An analytical solution to the thermal problems with varying boundary conditions around a moving source

Salimi, Solaleh; Bahemmat, Pouya; Haghpanahi, M.

doi:10.1016/j.apm.2016.02.012

Cited by 10 publications

(7 citation statements)

References 20 publications

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“…To avoid complexity, the proper values of boiling water convection coefficients for an underwater specimen in each region are equal to 11,480, 27,870 and 1350 W/ m 2 C, respectively. 42 In addition, the equivalent convection coefficient is considered to be 4600 W/m 2 C and 800 W/m 2 C in the pressurized area and the rest of the plate, respectively. 42 Using the mentioned input data, the temperature distribution and the RS filed have been computed based on the developed FEM solution procedure.…”

Section: Resultsmentioning

confidence: 99%

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Study on residual stresses caused by underwater friction stir welding: FE modeling and ultrasonic measurement

Salimi

Bahemmat

Haghpanahi

2018

Proceedings of the Institution of Mechanical Engineers, Part E:

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Predicting residual stresses arising from the thermal and mechanical loading history during engineering processes including welding would be a viable tool to reach the optimum process parameters. In the present article, an elastothermo-visco-plastic model has been employed to estimate the residual stress caused by the underwater friction stir welding, which are resulted by large thermo-mechanical deformations on one hand and rapid cooling arising from the enormous non-uniform boiling heat convention of water on the other hand. Finally, the numerical results are compared with experimental data acquired by the ultrasonic method to evaluate the accuracy of the simulation process. Regarding the low temperature during underwater friction stir welding, the employed constitutive equations result in acceptable residual stress fields, while for in-air case, the amount of error increases significantly due to experience of high temperatures and intensification in hardening precipitation phenomena.

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Section: Resultsmentioning

confidence: 99%

“…It is worth noting that the shape functions are of isoparametric class, which can decrease the computation time. Subsequently, the Gaussian quadrature rule is implemented to estimate the integral expressions in equations (42)to (45), which results in…”

Section: Mechanical Equationsmentioning

confidence: 99%

Study on residual stresses caused by underwater friction stir welding: FE modeling and ultrasonic measurement

Salimi

Bahemmat

Haghpanahi

2018

Proceedings of the Institution of Mechanical Engineers, Part E:

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“…Ω Ω = ∈   = ∈ ∂  (1) where L is a linear differential operator, B -a boundary operator, f(x, y) and g(x, y) are two known functions, and Ω ÎR 2 is an open bounded domain with boundary ¶Ω. The problem (1) arises in many fields such as fluid mechanics and thermal science, and has attracted more and more researchers in recent decades [1][2][3][4][5][6]. By the method of fundamental solutions [1], the problem (1) can be transformed uniformly to a set of linear equations C z b n =   with unknown vector z  , the circulant or block-circulant matrix C n , and the given vector b  .…”

Section: Lu X Y F X Y X Y Bu X Y G X Y X Ymentioning

confidence: 99%

Numerical method to a class of boundary value problems

Qiu

2018

THERM SCI

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“…The analytical temperature distribution due to a moving heat source has been derived for a vast variety of problems in both semi-infinite [7,8,9,10] and finite [7,11,12,13] three-dimensional domains, and with different heat source models. In this paper the problem under consideration is the heat equation in the lower half-space with a Gaussian distributed heat flux that travels over the surface.…”

Section: Introductionmentioning

confidence: 99%

Analytical solution for heat conduction due to a moving Gaussian heat flux with piecewise constant parameters

Forslund

Snis²,

Larsson

2019

Applied Mathematical Modelling

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We provide an analytical solution of the heat equation in the half-space subject to a moving Gaussian heat flux with piecewise constant parameters. The solution is of interest in powder bed fusion applications where these parameters can be used to control the conduction of heat due to a scanning beam of concentrated energy. The analytical solution is written in a dimensionless form as a sum of integrals over (dimensionless) time. For the numerical computation of these integrals we suggest a quadrature scheme that utilizes pre-calculated lookup tables for the required quadrature orders. Such a scheme is efficient because the required quadrature orders are strongly dependent on the parameters in the heat flux. The possibilities of using the obtained computational technique for the control and optimization of powder bed fusion processes are discussed.

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An analytical solution to the thermal problems with varying boundary conditions around a moving source

Cited by 10 publications

References 20 publications

Study on residual stresses caused by underwater friction stir welding: FE modeling and ultrasonic measurement

Study on residual stresses caused by underwater friction stir welding: FE modeling and ultrasonic measurement

Numerical method to a class of boundary value problems

Analytical solution for heat conduction due to a moving Gaussian heat flux with piecewise constant parameters

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