Vervenne, K.; de Boer, H.; van Keulen, F. Accuracy and implementation of refined second-order semi-analytical design sensitivities. (English) Zbl 1049.74742 ZAMM, Z. Angew. Math. Mech. 81, Suppl. 3, 699-700 (2001). Summary: Accurate second-order design sensitivities of finite element responses play an important role in the optimization process. The semi-analytical (SA) method is often used to compute these sensitivities. A disadvantage of the SA method is that severe inaccuracies may be observed for shape design variables. To improve the accuracy of the SA method, we propose and implement a refined second order method. The improvement is based on consistency conditions for rigid body modes and their derivatives. Both analytical and numerical examples indicate a considerable accuracy improvement of the refined method compared to the standard SA method. MSC: 74P10 Optimization of other properties in solid mechanics 74K10 Rods (beams, columns, shafts, arches, rings, etc.) Keywords:optimization; rigid body modes PDFBibTeX XMLCite \textit{K. Vervenne} et al., ZAMM, Z. Angew. Math. Mech. 81, 699--700 (2001; Zbl 1049.74742) Full Text: DOI References: [1] Lighthill, Proc. Roy. Soc. London A224 pp 1– (1954) [2] Nanda, J. Fluid Mech. 15 pp 419– (1963) [3] Eshghy, J. Appl. Mech. 32 pp 183– (1965) · doi:10.1115/1.3625716 [4] Muhury, Internat. J. Heat Mass Transfer 10 pp 717– (1967) [5] Singh, Acta Mech. 30 pp 111– (1978) [6] Kelleher, Z. Angew. Math. Phys. 19 pp 31– (1968) [7] Hossain, Internat. J. Non-linear Mech. 33 pp 541– (1998) [8] Hossain, Acta Mech. 126 pp 101– (1998) [9] Minkowycz, Num. Heat Transfer 1 pp 69– (1978) [10] Somers, J. Appl. Mech. 23 pp 295– (1965) [11] Wilcox, Chem. Engin. Sci. 13 pp 113– (1961) [12] Gill, Internat. J. Heat Mass Transfer 8 pp 1131– (1965) [13] Gebhart, Internat. J. Heat Mass transfer 14 pp 224– (1971) [14] Pera, Internat. J. Heat Mass Transfer 15 pp 269– (1972) [15] Chen, Internat. J. Heat Mass Transfer 23 pp 527– (1980) [16] Hossain, Internat. J. Energy Res. 16 pp 761– (1992) [17] Hossain, J. Heat Transfer 106 pp 664– (1984) [18] Hossain, Internat. J. Energy Res. 12 pp 25– (1988) · doi:10.1002/er.4440120203 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.