A FINITE-ELEMENT GEOMETRICALLY NONLINEAR DYNAMIC FORMULATION OF FLEXIBLE MULTIBODY SYSTEMS USING A NEW DISPLACEMENTS REPRESENTATION

In previous work (Mayo, 1993), the authors developed two geometrically nonlinear formulations of beams inflexible multibody systems. One, li ke most related methods, includes geometric elastic nonlinearity in th e motion equations via the stiffness terms (Mayo and Dominguez, 1995), but preseving terms in the expression for the strain energy, of a hig her-order than most available formulations. The other formulation reli es on distinguishing the contribution of the foreshortening effect fro m that of strain in modelling the displacement of a point. While inclu ding exactly the same nonlinear terms in the expression for the strain energy, the stiffness terms in the motion equations generated by this formulation are exclusively limited to the constant stiffness matrix for the linear analysis because the terms arising from geometric elast ic nonlinearity are moved from elastic forces to inertial, reactive an d external forces, which are originally nonlinear. This formulation wa s reported in a previous paper (Mayo et at, 1995) and used in conjunct ion with the assumed-modes method. The aim of the present work is to i mplement this second formulation on the basis of the finite-element me thod. IJ; in addition, the component mode synthesis method is applied to reduce the number of degrees of freedom, the proposed formulation t akes account of the effect of geometric elastic nonlinearity on the tr ansverse displacements occurring during bending without the need to in clude any axial vibration modes. This makes the formulation particular ly efficient in computational terms and numerically more stable than a lternative geometrically nonlinear formulations based on lower-order t erms.