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Comparative study of finite element method, isogeometric analysis, and finite volume method in elastic wave propagation of stress discontinuities
Berezovski, A. ; Kolman, Radek ; Blažek, Jiří ; Kopačka, Ján ; Gabriel, Dušan ; Plešek, Jiří
A comparative study of Finite Element Method, Isogeometric Analysis, and Finite Volume Method in numerical simulation of one-dimensional wave propagation problems of stress discontinuities in elastic solids is presented. The special attention is paid to accuracy, convergence, and stability of tested numerical methods and the appearance of spurious oscillations and damping effects occurring close to theoretical sharp wavefronts.
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Component-wise partitioned finite element method in linear wave propagation problems: benchmark tests
Kolman, Radek ; Cho, S.S. ; Červ, Jan ; Park, K.C.
A novel explicit time scheme for nite element computations of wave propagation problems in solids is presented. The presented algorithm, with the component-wise partition of equations of motion to the longitudinal and shear parts, is designed to more precisely integrate wave propagation in accordance with their dierent propagation wave speeds. The suggested three-time step integrator is fully explicit with the diagonal mass matrix, of second-order accuracy, conditionally stable and it exhibits minimal sensitivity behavior on time step size satisfying the stability limit. We present two numerical tests of wave propagation phenomena to show accuracy and performance of the proposed method.
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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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