14. starptautiskā konference 2012 - Latvijas Jūras akadēmija

Proceedings of 14th International conference „Maritime Transport and Infrastructure - 2012”The first of them (see Fig. 2, d) is a model of Kelvin - Voight, considering that the total load isperceived as by the Hooke’s so by Newton's body:σ σ Е σ η Е ε ηε. (4)Assuming = const and integrating, we obtain the law of deformation progress in time: 1 exp E t . Е (5)If at some moment of time the body would be unloaded ( = 0), then integrating equation(4), we obtain a law of reducing the deformation in time:exp E (t). (6)By equationЕ t оwe get so called relaxation time.For the Maxwell model (see Fig. 2, e) applying the load, first instantaneously the Hooke’sbody is deformed, after the Newton’s body begins to act. Because the bodies are connected in series,they have the same loads. The rate of deformation of the system consists of the rate of deformation oftwo bodies: Е Е (7)If we assume that = const, integrating, we obtain a law to reduce load in time: о exp t (8) ,where o the load at the initial moment of time. Both models (see Fig. 2, d, e) characterizethe behavior of viscoelastic bodies.Prandtl model (see Fig. 2, f), characterizes the behavior of viscoplastic bodies.For this model= E Tif - т т ; = - т sign if - т т,(9)here - elastic deformation, when T, where T - flowability boundary. While тonly the Hook’s body is deformed. As soon as т, the deformation increases indefinitely due toslippage of the Saint-Venant’s body at a constant deformation of the elastic element. Fig. 3 shows therheological curves for Kelvin - Voigt, Maxwell and Prandtl models.145