Zbigniew Cywiński

Is reduced integration just a numerical trick

Abstract On the grounds of a consistent approach an attempt to answer the title question is undertaken. For simplification purposes the particular case of a straight in-plane cantilever beam of rectangular cross-section is investigated. Rigorous analysis is performed on the beam element models based upon the principle of degenerated elements and resulting from the technical theory of beams. Analysing corresponding stiffness matrices, it is shown that reduced integration produces results conforming with those of analytical solution, while exact integration, disturbing the beam shear performance, is responsible for the locking phenomenon. Opinions on similar reasons in more complex problems are expressed.

Degenerated isoparametric finite elements in nonlinear analysis of 2D-problems

Abstract Geometrically nonlinear elastic-plastic analysis of 2D-problems of structural mechanics, based on the application of degenerated isoparametric finite elements, is carried out. The investigations concentrate on the derivation of nonlinear equilibrium equations using the total Lagrangian formulation. Large rotation increments and a displacement dependent pressure loading are taken into account, developing, in consequence, additional components of the corresponding stiffness matrix. For the elastic-plastic behaviour the Prandtl-Reuss associated flow rule and the von Mises plastic yield criterion are adopted. The Riks-Wempner constant arc length method, together with Newton-Raphson iterations, are employed to solve the incremental nonlinear equations in question. Several numerical sample problems are presented and compared with analytical reference solutions. A proof of the good accuracy of the presented method is given.

Postbuckling behaviour of hybrid plate girders with web openings

Abstract In a certain case study, the practical behaviour of initially imperfect, geometrically and statically identical hybrid and homogeneous I-beams with rectangular web openings, under bending and shear, has been investigated theoretically by a special finite element method—in order to determine the qualitative consequence of flange steel nature on the postbuckling carrying capacity of those beams. For simple loading and support conditions, depending on the opening longitudinal location, the bending or shear modes of failure have been found essential, showing a substantial effect on flange steel quality in the bending mode, and little such effect in the shear mode.

Study of a plate modelling a dock gate

Abstract Computer aided finite element analysis has been applied to evaluate the structural behavior of a solid plate representing statically certain box-type construction of a dry dock gate. Possible comparison of particular results following from different procedures, valid for constant plate stiffness and rigid supports, has been performed and the distribution of reactions for variable plate stiffness, within two different numerical accuracies, has been studied. For practical requirements the nonlinear elastic flexibility of dock gate packing has been taken into account and an adequate numerical step-by-step approach, satisfying the considered material characteristics, developed. For last case the deflections, reactions, and internal forces have been examined in detail and a comparison with those for rigid supports presented.