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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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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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