Summary
Two variational principles are proposed that describe equilibrium problems with connected nonlinear beams and solids. The principles extend the classical principle of minimum potential energy for beams and deformable bodies incorporating constraints that weakly enforce the beam kinematics at the common interface using either Lagrange multipliers or penalty terms. In contrast with existing alternatives, in the new approach, the surfaces of bodies connected to beams can deform in an energetically optimal way while globally behaving as beam cross sections. This allows, eg, warping and Poisson effects in beam/solid interfaces. Finite element implementations of the new principles are described in detail and application examples are provided that illustrate their use.