Papers by Keyword: Errors

Abstract: In this scientific work, mathematical modeling of tetrahedron elements in the finite element method is presented, which includes the determination of geometric shape, shape functions, and material properties. Unknown fields such as displacement vectors, strain, and stress tensors are considered. The methodology of applying the principle of virtual work and equilibrium equations is described, allowing the derivation of a system of differential equations to describe the behavior of the tetrahedral element. Integration over the volume and consideration of boundary conditions help reduce the equations to a system of linear algebraic equations for numerical solution using the finite element method. It was found that modeling tetrahedral elements with a specific given radius (for example, R=0.3 mm) involves stages such as geometry determination, element generation, shape function formation, stiffness matrix computation, and solving a system of linear equations. The radius R of tetrahedral elements is taken into account at all stages, ensuring accuracy and reliability in tetrahedra modeling. The research also focuses on the fact that the occurrence of minor errors in iterative processes may result from several factors, including iteration step, the number of iterations, stopping criteria, linear or nonlinear material behavior, solution method selection, the presence of geometric inhomogeneities, and element size.

Abstract: Additive Manufacturing (AM) does not yet have a standardized way to measure performance. Here a AM machines dimensional accuracy is measured trough acceptance test (AT) and AM machines capability is tested trough test parts. Test parts are created with specific geometrical features using a 3D AM machine. Performance of the machine is then evaluated trough accuracy of test parts geometry. AM machine here uses selective laser melting (SLM) process. This machine has done Factory acceptance test (FAT) to ascertain this machine ́s geometrical accuracy with material AISI 316L. Manufacturer promises accuracy of ±0.05 mm. These parts are used as comparison to AT parts made in this study. After installation two AT parts are manufactured with AM machine. One with AISI 316L and one AlSi10Mg. Dimensional accuracy of geometrical features on these parts are then compared to FAT part and to one another. Machines capability is measured trough two test parts done with material AlSi10Mg. Two of the test parts are done at the same time using same model as the FAT. Parts are printed without supports and with features facing same directions. Features of these parts were then evaluated. Another test to find out AM machines capability was to create part consisting of pipes doing 90˚ angle resulting in horizontal and vertical holes. Dimensional accuracy and circularity of holes was measured. Through these tests machines capability is benchmarked.

Abstract: Lighting conditions in buildings are verified by experts on a daily basis. Such verifications may be done at several phases in various ways. In the field of daylighting, it is common to make an assessment within the pre-design and in-design phases of a construction work throughout calculations, only rarely by measurements. This approach is the opposite of artificial lighting design, which is done within the in-design phase by calculations and is verified by measurements in post-realization phase. The verification of artificial lighting design is required by the building and public health authority otherwise buildings cannot be approved to use. In the field of daylighting, measurements could be performed as well, nevertheless those are often problematic because regulations usually require fulfilments of the daylight factor which can be determined only under CIE overcast sky. Howbeit, both artificial lighting and daylighting measurements are influenced by many errors, e.g. errors of light measurement instruments, measurement conditions, measurement methods and human factor. The paper is focused on this aspect of lighting design, more specifically on the daylighting measurement errors.