The present paper is dedicated to presentation and energy verification of the methods of stabilization the strain energy by penalty coefficients. Verification of the methods is based on the consistency and ellipticity conditions to be satisfied by the finite elements. Three methods of stabilization are discussed. The first does not satisfy the above requirements. The second is consistent but cannot eliminate parasitic energy terms. The third method, proposed by the author, is based on the decomposition of the element stiffness matrix. The method can help to eliminate locking of the finite elements. For two-noded beam element with linear shape functions and exact integration a stabilized free of locking (and elliptical) element is received (equivalent to reduced integration element). Two plate finite elements are analyzed: four-noded rectangular element and DSG triangle. A new method of stabilization with the use of four independent parameters is proposed. The finite elements with this kind of stabilization satisfy the consistency condition. In the rectangular element it was not possible to eliminate one parasitic term of energy which appears during the procedure. For DSG triangle all parasitic terms of energy are eliminated. The penalty coefficients depends on the geometry of the triangle.
The formulation of a plate finite element with so called ‘physical’ shape functions is revisited. The derivation of the ‘physical’ shape functions is based on Hencky-Bollé theory of moderately thick plates. The considered finite element was assessed in the past, and the tests showed that the solution convergence was achieved in a wide range of thickness to in-plane dimensions ratios. In this paper a holistic correctness assessment is presented, which covers three criteria: the ellipticity, the consistency and the inf-sup conditions. Fulfilment of these criteria assures the existence of a unique solution, and a stable and optimal convergence to the correct solution. The algorithms of the numerical tests for each test case are presented and the tests are performed for the considered formulation. In result it is concluded that the finite element formulation passes every test and therefore is a good choice for modeling plate structural elements regardless of their thickness.
Development of high-performance finite elements for thick, moderately thick, as well as thin shells and plates, was one of the active areas of the finite element technology for 40 years, followed by hundreds of publications. A variety of shell elements exist in the FE codes, but “the best” finite element is still to be discovered. The paper deals with an evaluation of some existing shell finite elements, from the point of view of the third of three requirements to be satisfied by theelement: ellipticity, consistency and inf-sup condition. It is difficult to prove the inf-sup condition analytically, so, a numerical verification is proposed. A set of numerical tests is considered for shell and plate problems. Two norm matrices and a selection of the stiffness matrices (bending, shear and membrane dominated) are analysed. Finite elements from various computer systems can be evaluated and compared with the use of the proposed tests.
This study presents an analysis of aluminium cast iron structure (as-cast condition) which are used in high temperatures. While producing casts of aluminium iron, the major influence has been to preserve the structure of the technological process parameters. The addition of V, Ti, Cr to an Fe-C-Al alloy leads to the improvement of functional and mechanical cast qualities. In this study, a method was investigated to eliminate the presence of undesirable Al4C3 phases in an aluminium cast iron structure and thereby improve the production process. V and Ti additions to aluminium cast iron allow the development of FeAl - VC or TiC alloys. In particular, V or Ti contents above 5 wt.% were found to totally eliminate the presence of Al4C3. In addition, preliminary work indicates that the alloy with the FeAl - VC or TiC structure reveals high oxidation resistance. The introduction of 5 wt.% chromium to aluminium cast iron strengthened the Al4C3 precipitate. Thus, the resultant alloy can be considered an intermetallic FeAl matrix strengthened by VC and TiC or modified Al4C3 reinforcements.
Metal alloys with matrix based on an Fe-Al system are generally considered materials for high-temperature applications. Their main advantages are compact crystallographic structure, long-range ordering and structural stability at high temperatures. These materials are based on an intermetallic phase of FeAl or Fe3Al, which is stable in the range from room temperature up to the melting point of 1240°C. Their application at high temperatures is also beneficial because of the low cost of production, very good resistance to oxidation and corrosion, and high mechanical strength. The casting alloy the structure of which includes the FeAl phase is, among others, highaluminium cast iron. This study has been devoted to the determination of the effect of vanadium and titanium on the transformation of the high-aluminium cast iron structure into an in-situ FeAl-VC composite.