Validation of Rayleigh-Ritz Deflection Equation for a Tapered Cantilever Beam using ANSYS Finite Element Software

Abstract

Models are like our eyes and ears as they provide the basis for making very important design decisions in engineering. They give predictions that help engineers to foretell or foresee a system’s behaviour in real life. Validation ensures that these models give proper or accurate representation of the real system. In this study, a model equation derived for predicting the end deflection of a tapered width, constant height cantilever beam was adopted for validation. This equation was derived using the Finite Element Method's Rayleigh-Ritz principle and the virtual work concept.  Using a finite element model developed in ANSYS as the representation of the real system and a basis for validation, this study aimed to validate the equation. Validation was achieved by the comparison of the load-deflection curve, the height-deflection curve and the end deflection of the model equation to that of the finite element model in ANSYS. Though the model equation was verified to really foretell deflection, the predictions of the equation was not in good agreement with that of the finite element model. The accuracy of the equation dwindled as the parameters of the tapered cantilever beam were varied. It gave an average percentage error of 30% higher than the allowable error of 5%. Though the equation was derived using the appropriate fundamental numerical principles as it basis, it’s accuracy can be exponentially increased by modifying it to include a larger number of discretized elements and a higher degree of shape/interpolation function.