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 $\left({\alpha }_n\right)$ in terms of the thickness $\left(h\right)$ and the radius of curvature $\left(R\right)$. 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 ${\alpha }_n=5/$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 $(h/R)$. 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.

中文翻译：

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曲率分析的Mindlin-Reissner隧道通风竖井分析模型

提出了一种用于隧道通风竖井墙分析的具有本构曲率的数学模型的建立及解析解。基于关于厚壳的Mindlin-Reissner理论，该模型还考虑了壳本构曲率，并考虑了剪切校正因子变量的表达式。$（{\alpha }_{ñ}）$ 就厚度而言 $（H）$ 和曲率半径 $（\mathrm{[R}）$。该模型的主要优点是可以分析薄，中和厚的隧道通风井筒。结果，进行了两个比较：第一个比较，是新模型和没有本构曲率且具有剪切修正因子的Mindlin-Reissner模型之间的比较。${\alpha }_{ñ}=5/$6为常数，另一个为新模型与通过有限元法针对不同细长比获得的三维数值模型（实体和壳）之间的常数 $（H/\mathrm{[R}）$。所提出的模型的局限性在于，要为质量具有连续分布的一般线性弹性和轴向对称状态制定模型。