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Creep and Relaxation of Prismatic Bar in State of Bending

The viscoelastic behavior of prismatic bar in state of bending is investigated in this paper. When describing the creep phenomenon of such bar it is assumed that the bar is in the state of the steady-state creep conditions, i.e. at such state of creeping at which the stresses do not change with time. The dependence of creep strain on stress and time at a given temperature can be written as a product of two functions, of which the first function is a function of stress and temperature, and the second one is a function of time and temperature, [1-3]. The mentioned methodology of calculating is often used in the theory of viscoelasticity for determining the stress distribution in the different structural components, [2-3]. In order to find out how much the stress distribution in a bar is accurate and reliable, the same problem was solved by one variation method, i.e. by applying the principle of minimum of complementary potential energy, [1]. The compatibility of the obtained results was even more than expected, excellently. A second phenomenon which was considered in this paper was relaxation phenomenon of bending moment in a cross section of prismatic bar. At the initial moment (t = 0), the bending moment acting on the bar amounts to If a curvature of the bar is kept constant over time, the decrease of the bending moment over time is investigated, [3]. The analytical methods and one approximate numerical method were used in the analysis of creep and relaxation of prismatic bar. Some results, especially relaxation of bending moment, and their graphic interpretations were obtained by means of software package Wolfram Mathematica 7.0. References [1] Malinin, N. N., Applied Theory of Plasticity and Viscoelasticity, Mashinostroenie, Moscow, 1975, (in Russian). [2] Pustaić, D., Steady-State Creep Analysis of Thick-Walled Pressure Vessels and Piping, In: Virag, Z., Kozmar, H. and Smojver, I., eds., Proceedings of 7th International Congress of Croatian Society of Mechanics – 7th ICCSM, 197- 198., CD-ROM (full papers), Croatian Society of Mechanics, Zagreb (Zadar), 2012. [3] Pustaić, D. and Pustaić, M., Torsion of a Circular Cross Section Shaft in the Steady- State Creep Conditions, In: Kožar, I., Bićanić, N., Jelenić, G. and Čanađija, M., eds., Proceedings of 8th International Congress of Croatian Society of Mechanics – 8th ICCSM, Book of Abstracts, p. 83, CD-ROM (full papers), Croatian Society of Mechanics, Zagreb, 2015.

Creep and relaxation, prismatic bar loaded on bending, viscoelastic strain, analytical method, variation method, Wolfram Mathematica 7.0

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