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

A mixed variational formula for geometrically non-linear elasticity problems is derived based on Hamilton's principle and Lagrange's multiplier method. Legendre's transformation is used to introduce in the variational statement the complementary energy density as a function of stresses only. The obtained mixed variational formula is used to present a generalized nth-order beam theory. The beam theory includes stresses that are consistent with a general traction field with normal and tangential components acting on the top and bottom beam surfaces. Therefore, this theory and all its lower-order special cases do not require any shear correction factors used in other beam 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.