Mixed variational formulation in geometrically non-linear elasticity and ageneralized nth-order beam theory

A mixed variational formula for geometrically non-linear elasticity problem s is derived based on Hamilton's principle and Lagrange's multiplier method . Legendre's transformation is used to introduce in the variational stateme nt the complementary energy density as a function of stresses only. The obt ained mixed variational formula is used to present a generalized nth-order beam theory. The beam theory includes stresses that are consistent with a g eneral traction field with normal and tangential components acting on the t op and bottom beam surfaces. Therefore, this theory and all its lower-order special cases do not require any shear correction factors used in other be am theories. Moreover, the other linear and non-linear beam theories in the literature may be obtained from the present beam theory as special cases. (C) 1999 Elsevier Science Ltd. All rights reserved.