Feszültségmezőre épülő magasabb rendű végeselem-modellek a szilárd testek mechanikájában = Stress-based higher-order finite element models in computational solid mechanics

Többmezős variációs elvek alkalmazásával három különböző hp-verziós végeselem-modell került kifejlesztésre. Háromdimenziós, lineáris rugalmasságtani feladatok megoldására a Fraeijs de Veubeke-féle kétmezős variációs elven alapuló, az elsőrendű feszültségfüggvényeket és a szögelfordulásokat közvetlenül approximáló hexaéder elemet és egy arra épülő végeselemes programot dolgoztunk ki. Forgásszimmetrikus körhengerhéj-feladatok megoldására két különböző, dimenzió szerint redukált héjmodellt és hp-verziós héjelemet dolgoztunk ki, melyeket egy-egy C++ nyelven megírt végeselemes programba építettünk bele. Az egyik elem-modell a Fraeijs de Veubeke-féle kétmezős variációs elven, a másik pedig a Hellinger-Reissner-féle hárommezős variációs elven alapul. A hárommezős elvben a nem a priori szimmetrikus feszültségmező és a forgásmező mellett az elmozdulásmező is függetlenül approximálandó ismeretlenként jelenik meg. Kimutattuk és numerikusan igazoltuk, hogy a kifejlesztett elem-modellekkel kapott numerikus megoldások konvergencia-sebessége független a Poisson tényezőtől és a héj vastagságától, vagyis erősen inkompresszibilis anyagok és vékony héjak esetében is numerikus konvergencia problémák nélküli megoldásokat adnak a mérnöki alkalmazások szempontjából elsőrendű fontosságú feszültségmezőre nézve is. | Three different hp-version finite element model has been developed using multi-field dual-mixed variational principles. The hexahedron element developed for three-dimensional linear elasticity problems is based on the two-field variational principle of Fraeijs de Veubeke with independent approximations of the six independent components of the first-order stress function tensor and three continuum rotations. The element and the corresponding research code, written in the C++ programming language, can be used for three-dimensional problems with simple geometry. Two other dimensionally reduced shell elements have also been developed, both of them for axisymmetric cylindrical shell problems: one is based on the two-field variational principle of Fraeijs de Veubeke, the other has been developed using the three-field dual-mixed principle of Hellinger-Reissner with independently approximated variables of not a priori symmetric stresses, continuum rotations and the displacements. The locking-free property of the elements has been demonstrated through test examples, and the solutions have been compared to analytical solutions as well as to results obtained using standard displacement-based elements. It has been shown that the dual-mixed approach and the related finite elements lead to robust, reliable and accurate stress computations for not only higher order p-, but also for low order h-type approximations

Többmezős variációs elvek és végeselem-modellek a nemlineáris rugalmasságtanban

Egy feszültségmezőn és forgásmezőn alapuló általános, nemlineáris héjelmélet került kidolgozásra. A dimenzió szerinti redukálás variációs hátterében a kiegészítő virtuális munka elv általánosított alakja áll. Az I. Piola-Kirchhoff feszültségvektorokra vonatkozó transzlációs egyensúlyi egyenletek a priori kielégítése két elsőrendű feszültségfüggvény-vektor bevezetésével, a forgási egyensúlyi egyenletek kielégítése pedig a forgásmező, mint Lagrange-multiplikátor alkalmazásával történt. A klasszikus héjelméletek alapjául szolgáló kinematikai és feszültségi hipotézisek nem kerültek alkalmazásra, így a háromdimenziós anyagegyenletek módosítások nélkül vehetők figyelembe.A kidolgozott héjelmélet alapján egy feszültségmezőn és forgásmezőn alapuló új hp-verziós lemezelem-modell és végeselem-program került kifejlesztésre lineárisan rugalmas lemezfeladatok megoldására. Numerikus úton igazolásra került, hogy a lemezmodell aszimptotikusan korrekt és modellezési hibája lényegesen jobb, mint a klasszikus Kirchhoff- és Reissner-Mindlin lemezmodelleké. A kifejlesztett hp-verziós elem-modell rendkívül vékony és összenyomhatatlan anyagú lemezek esetén is numerikus problémák (shear locking és incompressibility locking) nélküli feszültségeket eredményez, nemcsak magasabb rendű p-, hanem alacsony rendű h-típusú approximációnál is. | Starting from the three-dimensional principle of complementary virtual work, a stress-based dimensionally reduced shell model has been derived. The three-dimensional translational equilibrium equations, written in terms of the first Piola-Kirchhoff stress vectors, are a priori satisfied using two first-order stress function vectors. The rotational equilibrium equations are enforced in a weak sense using the rotations as Lagrangian multipliers. No conventional kinematical assumptions have been applied and the shell model uses unmodified three-dimensional constitutive equations.Based on the shell model derived, a new hp-version finite element model and a finite element code have been developed for linearly elastic plates (including the membrane problem). The numerical results show that rates of convergence in the energy norm and in the stress computations are practically independent of the Poisson ratio and thickness of the plate, i.e., the elements are free from both incompressibility locking and shear locking. The stress computation is robust, reliable and accurate for not only higher order p- but also for low order h-type approximations, even for extremely thin plates

