A Numerical Solution for Large Deformation of Compliant Cantilever Beams Under Combined Loads

Abstract

Cantilevered beam theory is the basic method for the study of output displacement of compliant mechanisms. In order to analyze the larger deformation of cantilever beams with geometric non-linearity under combined end loads, the Euler-Bernoulli theory was employed to build the large deflection differential equation of cantilever beams, and a simple and accurate series solution is obtained by homotopy analysis method (HAM), which avoided the complex calculation of transcendental functions. The rotation angle, dimensionless horizontal and vertical coordinates are calculated by HAM and compared with exact solutions obtained by elliptic integral. This analytic method provides a convenient and straightforward approach to calculate the horizontal and vertical coordinates of a cantilever beam with large deformation. The results show that the HAM method is effective and the analytical solutions are accurate for most practical engineering applications, which can be used for further analyzing of the larger deformation of cantilever beams with geometric non-linearity and optimizing the structure of compliant mechanisms