A hyperelastic extended Kirchhoff–Love shell model with out-of-plane normal stress: I. Out-of-plane deformation

Abstract This is the first part of a two-part article on hyperelastic extended Kirchhoff–Love shell model with out-of-plane normal stress. We present derivation new model, focus mechanics deformation. Accounting for stress distribution in direction affects accuracy calculating deformed-configuration position, and consequently nonlinear response shell. The improvement beyond what we get from accounting deformation mapping. By stress, traction acting can be specified upper lower surfaces separately. With that, free “midsurface” location terms specifying traction. also derivations related to variation kinetic energy form moment along edges. test computations unidirectional plate bending, saddle deformation, pressurized cylindrical spherical shells. use neo-Hookean Fung’s material models, compressible- incompressible-material cases, without, which plane-stress case.