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The upper tooth shell structure represents a sophisticated approach to load-bearing design in hydraulic infrastructure applications, functioning through a distinctive internal force distribution pattern that differentiates it fundamentally from traditional plate-based systems. Rather than relying primarily on bending stresses that vary significantly across the material thickness, the upper tooth shell predominantly resists external hydraulic and structural loads via middle plane stress conditions that distribute with considerable uniformity throughout the cross-sectional depth.

The theoretical framework governing upper tooth shell behavior operates within the domain of applied elasticity, a specialized branch of mechanics that examines how materials deform and distribute stress under various loading conditions.

The medium thick shell theory is an extension of the thin shell theory. It further considers the effect of shear deformation on the basis of thin shell theory. The theory of sandwich shell, which is widely used, is similar to the theory of sandwich plate in medium and thick plate in terms of its mechanical model. The solution of medium-thick shells is much more complicated than that of thin shells. The theory of medium thick shell is mainly applied in aerospace and navigation engineering, but rarely applied in water conservancy engineering.