Internal stresses and movements of the assembled shoes insole under the influence of load

The article describes the development of algorithms that always allow dealing with deformed states of systems. These systems include assembled shoe insoles. As a model, the author used an elastic beam loaded with concentrated forces (and, possibly, concentrated moments). The relatively smooth outlines of the assembled insoles are replaced by a broken outline. Infinitely small load - bearing elements are represented by assembled insoles connected by trapezoidal elastic bonds. Integration of approximate differential equations of plane bends resulted in the final construction of mathematical equations. Algebra made it possible to compactly formulate the equilibrium equations connecting the rear force factors. Recent changes in the matrix reflect the relationship between internal forces and deformations. However, the task of displacements finding is simplified. As a result, a matrix algorithm was found that allows not only to find the stress - strain state of the node trunk, but also to solve the problem of selecting its sections that provide the required displacements. The article describes an example of determining the deflections and rotation angles of a pinched assembled insole. The calculation results are comparable with experimental data.