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Discrete model of twisted rings

Gáspár Z., Németh R.

Computer Assisted Mechanics and Engineering Sciences

2004

Vol. 11, No. 2-3

211-222

A discrete model consisting N straight links and N springs is defined. The originally straight model is bent into a discrete torus, then it is twisted. The C2 symmetric shapes can be determined by four parameters, and there are three constrains. The equilibrium paths are determined by the simplex method (piecewise linear approximation). Global bifurcation diagrams, spatial equilibrium shapes and parasitic solutions are analysed.

Imperfection-sensitivity analysis by using classical and catastrophe theory methods

Kurutz M., Gáspár Z.

Computer Assisted Mechanics and Engineering Sciences

2001

Vol. 8, No. 4

567-577

Comparison of the classical methods and the tools of the catastrophe theory is presented through the imperfection-sensitivity analysis of the classical stable-symmetric bifurcation problem. Generally, classical global methods are related to a large interval, while catastrophe theory concerns the neighborhood of the critical point only, being a local method. Unfortunately, in most cases of practical problems, by using classical global methods, there can hardly be obtained analytical solutions for the multivalued imperfection-sensitivity functions and the associated highly folded imperfection-sensitivity surfaces. In this paper, an approximate solution based on the catastrophe theory is presented, in comparison with the exact solution obtained in graphical way. It will be shown that by considering the problem as an imperfect version (at a fixed imperfection) of a higher order catastrophe, a topologically good solution can be obtained in a considerably large, quasi in a nonlocal domain.

Rigidity of square grids with holes

Gáspár Z., Radics N., Recski A.

Computer Assisted Mechanics and Engineering Sciences

1999

Vol. 6, No. 3-4

329-335

Bolker and Crapo gave a graph theoretical model of square grid frameworks with diagonal rods of certain squares. Using this model there are very fast methods for connected planar square grid frameworks to determine their (infinitesimal) rigidity when we can use diagonal rods, diagonal cables or struts, long rods, long cables or struts. But what about square grids containing some kind of holes? We will show that the model can be extended to the problem of holes too.

Global numerical analysis of elasto-plastic frames

Gáspár Z., Nédli P.

Computer Assisted Mechanics and Engineering Sciences

1998

Vol. 5, nr 1

93-100

We discuss a global, iteration-free numerical scheme (based on the Piecewise Linear algorithm), with special respect to the computation of elasto-plastic frames. The plastic deformations are concentrated in plastic hinges which may appear at both ends of the bars, while the inner parts of the bars can have only elastic deformations but without limation on their magnitude. Our method is tested on a classical example and the resuts show very good match with those known from the literature. We discuss advantages and disadvantages and point out other, related applications.