The paper focuses on thermal and mechanical analysis of Periodic Surface Structure (PSS). PSS is a continuous surface with a specific topology that is mathematically formulated by geometric factors. Cubic P-surface (“primitive”), D-surface (“diamond”), and G-surface (“gyroid”) structures were simulated under load and heat transport using a numerical approach. We conducted our study by solving the stress and heat equations using the Finite Element Method (FEM). We achieved results using our software module, which generates PSS and simulates stress and temperature distribution. The stress model defined by dependence between stress and strain, gained from an experiment, and correlation of strain and displacement, gained from geometric conditions, was used in numerical experiments. The influence of geometric factors on the thermal and mechanical behavior of PSS was qualitatively determined. We showed decreasing effective stress values with an increased number of cells in the cubic domain for concerned PSS. It is important, because the increase in the number of cells does not increase the structure’s volume.
We present a description of the effects of thermal interactions, which take into account formation of a shrinkage gap, that affect the level of stresses in a system casting -mold. Calculations were carried out in our own computer program which is an implementation of the finite element method used to solve the equations describing a thermo-elastic-plastic model of material and the heat conduction, including solidification. In the computing algorithm we use our own criteria for mechanical interaction between the casting and mold domains. Our model of mechanical interactions between the casting and the mold allows efficient modeling of stresses occurring in the casting and an impact of development of the shrinkage gap on cooling course.
In the paper, we present the results of solidification simulation taking into account the movement of the liquid phase. The results are obtained from an author software which is implemented on the base of a stabilized finite elements method (Petrov-Galerkin formulation). Using that formulation the Navier-Stokes equation is solved together with the convection term (Boussinesq approximation). The Finite Element Method (FEM) formulation is responsible for solidification, approximating the solution of the heat conduction equation (with the internal heat source term responsible for the heat released during the phase transition). The movement of the liquid phase in a solidifying cast that is caused by convection can significantly affect the process of heat transfer from the casting to the mold, which in turn has an influence on the temperature distribution in the cast and may cause a change in the location of the defects. The presented results allow to assess under what conditions the effect of convection on the solidification process is significant.
The article presents the use of swarming algorithms in selecting the heat transfer coefficient, taking into account the boundary condition of the IV types. Numerical calculations were made using the proprietary TalyFEM program and classic form of swarming algorithms. A function was also used for the calculations, which, during the calculation, determined the error of the approximate solution and was minimalised using a pair of individually employed algorithms, namely artificial bee colony (ABC) and ant colony optimisation (ACO). The tests were carried out to select the heat transfer coefficient from one range. Describing the geometry for a mesh of 408 fine elements with 214 nodes, the research carried out presents two squares (one on top of the other) separated by a heat transfer layer with a κ coefficient. A type III boundary condition was established on the right and left of both edges. The upper and lower edges were isolated, and a type IV boundary condition with imperfect contact was established between the squares. Calculations were made for ABC and ACO, respectively, for populations equal to 20, 40 and 60 individuals and 2, 6 and 12 iterations. In addition, in each case, 0%, 1%, 2% and 5% noise of the reference values were also considered. The obtained results are satisfactory and very close to the reference values of the κ parameter. The obtained results demonstrate the possibility of using artificial intelligence (AI) algorithms to reconstruct the IV type boundary condition value during heat conduction modelling.
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