Nonlinear models of beams with variable stiffness

Abstract

Objective. The article examines beam structures with variable rigidity, in which physical nonlinearities of their supports and the material of the structure itself are manifested. The article examines issues of support nonlinearity, beam rigidity variability, and provides a solution to the corresponding differential equations containing variable coefficients. Method. The features of the operation of nonlinear elastic beam supports are presented, and the variability of rigidity of the specified structures, which exhibit significant physical nonlinearities, is described. By introducing special notations, differential equations containing variable coefficients are reduced to a form that allows constructing their classical solution. Result. Beams on nonlinear-elastic supports, beams with variable stiffness, as well as beam structures, beams, the material of which does not follow Hooke's law, are considered. A classical solution to the differential equation of transverse bending of beams with variable rigidity is constructed; calculation schemes, formulas, tables and graphs are provided. Conclusion. The developed algorithms and the obtained results allow taking into account the nonlinear operation of supports, the influence of variability of beam stiffness, physical nonlinearities of the material of the structure. The results of the study can be used in the practice of design and construction.