A phase field model for anti-plane shear crack growth in two dimensional isotropic elastic material is proposed. We introduce a phase field to represent the shape of the crack with a regularization parameter ϵ>0 and we approximate the Francfort-Marigo type energy using the idea of Ambrosio and Tortorelli. The phase field model is derived as a gradient flow of this regularized energy. We show several numerical examples of the crack growth computed with an adaptive mesh finite element method.
The paper deals with the method of transverse dispersion coefficient statement from field measurement and with a way of correction of their values through the mathematical modelling. A constant steady source of tracer was used by the method of the computation of transverse dispersion coefficient from the field measurements and the method can be applied in wide and shallow rivers. It is based on the work of Demetracopoulos and Stefan (1983). The transverse dispersion coefficients were determined by this method at about 4 km long part of the Hron River. There was found out that the applied method gives overestimated results of transverse dispersion coefficients, so they had to be corrected by application of 2-dimensional numerical model of dispersion MODI with which there were simulated the results of field measurements. The summary of result values of these coefficients are in Tab. 1. and Príspevok opisuje spôsob stanovenia koeficientov priečnej disperzie a korekciu ich hodnoty za pomoci matematického modelu MODI, vychádzajúc z terénnych meraní. Pri terénnych meraniach bola aplikovaná metóda stanovenia priečneho disperzného koeficienta publikovaná Demetracopoulosom a Stefanom (1983). Táto metóda využíva konštantný zdroj stopovacej látky a je aplikovateľná pre široké plytké korytá. Na jej základe boli stanovené hodnoty priečnych disperzných koeficientov na cca 4 km dlhom úseku rieky Hron medzi zaústením toku Istebník a mostom v Banskej Bystrici-Šalkovej. Metóda Demetracopoulosa a Stefana (1983) však dáva vo všeobecnosti nadhodnotené výsledky priečnych disperzných koeficientov, preto hodnoty týchto koeficientov boli na základe simulácie výsledkov terénnych meraní modelom MODI následne korigované. Výsledky sú zhrnuté v tab. 1.
The strength and stiffness of the differential cage is very important issue, because it affects the functionality of the other components of powered axles. The problem is that for the stress analysis of the differential cage is not possible to use conventional strength and elasticity approaches, because the differetial cage has very complex geometrical shape and is also loaded by the combination of forces generated by the load engagement of the bevel gear. Therefore numerical simulations are more and more frequently used to solve this complex problem when the main task is creation the computational model that correspond the real state. The present paper deals with designing the computational model of the cage differential drive of the rear powered axle of utility vehicle. This model is then used for the strength structural analysis of the differential cage assembly. Presented computational model takes into account also the load of the differential cage thanks to the preload in strength bolts which join the bevel crown gear and differential cage. and Obsahuje seznam literatury a názvosloví