Analysis of solid-state models using center-stress finite elements
DOI:
https://doi.org/10.55287/22275398_2026_59_24Keywords:
stress, bending moments, finite element model, star of node elements, finite element center, volumetric finite elements, result convergence, section weighting factorAbstract
When performing strength calculations of building structures on a computer using software packages based on the finite element method, it is necessary to use various finite element models to validate the obtained data. Models of spatial elasticity problems are the most informative, but are labor-intensive to analyze. This work is a continuation of a numerical experiment to determine the correct location of stresses in first-order volumetric finite elements of solid models when calculating bending moments. In the first part of the work, it was demonstrated that using stresses acting on the faces of the structure in the star of node elements ensures the necessary calculation accuracy, but requires analyzing a significant amount of data.
The aim of this work is to elucidate the feasibility of using average stresses acting at the centers of the outermost finite elements when calculating bending moments in solid models, taking into account the application of cross-sectional weighting factors. The study methodology involves comparing bending moments calculated using averaged normal fiber stresses in a model of an obliquely bent concrete cantilever beam with a cross-section of 300 x 600(h) mm and a length of 1800 mm. The model is constructed using an isoparametric eight-node first-order cubic finite element with a 50 mm edge size from the SCAD++ library with a regular finite element mesh.
The numerical experiment demonstrated good convergence of the results, with deviations from the analytical calculations amounting to -1.73% and +1.13%.
The practical significance of this study lies in the fact that when calculating bending moments in solid-state computer models consisting of first-order volumetric finite elements, it is convenient to use the stresses acting at the centers of the outermost finite elements, taking into account the application of cross-sectional weighting factors. This approach significantly reduces the computational effort compared to analyzing the star data of node elements.
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