Optimized designs for 2D and 3D thermoelastic structures

Pauli Pedersen, Niels Leergaard Pedersen

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearch


With design independent loads and only a constrained volume, the same optimal design does simultaneously lead to minimum compliance and maximum strength. However, for thermoelastic structures this is not the case and a maximum volume may not be an active constraint for minimum compliance. This is proved for thermoelastic structures by compliance sensitivity analysis that return localized determination of sensitivities.The compliance is not identical to the total elastic energy (twice strain energy). An explicit formula for the difference is derived and numerically illustrated with examples. In compliance minimization it may be advantageous to decrease the total volume, but for strength maximization it is argued to keep the total permissible volume. For direct strength maximization the sensitivity analysis of local von Mises stresses is demanding. A simple recursive procedure to obtain uniform energy density (or uniform von Mises stress) is presented and applied, and it is shown by examples that the obtained designs are close to fulfilling also strength maximization. Explicit formulas for equivalent thermoelastic loads in 2D and 3D finite element analysis are derived and applied, including the sensitivity analysisWorld Congress on Structural and Multidisciplinary Optimization.
Original languageEnglish
Title of host publication9th World Congress on Structural and Multidisciplinary Optimization
Publication date2011
Publication statusPublished - 2011
Event9th World Congress on Structural and Multidisciplinary Optimization - Shizuoka, Japan
Duration: 13 Jun 201117 Jun 2011
Conference number: 9


Conference9th World Congress on Structural and Multidisciplinary Optimization


  • Thermoelastic design
  • Sensitivity analysis
  • Uniform elastic energy density
  • Compliance


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