ОПТИМИЗАЦИЯ ПОЛОЖЕНИЯ ГЛАВНЫХ ПЛОСКОСТЕЙ ЖЕСТКОСТИ НЕОДНОРОДНОГО СТЕРЖНЯ ПРИ ПРОСТРАНСТВЕННОМ ИЗГИБЕ
ОПТИМИЗАЦИЯ ПОЛОЖЕНИЯ ГЛАВНЫХ ПЛОСКОСТЕЙ ЖЕСТКОСТИ НЕОДНОРОДНОГО СТЕРЖНЯ ПРИ ПРОСТРАНСТВЕННОМ ИЗГИБЕ
DOI:
https://doi.org/10.22337/2587-9618-2026-22-3-63-75Ключевые слова:
оптимальное проектирование неоднородных стержней, слоистый стержень, пространственный изгиб, критерий минимума энергии деформации, управляемые конструкцииАннотация
The problem of finding the optimal rotation angle of the principal planes of stiffness for a spatially loaded, inhomogeneous rod of variable cross-section is considered. This angle serves as an additional regulator of the stress state for inhomogeneous rod designed in accordance with the adopted optimization criteria. The rod rigidly connected to a movable coordinate system capable of rotation around rod's longitudinal axis is composed of quasi-homogeneous structural elements. The rod's structure is symmetrical with respect to one of the plane coordinates. The specified loads are applied to the rod's centerline and are located in two mutually perpen-dicular fixed planes. Based on the minimum strain energy criterion, a formula for the optimal rotation angle of the rod's rigidity planes was derived. This formula contains six integral strain energy components. These components represent the actual and potential work of internal forces in the original rigidity planes and those rotated by 90 degrees. A numerical example shows strain energy graphs for cross-sections with different layouts. The relationship between the energy criterion and the strength criterion is highlighted. Based on the minimum strain energy criterion, a formula for the optimal rotation angle of the rod 's rigidity planes was derived. This formula contains six integral strain energy components. These components represent the actual and possible work of internal forces initial rigidity planes and those rotated by 90 degrees. A numerical example shows strain energy graphs for cross sections with different layouts. The relationship between the energy criterion and the strength criterion is noted. In the example discussed, using axial rotation of the rod, without requiring changes to its physical structure or geometry, allows for an increase in its load-bearing capacity by 20-30% and a reduction in maximum stress levels. This method can also be applied to prefabricated standard structural elements, including homogeneous ones. In the example discussed, the use of axial rotation of the rod, without requiring changes to its physical structure or geometry, allowed for an increase in its load-bearing capacity by 20-30% and a reduction in maximum stress levels. This method can also be applied to prefabricated standard structural elements, including homogeneous ones. The development of this method is its application in “controlled structures”, which acquire the ability to effectively adapt to changes in the parameters of external force impact.
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