Bendsøe, M. P., and Kikuchi, N., 1988, “Generating Optimal Topologies in Structural Design Using a Homogenization Method,” Comput. Methods Appl. Mech. Eng., 71 (2), pp. 197–224.

[CrossRef]Hassani, B., and Hinton, E., 1999, "*Homogenization and Structural Topology Optimization*", Springer, Berlin.

Ananthasuresh, G. K., Kota, S., and Kikuchi, N., 1994, “Strategies for Systematic Synthesis of Compliant Mems,” Proceedings of the 1994 ASME Winter Annual Meeting , Chicago, pp. 677–686.

Nishiwaki, S., Frecker, M., Min, S., and Kikuchi, N., 1998, “Topology Optimization of Compliant Mechanisms Using the Homogenization Method,” Int. J. Numer. Methods Eng., 42 (3), pp. 535–559.

[CrossRef]Li, Y., Saitou, K., and Kikuchi, N., 2004, “Topology Optimization of Thermally Actuated Compliant Mechanisms Considering Time-Transient Effect,” Finite Elem. Anal. Design, 40 , pp. 1317–1331.

[CrossRef]Zhou, M., and Rozvany, G. I. N., 1991, “The COC Algorithm, Part II: Topological, Geometrical, and Generalized Shape Optimization,” Comput. Methods Appl. Mech. Eng., 89 , pp. 309–336.

[CrossRef]Mlejnek, H. P., and Schirrmacher, R., 1993, “An Engineering Approach to Optimal Material Distribution and Shape Finding,” Comput. Methods Appl. Mech. Eng., 106 , pp. 1–26.

[CrossRef]Bendsøe, M. P., 1995, "*Optimization of Structural Topology, Shape and Material*", Springer, Berlin.

Sigmund, O., 1997, “On the Design of Compliant Mechanisms Using Topology Optimization,” Mech. Struct. Mach., 25 , pp. 495–526.

Larsen, U. D., Sigmund, O., and Bouwstra, S., 1997, “Design and Fabrication of Compliant Micromechanisms and Structures With Negative Poisson’s Ratio,” J. Microelectromech. Syst., 6 (2), pp. 99–106.

[CrossRef]Bruns, T. E., and Tortorelli, D. A., 2001, “Topology Optimization of Nonlinear Elastic Structures and Compliant Mechanisms,” Comput. Methods Appl. Mech. Eng., 190 (26–27), pp. 3443–3459.

[CrossRef]Pedersen, C. B. W., Buhl, T., and Sigmund, O., 2001, “Topology Synthesis of Large-Displacement Compliant Mechanisms,” Int. J. Numer. Methods Eng., 50 (12), pp. 2683–2705.

[CrossRef]Sigmund, O., 2001, “Design of Multiphysics Actuators Using Topology Optimization—Part I: One-Material Structures,” Comput. Methods Appl. Mech. Eng., 190 (49–50), pp. 6577–6604.

[CrossRef]Sigmund, O., 2001, “Design of Multiphysics Actuators Using Topology Optimization—Part II: Two-Material Structures,” Comput. Methods Appl. Mech. Eng., 190 (49–50), pp. 6605–6627.

[CrossRef]Guest, J. K., Prévost, J. H., and Belytschko, T., 2004, “Achieving Minimum Length Scale in Topology Optimization Using Nodal Design Variables and Projection Functions,” Int. J. Numer. Methods Eng., 61 , pp. 238–254.

[CrossRef]Rahmatalla, S. F., and Swan, C. C., 2004, “A Q4/Q4 Continuum Structural Topology Optimization Implementation,” Struct. Multidiscip. Optim., 27 , pp. 130–135.

[CrossRef]Wang, M. Y., Chen, S. K., Wang, X. M., and Mei, Y. L., 2005, “Design of Multi-Material Compliant Mechanisms Using Level Set Methods,” ASME J. Mech. Des., 127 , pp. 941–956.

[CrossRef]Luo, Z., Tong, L. Y., Wang, M. Y., and Wang, S. Y., 2007, “Shape and Topology Optimization of Compliant Mechanisms Using a Parameterization Level Set Method,” J. Comput. Phys., 227 , pp. 680–705.

[CrossRef]Luo, J. Z., Luo, Z., Chen, S. K., Tong, L. Y., and Wang, M. Y., 2008, “A New Level Set Method for Systematic Design of Hinge-Free Compliant Mechanisms,” Comput. Methods Appl. Mech. Eng., 198 , pp. 318–331.

Díaz, A., and Sigmund, O., 1995, “Checkerboard Patterns in Layout Optimization,” Struct. Optim., 10 , pp. 40–45.

[CrossRef]Jog, C. S., and Haber, R. B., 1996, “Stability of Finite Element Models for Distributed Parameter Optimization and Topology Design,” Comput. Methods Appl. Mech. Eng., 130 , pp. 203–226.

