An Energy Approach to Nonlinear Analysis of Roll Bars
Roll bars are currently a primary source of operator protection for recreational vehicles, for certain lawn and garden tractors and for small agricultural tractors. In this paper we describe a family of nonlinear models to predict the large deflection response of a roll bar due to yielding of the material. This yielding permits the structure to absorb energy. The stress-strain relationship employs a power law model. Subsequent calculation of the complementary energy stored in the structure and application of Castigliano's second theorem yield the deflection at the point of loading. To demonstrate the feasibility of this energy method in the simulation of testing of roll bars, we present numerical results for the side, vertical, and fore-aft loading cases. Results include the load-deflection response for each load case as well as the strain energy stored in the roll bar as it deforms.