Large Deflections of Curved Cantilever Springs of Trapezoidal Profile

Abstract

The large deflections of a circular-arc cantilever spring of trapezoidal profile subjected to a concentrated force at the free end in the lateral direction have been studied. A solution of the nonlinear beam equation is obtained in the form of power series. However, the power series used yields poor convergency as the shape of spring approaches the triangular profile and it diverges lastly. An approximate solution is also derived from the nonlinear beam equation after approximated appropriately. In comparison between the results calculated from the series-form and approximate solutions, respectively, it is seen that the approximate one gives practically satisfactory results. Numerical results according to both the series-form and approximate solutions are also presented.