[CrossRef]Yin, L., and Ananthasuresh, G. K., 2003, “A Novel Formulation for the Design of Distributed Compliant Mechanisms,” Mech. Based Des. Struct. Mach., 31 (2), pp. 151–179.

[CrossRef]Saxena, R., and Saxena, A., 2007, “On Honeycomb Representation and SIGMOID Material Assignment in Optimal Topology Synthesis of Compliant Mechanisms,” Finite Elem. Anal. Design, 43 (14), pp. 1082–1098.

[CrossRef]Mankame, N. D., and Saxena, A., 2007, “Analysis of the Hex Cell Discretization for Topology Synthesis of Compliant Mechanisms,” ASME Paper No. DETC 35244.

Sigmund, O., 1994, “Design of Material Structures Using Topology Optimization,” Ph. D. thesis, DTU, Denmark.

Bonnetier, E., and Jouve, F., 1998, “Checkerboard Instabilities in Topological Shape Optimization Algorithms,” Proceedings of the Conference on Inverse Problems, Control and Shape Optimization (PICOF’98) .

Poulsen, T. A., 2003, “A New Scheme for Imposing Minimum Length Scale in Topology Optimization,” Int. J. Numer. Methods Eng., 57 , pp. 741–760.

[CrossRef]Hull, P., and Canfield, S., 2006, “Optimal Synthesis of Compliant Mechanisms Using Subdivision and Commercial FEA,” ASME J. Mech. Des., 128 , pp. 337–348.

[CrossRef]Saxena, R., and Saxena, A., 2009, “Design of Electrothermally Compliant MEMS With Hexagonal Cells Using Local Temperature and Stress Constraints,” ASME J. Mech. Des., 131 (5), pp. 051006.

[CrossRef]Saxena, R., and Saxena, A., 2003, “On Honeycomb Parameterization for Topology Optimization of Compliant Mechanisms,” ASME Paper No. DETC2002/DAC-48806.

Saxena, A., 2009, “A Material-Mask Overlay Strategy for Continuum Topology Optimization of Compliant Mechanisms Using Honeycomb Discretization,” ASME J. Mech. Des., 130 (8), pp. 082304.

Talischi, C., Paulino, G. H., and Le Chau, H., 2009, “Honeycomb Wachspress Finite Elements for Structural Topology Optimization,” Struct. Multidiscip. Optim., 37 (6), pp. 569–583.

[CrossRef]Langelaar, M., 2007, “The Use of Convex Uniform Honeycomb Tessellations in Structural Topology Optimization,” Proceedings of the Seventh World Congress on Structural and Multidisciplinary Optimization , Seoul, South Korea.

Sethian, J. A., and Wiegmann, A., 2000, “Structural Boundary via Level Set and Immersed Interface Methods,” J. Comput. Phys., 163 (2), pp. 489–528.

[CrossRef]Belytschko, T., Xiao, S. P., and Parimi, C., 2003, “Topology Optimization With Implicit Functions and Regularization,” Int. J. Numer. Methods Eng., 57 , pp. 1177–1196.

[CrossRef]Chang, S. Y., and Youn, S. K., 2006, “Material Cloud Method—Its Mathematical Investigation and Numerical Application for 3D Engineering Design,” Int. J. Solids Struct., 43 (17), pp. 5337–5354.

[CrossRef]Horoba, C., and Newmann, F., 2008, “Benefits and Drawbacks for the Use of ε-Dominance in Evolutionary Multi-Objective Optimization,” GECCO’08 , Atlanta, GA.

Tóth, L. F., 1964, “What the Bees Know and What They Do Not Know,” Bull. Am. Math. Soc., 70 (4), pp. 468–481.

[CrossRef]Bleicher, M. N., and Toth, L. F., 1965, “Two-Dimensional Honeycombs,” Am. Math. Monthly, 72 (9), pp. 969–973.

[CrossRef]Hales, T. C., 2001, “The Honeycomb Conjecture,” Discrete Comput. Geom., 25 , pp. 1–22.

Weaire, D., and Phelan, R., 1994, “Optimal Design of Honeycombs,” Nature (London), 367 (13), pp. 123–123.

[CrossRef]Kreyszig, E., 1999, "*Advanced Engineering Mathematics*", 8th ed., Wiley, New York.

Rai, A. K., Saxena, A., and Mankame, N. D., 2007, “Synthesis of Path Generating Compliant Mechanisms Using Initially Curved Frame Elements,” ASME J. Mech. Des., 129 , pp. 1056–1063.

[CrossRef]Frecker, M., Ananthasuresh, G. K., Nishiwaki, N., Kikuchi, N., and Kota, S., 1997, “Topological Synthesis of Compliant Mechanisms Using Multi-Criteria Optimization,” ASME J. Mech. Des., 119 , pp. 238–245.

[CrossRef]Saxena, A., and Ananthasuresh, G. K., 2000, “On an Optimality Property of Compliant Topologies,” Struct. Multidiscip. Optim., 19 , pp. 36–49.

[CrossRef]