The success of compliant mechanism design by structural topology optimization approach depends,to a large extent,on its structural geometry representation scheme.In this work,a novel representation scheme based on pairs of curves is presented.In the representation,the structure is characterized by a set of input/output(I/O) regions.While it is still unknown how the rest of the design space will be occupied by the structure,the I/O regions must exist somewhere because any structure must have parts which interact with its surroundings by way of at least one loading region,one support region,and one output region.For a valid structural design,pairs of Bezier curves are used to connect I/O regions in order to form one single connected load-bearing structure.The boundary is explicitly described,so the need for smoothening of the blurred and jagged edges can be avoided by developing such a representation scheme to directly generate smooth boundary structures.With the scheme,shape and topology can be optimized simultaneously,and the obtained topology solutions have no check-board phenomena nor intermediate zones.A multi-objective genetic algorithm is then applied to couple with the representation scheme for defining and encoding the structural geometry in the form of graph.The solution framework is integrated with a nonlinear fixed grid finite element method(FG-FEM) code for large-displacement analyses of the compliant structures.Simulation results from a displacement inverter indicated that the proposed representation scheme is appropriate. The success of compliant mechanism design by structural topology optimization approach depends, to a large extent, on its structural geometry representation scheme. In this work, a novel representation scheme based on pairs of curves is presented. In the representation, the structure is characterized by a set of input / output (I / O) regions.While it is still unknown how the rest of the design space will be occupied by the structure, the I / O regions must exist somewhere because any structure must have parts which interact with its surroundings by way of at least one loading region, one support region, and one output region. For a valid structural design, pairs of Bezier curves are used to connect I / O regions in order to form one single connected load-bearing structure. boundary is explicitly described, so the need for smoothening of the blurred and jagged edges can be avoided by developing such a representation scheme to directly generate smooth boundary structures .With the scheme, shape and topolog y can be optimized simultaneously, and the obtained topology solutions have no check-board phenomena nor intermediate zones. A multi-objective genetic algorithm is then applied to couple with the representation scheme for defining and encoding the structural geometry in the form of graph. solution framework is integrated with a nonlinear fixed grid finite element method (FG-FEM) code for large-displacement analyses of the compliant structures. Simulation results from a displacement inverter indicated that the proposed representation scheme is appropriate.