Solution of the generalized eigenvalue problem using overlapping finite elements. (November 2022)

• Record Type: Journal Article
• Authors: Lee, Sungkwon; Bathe, Klaus-Jürgen
• Is Part Of: Advances in engineering software. Volume 173(2022)
• Publication Date: 2022-11
• Subjects: Overlapping finite elements and AMORE -- Generalized eigenvalue problem -- Frequencies and mode shapes -- Mode superposition -- Accuracy and convergence -- Computational effort; Computer-aided engineering -- Periodicals; Engineering -- Computer programs -- Periodicals; Engineering -- Software -- Periodicals; Periodicals; 620.0028553
• DOI: 10.1016/j.advengsoft.2022.103241
• Languages: English
• ISSNs: 0965-9978

Abstract

Highlights: We present the use of the 'overlapping finite elements' for the solution of the generalized eigenvalue problem. We also present the use of the elements and AMORE in mode superposition. For the calculation of the eigenpairs we use the Bathe enriched subspace iteration scheme. Our studies show that the use of the overlapping finite elements for these dynamic solutions can be effective. Abstract: Our objective in this paper is to present the use of the overlapping finite elements and the AMORE scheme for the solution of the generalized eigenvalue problem of solids and structures – to calculate frequencies and mode shapes – and the solution of dynamic response by mode superposition. For the solution of eigenvalues and vectors, we use the enriched subspace iteration scheme. We focus on the differences in use that arise when employing the overlapping finite elements versus traditional finite elements and the convergence of the eigenvalues and vectors as the mesh is refined. Our studies show that the use of the overlapping finite elements for frequency and dynamic solutions can be quite effective.