A derived theory of elastic-plastic shells

The key to a theory for elastic-plastic shells is the formulation of constitutive equations. Here, incremental equations are derived from the Hooke, Prandtl-Reuss equations of elastic, plastic deformations. The theory does not embody an initial yield condition, but admits immediate, though gradual, evolution of inelastic strain. Consequently, the abrupt transitions and interfaces between elastic and plastic regions are nonexistant.Legendre polynomials are employed to approximate the distribution of stresses; the polynomials of first and second degree are identified with the active forces and couples. Higher polynomials represent residual stresses.The balance of work and rate of dissipation serve to establish the constitutive equations and conditions of loading.