Longitudinal-transverse thermal- force bending and stability layered inhomogeneous profiled rod

Abstract

Abstract The solution to the problem of the stress-strain state of an inhomogeneous profiled rod is based on the use of nonlinear equilibrium conditions and physical relations of a layered thermo elastic thin rod. A differential equation of bifurcation inhomogeneous rod stability of variable cross-section is obtained. The equation has variable functional coefficients. In the initial state, the rod is subjected to bending with the implementation of one of the asymmetric shapes. The critical state occurs under the action of a longitudinal load corresponding to one of the lowest symmetrical shapes, orthogonal to the initial shape. In the first series, numerical calculations of an inhomogeneous I-rod with a variable cross section height are performed. Shelves and wall I-rod are made of steel, aluminum and titanium alloys. The graphs of maximum deflection and normal stresses acting at the calculate points at the boundaries of the layers are plotted depending on the longitudinal load at the given levels of transverse loads and thermal field. A significant influence of the rod physical structure, the profiling its form and the factor of nonlinearity of static relations on the stress fields has been established. A homogeneous temperature field with a nominal value of 80°C creates fields of self-balanced stresses in an inhomogeneous rod. The components of normal stresses in this case reach 20-40% of the materials permissible resistance level. The presence of rod parts with a significant difference in the coefficients of thermal expansion in the composition enhances this effect. In the second, the stability analysis of an inhomogeneous I-rod with a variable width cross section was performed. The transition of the initial S-shaped bend to an unstable state is shown.