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 an adaptive methodology for the solution of (linear and) nonlinear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns instead of marching sequentially in time. The methodology is a combination of a computationally efficient implementation of a parallel-in-space-time finite element solver coupled with a posteriori space-time error estimates and a parallel mesh generator. While we focus on spatial adaptivity in this work, the methodology enables simultaneous adaptivity in both space and time domains. We explore this basic concept in the context of a variety of time steppers including $\Theta$-schemes and backward difference formulas. We specifically illustrate this framework with applications involving time dependent linear, quasi-linear, and semilinear diffusion equations. We focus on investigating how the coupled space-time refinement indicators for this class of problems affect spatial a...

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.

The paper aims to present the possibility of performing engineering calculations in domains of complex shapes expressed by mathematical descriptions. We focus on calculations done with the use of the Finite Element Method. An example of the compound structure is gyroid, which is a periodic structure representing an area close to the porous structure. The presented gyroid structure exhibits circular struts and a spherical core and spatially occupies a cube. The side length of the cube is defined as unit cell size, and the volume percentage of the struts inside the cube is referred to as volume fraction. The periodic cellular lattice structures are generated by our own software module. One of the uses of such structures is their employment in additive manufacturing (AM) of the so-called 3D printing (layer-by-layer AM technique), where they can contribute reducing the weight of an item and limiting the material consumption. It is important to answer the question of what effect does an element with a gyroid structure have on the thermal properties (e.g. the heat flow versus the volume fraction) compared to an element with full structure. The paper will show the results of such a comparison.

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.