Symbolic Computation to Derive a Linear-Elastic Buckling Theory for Solids with Periodic Microstructure. Issue 6 (2nd November 2019)

• Record Type: Journal Article
• Authors: Neves, Miguel Matos
• Is Part Of: International journal for computational methods in engineering science and mechanics. Volume 20:Issue 6(2019)
• Page Start: 523
• Page End: 539
• Publication Date: 2019-11-02
• Subjects: Symbolic computation -- Two-scale asymptotic method -- Classic homogenization -- Eigenvalue buckling -- Periodic microstructures; Engineering -- Data processing -- Periodicals; Engineering mathematics -- Periodicals; Computer-aided engineering -- Periodicals; 620.00420285
• DOI: 10.1080/15502287.2019.1566286
• Languages: English
• ISSNs: 1550-2287

Abstract

Abstract: A symbolic computation of a double scale asymptotic technique is used to derive a linear-elastic buckling theory for solids with periodic microstructure. From the stationary potential energy, equations are obtained for the classic homogenization problem, and for its extension to the buckling problem at macro, micro and mixed scales. The limitation to #Y-periodic instability modes can be treated afterwards using a Floquet-Bloch theory. The symbolic procedure is worked out step-by-step and results are presented. The obtained equations present a theoretical framework for the topology optimization of structures and microstructures involving linear elastic buckling criteria.