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M. Bruggi, C. Cinquini, "Efficient Truly-Mixed Finite Elements for the Optimal Design of Structures", in J. Kruis, Y. Tsompanakis, B.H.V. Topping, (Editors), "Proceedings of the Fifteenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 163, 2015. doi:10.4203/ccp.108.163

Keywords: topology optimization, stress constraints, truly-mixed finite elements, Hellinger-Reissner variational principle.

Summary

The so-called truly-mixed version of the Hellinger-Reissner variational principle implements a regular stress field as main variable of the elasticity problem. A small number of robust discrete schemes are available in the literature that fulfil the stability condition, mainly through ad hoc composite finite elements or weak enforcements of the symmetry of the stress tensor. This is generally tied to increased computational cost with respect to conventional displacement-based finite elements. Recently, new families of mixed finite elements have been proposed in the literature to address the analysis of linear elastic bodies adopting regular grids and a limited number of degrees of freedom per element. The lowest order two-dimensional finite element of this new family is adopted to formulate a topology optimization problem where stresses play the role of main variables. The compliance is computed through the evaluation of the complementary energy and the enforcement of stress constraints is straightforward. Preliminary numerical simulations investigate the features of the proposed framework, providing comparisons with a conventional displacement-based scheme.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 108 PROCEEDINGS OF THE FIFTEENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: J. Kruis, Y. Tsompanakis and B.H.V. Topping Paper 163 Efficient Truly-Mixed Finite Elements for the Optimal Design of Structures M. Bruggi¹ and C. Cinquini² ¹Department of Civil and Environmental Engineering, Politecnico di Milano, Milano, Italy ²Department of Civil Engineering and Architecture, University of Pavia, Pavia, Italy doi:10.4203/ccp.108.163 purchase the full-text of this paper Full Bibliographic Reference for this paper M. Bruggi, C. Cinquini, "Efficient Truly-Mixed Finite Elements for the Optimal Design of Structures", in J. Kruis, Y. Tsompanakis, B.H.V. Topping, (Editors), "Proceedings of the Fifteenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 163, 2015. doi:10.4203/ccp.108.163 Keywords: topology optimization, stress constraints, truly-mixed finite elements, Hellinger-Reissner variational principle. Summary The so-called truly-mixed version of the Hellinger-Reissner variational principle implements a regular stress field as main variable of the elasticity problem. A small number of robust discrete schemes are available in the literature that fulfil the stability condition, mainly through ad hoc composite finite elements or weak enforcements of the symmetry of the stress tensor. This is generally tied to increased computational cost with respect to conventional displacement-based finite elements. Recently, new families of mixed finite elements have been proposed in the literature to address the analysis of linear elastic bodies adopting regular grids and a limited number of degrees of freedom per element. The lowest order two-dimensional finite element of this new family is adopted to formulate a topology optimization problem where stresses play the role of main variables. The compliance is computed through the evaluation of the complementary energy and the enforcement of stress constraints is straightforward. Preliminary numerical simulations investigate the features of the proposed framework, providing comparisons with a conventional displacement-based scheme. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £75 +P&P)
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