LOAD-DEFORMATION RELATIONS IN 2ND-ORDER ELASTICITY

A method for determining overall load-deformation relations for small- strain elastic deformations has been adapted so that second-order elas tic effects can be included in certain overall quantities, such as ben ding stiffness, without explicit determination of the second-order sol ution. The approach uses Betti's Reciprocal Theorem. The strains are c onsidered small enough that third-order effects can be neglected but t here is no restriction on the magnitude of the displacements. The meth od is applied to obtain the resultant force and moment to second order for cylindrical bars with arbitrary cross section under torsion, exte nsion and torsion, bending by an end bad, and twisting and bending to helical form.