TOP Webinar Tutorials: Density methods 2 - Filtering

The second of three tutorial lectures by Professor Ole Sigmund on density-based methods. The second lecture covers filtering and derived techniques. 00:00 Welcome to webinar 00:40 Introduction of Prof. Ole Sigmund 01:42 Beginning of lecture 02:25 Recap of first lecture 04:50 Eliminating mesh-dependence 05:47 Filtering approaches 06:21 Image-based filtering 08:30 PDE-based filtering 09:53 Compliant mechanism design 14:44 Filtering issues: hinges and grayscale 15:17 Thresholding/projection/mapping 17:01 Smoothed Heaviside projection 18:08 Sensitivity analysis flow diagramme 19:15 Threshold value 21:26 Robust approach 24:52 Convergence for robust compliant mechanism 27:03 "Smart mans" robust formulation 29:21 Measure of non-discreteness 30:04 Robust electrostatic actuator design 31:50 On requirements for discreteness 34:38 Behaviour similar to level set approaches 35:20 Level-set-like example 36:42 Upper bound of beta for stress constraints 38:17 Robust stress-constrained problems 40:22 Localised random variations 42:48 Other uncertainty schemes 43:27 Advanced filtering approaches 43:37 Coating and interface structures 46:44 Controlling overhang 47:42 Local volume constraint 50:25 Conclusions 52:09 Question sessions 52:26 Which filter approach? 53:06 Total variation approach? 54:52 Level-set/SIMP follow-up? 57:04 Cost of local volume constraint? 57:49 Explicit topology optimisation methods? 59:35 Intermediate densities for stress-constraints? 1:00:40 Suggestions for beginners? 1:01:53 Errors in filtering? 1:04:09 Continuation on SIMP exponent? 1:05:07 Computational expense of robust approach? 1:06:44 Constraint on gray measures? 1:07:56 Level set vs SIMP for void islands? 1:09:07 Thank you and rounding off