4D31 front shell

The front shell resists the external load mainly by the medium surface 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 belongs to the category of applied elasticity, which needs to introduce new hypotheses in addition to the basic assumptions of elasticity. It includes thin shell theory and medium thick shell theory.

Thin shell theory is a classical theory of shells. It is based on the assumption of direct normals. These assumptions are as follows: ① The positive strain perpendicular to the midplane direction is extremely small and negligible. (2) The middle normal remains straight, and the right Angle between the middle normal and its vertical line segment remains unchanged, that is, the shear strain in the two directions is zero. (3) The normal stress on the section parallel to the middle plane (that is, the extrusion stress) is much less than the normal stress on the vertical plane, so its effect on deformation is negligible. According to elasticity, the basic equation of thin shell can be established by using the above hypothesis. They include: the balance equation of the shell surface, the geometric equation, the physical equation and various boundary conditions on the boundary. The internal forces in the middle surface of the thin shell include: normal force T1, T2, tangential force T12, T21, transverse shear force N1, N2, bending moment M1, M2 and torque M12, M21. The midplane deformation consists of the positive strain ε1 and ε2 in two orthogonal directions, the shear strain λ12 in the midplane, the change of midplane curvature κ1 and κ2 in both directions, and the midplane torsion κ12.