Abstract
To limit the risk of fatal injury to the driver in the case of an agricultural tractor roll-over, the OECD (Organization for Economic Co-operation and Development) Code-4 standard mandates the use of a Roll Over Protective Structure (ROPS). The primary function of a ROPS is to absorb the energy of tractor roll-over without deforming into the safety zone. Designing a ROPS structure to meet the above mentioned requirement is highly challenging due to its non-linear behavior during deformation. Basically there are two types of nonlinearity involved in ROPS design- (i) Material non-linearity: as major portion of the energy absorption should happen in the plastic range. (ii) Geometric non-linearity: as large displacements lead to change in the location of applied load. Literature is abundant with closed formed solution of nonlinear deflection in beams, taking account of either geometric nonlinearity or material nonlinearity, but not both. Currently, commercially available nonlinear finite element (FE) solvers are used for detailed design and analysis of ROPS. However, these solvers are very costly, and require detailed inputs which is difficult to provide in initial stage of design, being a limitation for quicker & multiple design iterations. In this paper, authors are proposing a new algorithm for performing nonlinear structural analysis on a cantilever beam having rectangular cross-section. Using extension of Euler-Bernoulli beam theory, this algorithm incorporates material nonlinearities (bi-linear stress-strain curve) and geometric nonlinearities simultaneously. This approach can be used for simple as well as complex load-cases & beam-geometry. This algorithm is further extended to perform the nonlinear structural analysis on a two post ROPS. The results are verified with ABAQUS [7], achieving a good correlation. A Graphical User Interface (GUI) based application in MATLAB [6] has been created and deployed for the utility of designers. In the GUI, the designer has to provide the parametric geometry of ROPS with material properties and clearance space geometry, which are used to determine the energy absorption capacity of the ROPS. Here, designer can perform multiple design iterations within few minutes for preliminary fixing of ROPS geometry during conceptual phase. Currently, this algorithm is applicable for analyzing deformation of ROPS in longitudinal load case only, and it has been planned to extend it for analyzing lateral & crushing load cases in the next phase.