Postbuckling Behavior of Compressed Bars with Nonlinearly Elastic Supports

Supercritical bending of a rod compressed by longitudinal force and having non-linearly elastic resistance to rotation its axis in hinged supports is considered. Hooke's law adopted for the material. The deflection presented as trigonometric series, which only first three terms are left. Through this row, angle inclination expressed. It chosen desired function, with respect resolving nonlinear integro-differential equation obtained. To simplify it, case considered when bent gentle curve. revealed that usual approach, compressive given, leads trivial solution zero values coefficients series. Therefore, coefficient through represented, was initial parameter. containing remaining load solved simple collocation method, since use predetermined method impossible due nonlinearity resulting system equations. calculation results were analyzed depending on choice points, showed small difference between obtained solutions (the quadratic discrepancy calculated did not exceed one percent, indicates sufficient accuracy approximation form proposed work). In contrast approach used numerical methods, here it necessary enter any parameter loading process (such length arc method) pass limit points. An an approximate compliance rods compression, taking into account their supercritical bending. studies behavior various geometric mechanical characteristics presented, dependences parameters stress-strain state Their analysis made possible reveal number features properties supports. particular, found under consideration, compression support related relationship close linear, compressible can increase tens or more times stiffness springs, lose stability snap at some