General theory of cross-sections kinetics in calculating rod elements of structures. Cartesian coordinates

Abstract

The applied mechanics of deformable bodies evolves to its more rigorously substantiated predominant empirical approaches, which significantly limit calculation possibilities. The most "severe" limitation is applying exclusively the hypotheses of non-warping cross-sections in calculating the structural rod elements. The research was carried out to expand the possibilities and to systematically generalize and complete a traditional approach within the theory of strength of materials, which is based on isolating a subsystem of points in a cross-sectional form. The presented theory is a synthesis of the theory of strength of materials and the applied theory of elasticity. The theory of strength of materials contributed with the paradigm of monitoring the behaviour of cross-sections as a subsystem of points of a deformable body. The theory of elasticity provided differential equations of internal constraints, modifiable according to the traditional assumptions of the theory of material strength, except for those relating to the behavior of cross-sections. The study touches upon the analytical issue of optimizing the forms of various rod junctions, such as threaded, toothed, and strained junctions, and also on the issue of stress concentration in the regions of curvilinear transitions.