Design of Multimaterial Compliant Mechanisms Using Level-Set Methods

Abstract

A monolithic compliant mechanism transmits applied forces from specified input ports to output ports by elastic deformation of its comprising materials, fulfilling required functions analogous to a rigid-body mechanism. In this paper, we propose a level-set method for designing monolithic compliant mechanisms made of multiple materials as an optimization of continuum heterogeneous structures. Central to the method is a multiphase level-set model that precisely specifies the distinct material regions and their sharp interfaces as well as the geometric boundary of the structure. Combined with the classical shape derivatives, the level-set method yields an Eulerian computational system of geometric partial differential equations, capable of performing topological changes and capturing geometric evolutions at the interface and the boundary. The proposed method is demonstrated for single-input and single-output mechanisms and illustrated with several two-dimensional examples of synthesis of multimaterial mechanisms of force inverters and gripping and clamping devices. An analysis on the formation of de facto hinges is presented based on the shape gradient information. A scheme to ensure a well-connected topology of the mechanism during the process of optimization is also presented.

Topology synthesis of multi-material compliant mechanisms with a Sequential Element Rejection and Admission method

“…The derivative of the stiffness matrix with respect to the density can only be approximated to the variation of the elemental stiffness (15). This is because the design variables are discrete (density can only be zero or one) and as a consequence, the elemental stiffness can only be the value of the stiffness of the m real material, or a negligible value equivalent to zero.…”

“…It is the case, among others, of piezoelectric devices [24], bimorph actuators [13], grippers and clamping devices [15] or biologically inspired mechanisms in which multiple materials such as bones, muscles or skin are connected together to perform the desired function effectively [25]. It is specially interesting when:…”

“…Wang and Chen [15] extended the Level Set approach to the design of monolithic compliant mechanisms made of multiple materials. The mechanical advantage of the mechanisms was used as objective function.…”

Level set based method for design of compliant mechanisms

“…It is now widely used in various applications. The level set method has recently been introduced in the topology and shape optimization field (see (Allaire et al,, 2002), (Allaire et al,, 2004), (Allaire et al,, 2005c), (Wang et al,, 2003), (Wang et al,, 2005)) and has become very popular because of its ability to handle arbitrary objective functions and state equations, and also for its great efficiency and versatility.…”

“…In the context of compliant mechanism optimization, many fitness functions are useful, that lead to different optimal designs. The most used in the literature are available in our numerical implementation of the level set method: mechanical advantage (MA), geometrical advantage (GA), work ratio (WR) (or mechanical efficiency ME) and a least square error criterion (for details, see (Allaire et al,, 2004), (Allaire et al,, 2005a), (Wang et al,, 2005), (Jouve et al,, 2007)). Only one of them will be described bellow.…”