Finite element analysis of flexible multibody systems with fuzzy parameters Original Research Article

A computational procedure is presented for predicting the dynamic response and evaluating the sensitivity coefficients of flexible multibody systems whose characteristics include fuzzy parameters. Time-histories of the possibility distributions of the response and the sensitivity coefficients are generated. These coefficients measure the sensitivity of the dynamic response to variations in the material, geometric and external force parameters of the system. The five key components of the procedure are: a) a corotational frame approach used in conjunction with a total Lagrangian formulation; b) beam and shell elements with the Cartesian coordinates of the nodes selected as degrees of freedom, and with continuous inter-element slopes; c) use of an approximate method of extension, based on the α-cut representation, called the ‘vertex method’ for generating the possibility distributions of the desired response quantities and their sensitivity coefficients; d) semi-explicit temporal integration technique for generating the dynamic response; and e) direct differentiation approach for evaluating the sensitivity coefficients. The effectiveness of the procedure and the usefulness of the fuzzy output are demonstrated through numerical examples, including an articulated space structure consisting of beams, shells and revolute joints.