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Modelling approaches to the stress wave propagation in a cracked specimen
Kruisová, Alena ; Kopačka, Ján ; Kober, Jan
One of the essential tasks of non-destructive testing is to detect a crack in a specimen. It is well known that a component with a crack exposed to a harmonic excitation of a given frequency\nhas a nonlinear response as a function of the excitation amplitude. The focus of this paper is the numerical modelling of this phenomenon using the finite element method with the consideration\nof the contact constraint at the crack interface. In addition to the nonlinear transient dynamic problem solved by explicit time integration, a more efficient procedure based on the harmonic\nbalance method is developed. The results of numerical simulations are also compared with experimentally obtained data.
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Inverse mass matrix for higher-order finite element method in linear free-vibration problems
Kolman, Radek ; González, J.G. ; Cimrman, Robert ; Kopačka, Ján ; Cho, S.S. ; Park, B.G.
In the paper, we present adirect inverse mass matrix in the higher-orderfinite element method forsolid mechanics. The direct inverse mass matrix is sparse, has the same structure as the consistent mass matrixand preserves the total mass. The core of derivation of the semi-discrete mixed form is based on the Hamilton’s principle of leastaction. The cardinal issue is finding the relationship between discretized velocities and discretized linear momentum. Finally, the simple formula for the direct inversemass matrix is presented as well as thechoice of density-weighted dual shape functions for linear momentum with respect to the displacement shape functionwith achoice of the lumping mass method for obtaining the correct and positive definitive velocity-linear momentum operator. The application of Dirichlet boundaryconditions into the direct inversemass matrix forafloating system is achieved usingthe projection operator. The suggested methodology is tested on a free-vibration problem of heterogeneous bar for different ordersof shape functions.
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Bi-penalty stabilized explicit finite element algorithm for one-dimensional contact-impact problems
Kolman, Radek ; Kopačka, Ján ; Tkachuk, A. ; Gabriel, Dušan ; Gonzáles, J.A.
In this contribution, a stabilization technique for finite element modelling of contact-impact problems based on the bipenalty method and the explicit predictor-corrector time integration is presented. The penalty method is a standard method for enforced contact constrains in dynamic problems. This method is easily implemented but the solution depends on numerical value of the stiffness penalty parameter and also the stability limit for explicit time integration is effected by a choice of this parameter. The bipenalty method is based on penalized not only stiffness term but also mass term concurrently. By this technique with a special ratio of mass and stiffness penalty parameters, the stability limit of contact-free problem is preserved. In this contribution, we also present a modification of the explicit time scheme based on predictor-corrector form. By meaning of this approach, spurious contact oscillations are eliminated and the results do not depend on numerical parameters.
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Recent progress in numerical methods for explicit finite element analysis
Kolman, Radek ; Kopačka, Ján ; Gonzalez, J. ; Gabriel, Dušan ; Cho, S.S. ; Plešek, Jiří ; Park, K.C.
In this paper, a recent progress in explicit finite element analysis is discussed. Properties and behaviour of classical explicit time integration in finite element analysis of elastic wave propagation and contact-impact problems based on penalty method in contact-impact problems are summarized. Further, stability properties of explicit time scheme and the penalty method as well as existence of spurious oscillations in transient dynamics are mentioned. The novel and recent improving and progress in explicit analysis based on a local time integration with pullback interpolation for different local stable time step sizes, bipenalty stabilization for enforcing of contact constrains with preserving of stability limit for contact-free problems and using a direct inversion of mass matrix are presented. Properties of the employed methods are shown for one-dimensional cases of wave propagation and contact-impact problems.
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Development, assessment and verification of finite element procedures for contact problems
Gabriel, Dušan ; Kopačka, Ján ; Masák, Jan ; Plešek, Jiří
A frictionless three-dimensional contact algorithm based on the pre-discretization penalty formulation was proposed. The algorithm proved to be robust, accurate and symmetry preserving—no master/slave surfaces have been introduced. It was implemented in the finite element code PMD (Package for Machine Design) for the solution of complex engineering problems. The capability of the algorithm was demonstrated in creep analysis of T-piece of the steam distributor of the CHEMOPETROL heating plant T200. Material properties were described by the probabilistic exponential model with damage. The purpose of the analysis was to compare the original version and the proposed design modification applied to one of T-pieces of the distributor when the proposed contact algorithm was employed to simulate the interaction between the collar and the pipe.
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Metodika pro modelování dynamických deju metodou konecných prvku - fáze II
Mochar, Dominik ; Mračko, Michal ; Gabriel, Dušan ; Kolman, Radek ; Kopačka, Ján
Zpráva navazuje na metodiku Z-1546/15 popisující základní metody, algoritmy a postupy pro numerické rešení MKP úloh rázové dynamiky pri vývoji komponent zbraní. V této práci byly testovány disperzní vlastnosti bilineárních ctyruzlových prvku s redukovanou integrací na úloze rázu dvou elastických válcu, pro které je k dispozici analytické rešení. Pozornost byla zamerena na zkoumání vlivu velikosti prvku a casového integracního kroku na presnost numerického rešení. Výsledky získané z MKP programu PMD, Abaqus a Ansys byly diskutovány a porovnány s analytickým rešením.
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Creepová analýza VT vnitřního tělesa DSPWR – kontaktní úloha
Kopačka, Ján ; Masák, Jan ; Gabriel, Dušan ; Plešek, Jiří
Zpráva shrnuje výsledky III. etapy rešení creepové analýzy vysokotlakého vnitrního telesa Doosan Škoda Power. Je provedena analýza vysokotlakého vnitrního VT telesa s respektováním kontaktních okrajových podmínek v delicí rovine a použitím komplexního creepového materiálového modelu. Výsledky kontaktní analýzy v programu PMD jsou porovnány s namerenými hodnotami a též srovnány s programem ANSYS, kde byl použit Nortonuv-Baileyuv model creepu.
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Explicit dynamic finite element analysis of a firing pin assembly
Mochar, Dominik ; Gabriel, Dušan ; Masák, Jan ; Kopačka, Ján ; Kolman, Radek ; Plešek, Jiří ; Hynek, P. ; Vtípil, J.
In this paper, explicit dynamic finite element analysis of a firing pin assembly was performed. Two different geometries of the firing pin were considered using the finite element software PMD and Abaqus. For both variants there was evaluated a stress distribution at the critical point of a tested component, that is going to be later used for a fatigue analysis of the firing pin.
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