Approximate Closed-Form Equations for Elastic Beam Experiencing Large Deflection

The problem associated with beams subject to large elastic deflection finds application in micro switches and other MEMS. Perhaps the most challenging task in finding approximate closed form equations is the choice of the function form. While systematic least squares fit of polynomial or power functions are means of finding such approximations, usually the error in the approximations rises with increase in the range of deflection. An interactive/optimization based scheme is employed in this paper to derive the closed form approximate equations for elastic beams experiencing large angular and transverse deflections as a result of application of relatively large loads. It is shown that the approximate equations provide prediction of beam tip angular deflection in the range 0–82 degrees, with error less than 0.2 degrees. The approximate equations are employed to define a pseudo-rigid body link of a compliant MEMS.