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Lecture 4: follow-up Some results and discussion

Lecture 4: follow-up Some results and discussion. What happens to topology when the volume is reduced? What happens if the desired direction of the output is changed? What are the things to watch out for?. Your specifications for a stiff structure. Distributed ramp force. Fixed.

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Lecture 4: follow-up Some results and discussion

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  1. Lecture 4: follow-upSome results and discussion What happens to topology when the volume is reduced? What happens if the desired direction of the output is changed? What are the things to watch out for? Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  2. Your specifications for a stiff structure Distributed ramp force Fixed Use 40 % material that can fit into this rectangle Fixed Point force Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  3. 40% volume 30% volume 20% volume 10% volume Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  4. Your specifications for the compliant mechanism Output deflection Fixed Hole Fixed Input force Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  5. 30% volume 40% volume 20% volume Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  6. Effect of changing desired direction of output deflection Use 20 % material Output deflection Fixed Hole Fixed Input force Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  7. Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  8. Some things to watch out for A checker-board pattern is artificially stiff. A point flexure is artificially flexible while minimizing the strain energy. • Mesh dependency • Non-convexity • Numerical artifacts: • Checker-board pattern in structures • Point flexures in compliant mechanisms Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  9. Ways to avoid the checker-board pattern • Perimeter constraintHaber, R.B., Bendsoe, M.P., and Jog, C., “A new approach to variable-topology shape design using a constraint on the perimeter,” Structural Optimization, 11, 1996, pp. 1-12. • Global constraint on artificial density variation • Local constraints on artificial density variations • Filters Bendsoe, M.P., Optimization of Structural Topology, Shape, and Material, Springer, Berlin, 1995. Petersson, J. and Sigmund, O., “Slope constrained Topology Optimization,” Int. J. Numer. Meth. In Engineering, 41, 1998, pp. 1417-1434. Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  10. Filters to avoid the checkerboard pattern Distributed interpolation of the material properties Bruns, T.E. and Tortorelli, D., “Topology Optimization of Nonlinear Elastic Structures and Compliant Mechanisms,” Comp. Meth. In App. Mech. And Engrg., 190 (26-27), 2001, pp. 3443-3459. See for a more mathematical treatment of filters: Bourdin, B., “Filters in Topology Optimization,” Int. J. for Numer. Meth. In Engrg., 50(9), 2001, pp. 2143-2158. Compute sensitivity as a weighted average of sensitivities of elements within a prescribed radius. Sigmund, O., Design of Material Structures Using Topology Optimization, Ph.D. Thesis, Dept. Solid Mechanics, Technical University of Denmark. Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  11. Ways to avoid point flexures Desired disp. • Restraining relative rotation at all material points Force 4 3 d c iv a b ii 1 2 Relative rotations at a node Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

  12. A way to avoid point flexures Noting that Minimize Subject to Equilibrium equations Yin, L. and Ananthasuresh, G.K., “A Novel Formulation for the Design of Distributed Compliant Mechanisms,” Mechanics Based Design of Structures and Machines, Vol. 31, No. 2, 2003, pp. 151-179. Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh

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