Zinc-rich paint coatings containing either ionic surfactant-modified or functionalized multi-walled carbon nanotube-supported polypyrrole utilized to protect cold-rolled steel against corrosion

The intense anodic action of sacrificial zinc pigments ensured viable galvanic function of the highly porous liquid zinc-rich paints (ZRPs) result in deteriorated long-term corrosion resistance often accompanied by cathodic delamination phenomena. In our approach, such a efficacy problem related to the corrosion preventive function of ZRPs is addressed by the application of intimately structured anodic inhibitor particles composed of nano-size alumina and either polyelectrolyte-modified or chemically functionalized multi-walled carbon nanotubes (MWCNT) supported polypyrrole (PPy) in one specific zinc-rich hybrid paint formulation providing balanced active–passive protective functionality. High dispersity of the nanotube-free PPy-deposited inhibitor particles (PDIPs) with uneven polymer distribution on the alumina carrier was confirmed by transmission electron microscopy (TEM) observations. Furthermore, the MWCNT-embedded PDIPs indicated almost complete surface coverage of the alumina-nanotube carriers by PPy with decreased microstructure dispersity which is attributed to the effect of double-flocculants type co-deposition of the oppositely charged polymers causing coalescence of the modified particles. Depending on the amount of the nanotubes and their proportion to the quantities of the deposited PPy and polyelectrolyte as well as the concentration of the surfactant, varied micron-scale association of the PDIPs in the suspensions of dissolved alkyd matrix was disclosed by rheology characterization carried out at particular solid contents similar to hybrid paint formulation. The evenly distributed but less densely packed nano-structure of PPy was evidenced on the polyelectrolyte-modified nanotubes by Fourier-transform infrared (FTIR) spectroscopy whereas more compact polymer film formation was confirmed on the surface of functionalized nanotubes. According to the greater electrical conductivity, enhanced electroactivity and reversibility of the nanotube-embedded PDIPs were indicated over the nanotube-free particles by cyclic voltammetry, depending on the type and the amount of the nanotubes and their modification. Protection function of the hybrid paint coatings (formulated with spherical zinc pigment at 70 wt.%) was investigated by immersion and salt-spray chamber tests over 254 and 142 day periods, respectively. Firm barrier nature of the nanotube-embedded PDIP contained hybrids was proved by electrochemical impedance spectroscopy (EIS) and radio-frequency glow-discharge optical-emission-spectroscopy (RF-GD-OES). Furthermore, due to the increased conductivity of the nanotube-embedded PDIPs cemented in epoxy primers optimally at 0.4 and 0.6 wt.%, altered corrosion preventive behaviour of the hybrid coatings was indicated by the positively polarized open-circuit potentials (OCPs) and the X-ray photoelectron spectroscopy (XPS) detected lower relative quantities of the interfacially accumulated zinc corrosion products, moderate oxidative degradation of the epoxy vehicle. Decreasing oxidative conversion of iron at the surface was indicated by XPS found to correlate with the increasing intensity of zinc corrosion and decreasing oxidative degradation of the epoxy binder, according to the higher nanotube contents of hybrid coatings. In addition, inhibited zinc corrosion caused low rate of oxidative degradation of epoxy, allowing increased durability of coating adhesion and cohesion thereby ensuring reliable protection by zinc-rich compositions. As a conclusion, modified or functionalized MWCNTs acting as unexchangeable doping agents promote enhanced reversibility and increased conductivity of PPy, forming nano-size inhibitor particles with advanced features. Thus, such inhibitor nano-particles in zinc-rich hybrid compositions afford improved barrier and high efficiency galvanic–cathodic corrosion preventive function, exceeding long-term protection capability of the conventional ZRPs

SURFACE CHARACTERIZATION OF RAPIDLY SOLIDIFIED AI ALLOYS

Rapidly solidified aluminium alloys with Mn, Fe and Mg were studied by depth profiling XPS and SIMS. Most of the Mn and Fe were found in deeper layers in metallic form while the Mg on the surface in oxide and carbonate state