Alternative elliptic integral solution to the beam deflection equations for the design of compliant mechanisms

The interactive design for industrial applications is today carried out through methods and tools, with different level of accuracy and simulation times. Consequently, the time necessary for virtual prototyping and analysis phases are often long and may be definitely reduced by means of optimization of tools and methodologies. Compliant mechanisms are increasingly used in the industrial field and the design methods are the subject of several studies, to improve their performance and reliability. This paper provides the reader with reliable numerical expressions to describe flexural beams with large deflections in case of combined end loads and without inflection points. Most of the numerical expressions describing beam deflection already existing in the literature are based on elliptic integrals that take into account strict limitations on the maximum slope angle. Here, we go beyond these limitations at the same time trying to give an order to the most relevant formulations used for determining large deflections of beams subject to combined tip loads. The proposed method provides the same results of the comprehensive elliptic integral solution described in a recent study.