A lamellar structure characterized by two distinct inner and outer surfaces, wherein the thickness t is substantially smaller than both the curvature radius R at the center and the overall size of the structure, represents the foundational definition encompassing thin shell and medium thick shell categories within engineering and manufacturing disciplines. These structural elements are fundamental components in aerospace, automotive, pressure vessel, and industrial equipment applications where weight optimization and material efficiency play critical roles.
The shell resists the external load mainly by the medium plane stress distributed uniformly along the thickness, rather than by the bending stress varying along the thickness. This internal force characteristic of the shell makes it more fully use the strength of the material than the plate, so that it has greater bearing capacity. In hydraulic engineering, shell is widely used, such as double curved flat shell gate, arch dam, etc.
The shell theory constitutes a specialized branch within applied elasticity that extends beyond the fundamental postulates of classical elasticity mechanics by incorporating additional working hypotheses tailored to shell structures.
Thin shell theory represents a fundamental framework within structural mechanics and engineering analysis, developed to characterize the behavior of curved surface structures under various loading conditions. This classical theoretical approach relies fundamentally on the assumption of direct normals, which establishes several key suppositions about how these structures deform and respond to applied forces. The first foundational assumption states that the positive strain perpendicular to the midplane direction remains extremely small in magnitude and is therefore negligible for practical analysis purposes, allowing engineers to disregard thickness-direction deformation in their calculations. The second critical assumption establishes that the middle normal, also referred to as the shell's midsurface normal, maintains its straight configuration throughout deformation, with the right angle relationship between this middle normal and its associated vertical line segment remaining unchanged, thereby indicating that shear strain in both perpendicular directions equals zero, a simplification that significantly reduces computational complexity. The third assumption recognizes that normal stress components on sections parallel to the middle plane, commonly known as extrusion stress or thickness-direction stress, demonstrate magnitudes substantially smaller than normal stresses acting on vertical planes, such that their consequent effects on the overall deformation pattern remain negligible and can be safely excluded from the analysis.
