Modeling and sensitivity analysis of multibody systems using new solid, shell and beam elements

A computational procedure is presented for predicting the dynamic response and evaluating the sensitivity coefficients of large, flexible multibody systems consisting of beams, shells and solids undergoing arbitrary spatial motions. The sensitivity coefficients measure the sensitivity of the dynamic response to variations in the material, geometric and external force parameters of the system. The four key components of the procedure are: a) new beam, shell and solid elements with the Cartesian coordinates selected as degrees of freedom and with continuous inter-element slopes; b) a corotational frame approach used in conjunction with a total Lagrangian formulation; c) semi-explicit temporal integration for generating the dynamic response; and d) direct differentiation approach for evaluating the sensitivity coefficients. The nonlinear interactions between the elastic and the large rigid body motions are naturally incorporated in the present formulation. The effectiveness of the procedure is demonstrated through numerical examples, including an articulated space structure consisting of beams, shells and revolute joints.