Symbolic Finite Element Modeling of Structural Systems

Abstract

The application of light materials to space structures, aircraft, robots and automobiles has increased the demand for effective algorithms to model and predict the response of structural multibody systems. The understanding of mechanics can assist in developing better design and control strategies. Formulation of mathematical models of a multibody system using manual approaches is a difficult task and prone to errors. For non-linear and/or time-varying systems, numerical formulation provides limited information about physical insight. In this study, a computer-aided symbolic method is used to generate the equations of motion from Lagrange's method. Equations are converted into FORTRAN form ready for simulations and control synthesis. The 4-5th order RungeKutta-Fehlberg method (RKF45) was used to numerically solve the system of equations. Two examples, namely a slider-crank mechanism and an aircraft model are presented.