Modeling large deflections of initially curved beams in compliant mechanisms using chained beam-constraint-model

Understanding and analyzing large and nonlinear deflections is one of the major challenges of designing compliant mechanisms. Initially curved beams can offer potential advantages to designers of compliant mechanisms and provide useful alternatives to initially straight beams. However, the literature on analysis and design using such beams is rather limited. This paper presents a general and accurate method for modeling large planar deflections of initially curved beams of uniform cross-sections, which can be easily adapted to curved beams of various shapes. This method discretizes a curved beam into a few elements and models each element as a circular-arc beam using the beam constraint model (BCM). Two different discretization schemes are provided for the method, among which the equal discretization is suitable for circular-arc beams and the unequal discretization is for curved beams of other shapes.