Abstract
In the present note, some elastica problems of beams and frames are studied by a mixed variational method. The bending moments and the discontinuities in tangential slope of the displacement field at nodes are interpolated by the bilinear spline functions and by the point-wise defined spline functions respectively. These interpolations enable the energy terms in the mixed functional to disappear or to be linearized, whereas only the load potentials become nonlinear and need to be estimated by a kinematic approach. The resulting simultaneous nonlinear equations are then solved by an iterative method. Some applications of the mixed method are illustrated. Compared to conventional methods like displacement approaches, numerical aspects of the presented procedure are discussed.
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