Mathematical modeling of processes of geometrical nonlinear deformation of spatially loaded rods under thermal influence.

The article delves into an enhanced algorithm aimed at assessing the stress-strain characteristics of spatially loaded rods with diverse geometric configurations, taking into account thermal influences. It introduces a mathematical framework grounded in the Hamilton-Ostrogradsky variational principle to model the stress-strain behavior of rods under spatial loading while considering temperature fluctuations. The derivation of vibration equations for the rods incorporates relevant natural initial and boundary conditions. Furthermore, a computational algorithm, utilizing the matrix sweep method with second-order accuracy, is developed to analyze the statics and dynamics of rod vibrations amidst thermal variations, relying on central finite-difference relations. [ABSTRACT FROM AUTHOR]