Weak discontinuity annihilation in solidification modelling

Dynamic buckling of an imperfect elastoplastic beam subjected to an impulsive load analyzed using transport equations

“…refer to a material reference system, a spatial reference system and a computational reference system coordinate respectively. The relations between the material derivative and an arbitrary Lagrangian-Eulerian derivative with respect to the spatial derivative are defined by the following expressions [1][2][3][4][5][6][7];…”

“…By considering as arbitrary space, the general form of continuity, energy and momentum equations are derived as [1][2][3][4][5][6][7] ( )…”

“…For this purpose, the continuous shape functions were used in the entire element. The new approach proposed by Mondragon and Davey [7] provides the simultaneous possibility for capacity and source to remove the discontinuity and this simultaneous operation do not exist in other methods. Extensive researches have been undertaken on the static and dynamic buckling behavior of structures under various boundary and loading conditions .…”

“…Davey used the transport equations in the field of modeling heat transfer in the presence and absence of boundary and material discontinuities [1][2][3][4][5][6][7]. The performance of the capacity control methods for convection-solidification problems was investigated by Davey [1].…”