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In the paper mathematical and numerical models of strains calculation during the heating and cooling process of the medium-carbon steel element on the basis of the finite element method are presented. In the model the melting phenomenon of the superficial layer is taken into account. In the modelling of strains, except thermal strains, structural strains occurring during the phase transformation in the solid state are also included. The phenomena of partly overlapping heat affected zones for a successive path of the moving heat source are taken into account. To determine the phase transformations in the solid state the macroscopic model based on the analysis of the CCT and CHT diagrams is used. In the model the influence of the heating rate on the temperature of sorbite transformation during tempering of the C45 steel element is taken into account. It has a particular importance in the process when heat treatment is performed by the moving heat source. The plastic and transformation strains distributions for the heat treatment with the use of the parallel path of the heat source are calculated. The presented results obtained from copyright software, in which the algorithm of modeling of the hardening phenomena (FEM task 3D) are implemented. [ABSTRACT FROM AUTHOR]

The main objective of this study is to compare results obtained from some widely used simplified analytical formulas of plate welding problem to results obtained from numerical analysis of this problem based on the solution of transient three-dimensional heat conduction equation with the heat source modeled by Gaussian function. In simplified formulas, peak temperature of the thermal cycle and cooling time from 800 to 500°C are proportional to the ratio of the power and the velocity of the heat source. Therefore, special attention is paid to the variation of the solution due to change in values of these two input parameters while their ratio is kept constant. [ABSTRACT FROM AUTHOR]

Sensitivity analysis of transient three-dimensional heat conduction in a plate during process of welding is performed. Crank-Nicolson method with multi-step Douglas-Gunn Alternating Direction Implicit (ADI) method is used for the solution of heat conduction equation with convection boundary conditions at all surfaces, and with heat source at the top surface moving with a constant velocity. Sensitivity equation method (SEM) is applied for sensitivity calculations. It is shown that SEM is a set of straightforward operations in the case of heat conduction equation. Development of the sensitivity equation with respect to the power of the heat source is demonstrated and final results for this sensitivity are presented. [ABSTRACT FROM AUTHOR]

This paper is concerned to study temperature distribution, thermal stresses and displacement components for a magnetothermoelastic problem of a half-space subjected to (i) moving heat source and (ii) moving load. Classical Dynamical Coupled, Lord-Shulman and Green Lindsay theories of thermoelasticity are used for mathematical analysis. It is found that the Lord-Shulman theory is more pronounced than coupled theory and Green Lindsay theories. Numerical computations have been performed for computing temperature, stresses and displacement for these theories. The results obtained using these theories are compared and depicted graphically. [ABSTRACT FROM AUTHOR]