Accurate Solution of Problem of the Stress-strain State of a Multi-span Compressed-bent Elastic Bar in the Linear Statement

Abstract

The system of linear differential equations of the 4th order has been written subsequently for all the plane strain spans of a multi-span elastic bar with regard to accurate geometric and static matching conditions in the areas between the spans, and it is solved with the numerical method of the 8th order of accuracy previously suggested by the authors and based on the application of a fundamentally new interpolation procedure. It is carried out only by the joints with the interval of integration which enables to avoid the need to execute off-standard transformations connected with the exclusion of additional unknowns from the obtained system of nonlinear algebraic equations as a result of interpolation – as it is recommended in the well-known Handbook on Mathematics when using the traditional techniques of interpolation.The explicit solution results of the test problem on the stress-strain state (SSS) are given for a three-span compressed bent bar.