Publisher DOI: 10.1142/S0219876221500420
Title: Optimally blended spectral elements in structural dynamics: Selective integration and mesh distortion
Language: English
Authors: Radtke, Lars 
Müller, David 
Düster, Alexander 
Keywords: Eigenvalue analysis; Optimally blended spectral elements; Structural dynamics
Issue Date: 1-Dec-2021
Source: International Journal of Computational Methods 18 (10) : 2150042 (2021-12-01)
Abstract (english): 
In the field of structural dynamics, spectral finite elements are well known for their appealing approximation properties. Based on a special combination of shape functions and quadrature points, a diagonal mass matrix is obtained. More recently, the so-called optimally blended spectral element method was introduced, which further improves the accuracy but comes at the cost of a non-diagonal mass matrix. In this work, we study and compare the approximation properties of the different spectral and finite element methods. For each method, an h-version (fine meshes and low-order shape functions) as well as a p-version (coarse meshes and high-order shape functions) are considered. Special attention is paid to the influence of the quadrature rule used to compute the stiffness matrix and the element distortion on the convergence behavior. The investigations reveal the importance of a correct (full) integration of the stiffness matrix in order to achieve the theoretically predicted convergence rates. However, looking at the full spectrum, novel variants of the method that apply only a single (reduced) quadrature rule for mass and stiffness matrix show a higher accuracy.
ISSN: 0219-8762
Journal: International journal of computational methods 
Institute: Konstruktion und Festigkeit von Schiffen M-10 
Document Type: Article
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