STABILITY OF COMPRESSED RODS WITH VARIABLE RIGIDITY
Abstract
The problems of stability of compressed rods with continuous resizing of the cross sections in different directions are considered. Such structures include columns, chimneys, various supports, TV and radio towers, towers, parts of cranes, machines and mechanisms, various shafts and axles. It is shown that these problems are reduced to boundary problems for ordinary differential equations with variable coefficients. It is noted that analytical solutions of such equations cause the serious mathematical difficulties. For this reason, there are few cases of solving similar problems of stability of compressed rods in a closed form. In this regard, it was proposed to simplify significantly the algorithms for solving boundary problems for differential equations with variable coefficients based on the theory of a numerical-analytical version of the boundary element method that was developed in the writings of the authors of this work. For the application of technology of the boundary element method rods with variable rigidity are divided into a number of sections with constant rigidity and in such case matrices of the fundamental functions of differential equations with constant coefficients can be used. When the number of plots is more than 50, the solution of problems of stability converges to exact values. This conclusion is confirmed by the given examples of solutions of problems of stability with different boundary conditions.
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References
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