Application of the MEBDFV solver to dynamic simulation of some specific multibody systems: an example of a cervical spine model

Abstract

Application of the MEBDFV code in multibody dynamics is discussed. The solver is based on the modified extended backward differentiation formulae of Cash. It is especially suited for the solution of differential-algebraic equations with time- and state-dependent mass matrix. Such a case can occur when motion of a multibody open-chain system is described within the classical Lagrangian formalism, which still has some advantages. An outline of the numerical algorithm is given. As an example, a simplified mathematical model of the human head-cervical spine system is presented. In a numerical experiment the model is used to analyze motion of the head–neck during rear-end impact which may lead to whiplash injury. The obtained results are compared to literature data. Performance of the MEBDFV solver is examined in terms of algorithmic energy conservation. The test is based on an appropriately formulated ‘kinetic energy–work’ relation.