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EUROMECH Colloquium 540 - Advanced Modelling of Wave Propagation in Solids
Kolman, Radek ; Berezovski, A. ; Okrouhlík, Miloslav ; Plešek, Jiří
The Euromech Colloquium 540 - Advanced Modelling of Wave Propagation in Solids took place at the Institute of Thermomechanics in Prague from 1st to 3rd October 2012. It aimed at bringing together engineers and scientists interested in modelling of wave propagation in solids. The Colloquium focused on topics related to effects in linear and non-linear wave propagation in solids. Recent advances in numerical and analytical approaches and strategies were discussed. The main purpose of the Colloquium was to discuss novel methods of wave propagation modelling and to assess the credibility of results especially in cases when experiment validation had not been available.
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Mass lumping methods for the semi-loof shell element
Sháněl, Vít ; Kolman, Radek ; Plešek, Jiří
Mass matrix diagonalization in terms of a finite element method (FEM) is essential for an effective deployment of the explicit method as one of the direct integration methods of the motion equations of elastodynamics. A particular attention is focused on the mass matrix diagonalization of the semi-loof shell element. Its diagonalization requires a specially designed universal diagonalization scheme that is derived from the scaling HRZ method. Another analyzed aspect is the problem of preserving the moment of inertia for various types of finite elements. The proposed scheme is implemented in the finite element program and consequently tested on several problems
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SIGA 2011
Kolman, Radek ; Linkeová, I. ; Okrouhlík, Miloslav ; Pařík, Petr
The conference SIGA 2011 aimed to bring together mathematicians, physicists, computer designers and engineers dealing with splines who are using them for the numerical solutions of partial differential equations of various problems in mechanics and physics. In computational mechanics, it is isogeometric analysis (IGA) which is being dynamically developed. This numerical method employs shape functions based on different types of splines (B-splines, NURBS, T-splines and many others), and the fields of unknown quantities are consequently described the same way as the geometry of the studied domain. In addition, this approach provides a higher degree of continuity than that offered by the classical finite element (FE) method based on Lagrangian polynomials. Isogeometric analysis aims to integrate FE ideas in CAD systems without necessity to regenerate mesh. The conference intends to create a forum for further discussion in multidisciplinary scientific areas involving mathematics, computer graphics, geometry, physics, engineering and software engineering, respectively.
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Analysis of classical and spectral finite element spatial discretization in one-dimensional elastic wave propagation
Kolman, Radek ; Plešek, Jiří ; Okrouhlík, Miloslav ; Gabriel, Dušan
The spatial discretization of continuum by finite element method introduces the dispersion error to numerical solutions of stress wave propagation. For higher order finite elements there are the optical modes in the spectrum resulting in spurious oscillations of stress and velocity distributions near the sharp wavefront. Spectral finite elements are of h-type finite element, where nodes have special positions along the elements corresponding to the numerical quadrature schemes, but the displacements along element are approximated by Lagrangian interpolation polynomials. In this paper, the classical and Legendre and Chebyshev spectral finite elements are tested in the one-dimensional wave propagation in an elastic bar.
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Stability Analysis of Plane Serendipity Finite Element for Explicit Linear Elastodynamics
Kolman, Radek ; Plešek, Jiří ; Gabriel, Dušan
The central difference method is widely used for the numerical solution of the transient elastodynamics problems by the finite element method. The effectiveness of this explicit conditional stable direct time integration methods is limited by using diagonal mass matrix, which entails significant computational savings and storage advantages. However, for the serendipity type element the construction of such diagonalized matrices is not uniquely defined and various class of lumped mass matrices can be assembled. In this paper the stability analysis for the plane square serendipity finite element is performed for various class of lumped mass matrices.
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