6 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 <semantics>(h/R)</semantics>. 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.