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Isogeometric contact analysis: a study of an explicit dynamic contact algorithm
Kopačka, Ján ; Gabriel, Dušan ; Kolman, Radek ; Plešek, Jiří
The isogeometric NURBS based variant of symmetry preserving explicit FE contact-impact algorithm, has been proposed. The algorithm was studied by means of a numerical example, which involves 2d frictionless dynamic Hertz contact problem of two equally shaped cylinders. The attention was paid to the influence of different lumping techniques on the oscillations of contact force and contact pressure. The standard Lagrange finite elements were compared with the NURBS isogeometric elements. Both the first and second order were considered.
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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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Finite element contact-impact algorithm in explicit transient analysis
Gabriel, Dušan ; Kopačka, Ján ; Plešek, Jiří ; Ulbin, M.
This work addresses three issues in computational modelling of contact-impact problems: i) overviews a contact algorithm proposed by these authors, ii) local search treatment based on the modification of the Nelder-Mead simplex method, iii) discusses an algorithmic aspects of contact algorithm in conjunction with the explicit time integration scheme. The talk closes with the presentation of several numerical examples including the longitudinal impact of two thick plates, for which analytical solution is available.
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Application of Methods for Unconstrained Optimization in Computation of Normal Contact Vector
Kopačka, Ján ; Gabriel, Dušan ; Plešek, Jiří ; Ulbin, M.
The stability of the contact algorithm using the penalty method is significantly affected by choosing of the penalty function. The penalty function is defined like a magnitude of the penetration vector multiplied by the users-defined constant - the penalty parameter. The penetration vector is obtained by solution of the minimum distance problem between the node/Gaussian integration point and the segment of the element. For a general quadrilateral contact segment this task leads to the system of two nonlinear equations. It is shown that the popular Newton-Raphson method is inadvisable for this problem. In this paper, alternative methods like quasi-Newton methods, gradient methods and the simplex method are presented. Especial attention is put on the line-search method that is crucial for a general success of quasi-Newton methods as well as gradient methods. All mentioned methods are tested by means of numerical example, which involves bending of two rectangular plates over a cylinder.
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Review of methods for local contact search
Kopačka, Ján ; Gabriel, Dušan ; Plešek, Jiří
The local contact search is a numerical procedure of a contact algorithm which is used for computing of a penetration vector between so-called master and slave segments of contact surfaces. There are several approaches. In this paper the minimum distance problem between the master segment and the integration point of the slave segment is used. For quadrilateral elements this approach leads to the system of two nonlinear equations. For its solution several methods was tested (Newton-Raphson method, least square projection, method of steepest descent, Broyden's method, BFGS method, DFP method and simplex method) and efficiency was compared.
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