Optimization of compressed wooden bars of variable section according to the criterion of maximum critical load

Abstract

The article presents a numerical and analytical solution to the problem of optimizing compressed rods according to the criterion of the maximum critical load with a possible loss of stability in two planes. We consider a wooden bar of rectangular cross section, the height of which varies according to a linear law, and the width is constant. The calculation is performed in an elastic formulation. A constraint on the constancy of the rod mass is introduced. Variable parameters are the ratio of the minimum section height to the maximum, as well as the ratio of the section width to the maximum height. Numerical search for the optimal solution is performed in the MATLAB environment using the method of sequential quadratic programming. It has been established that the use of rods with a cross-sectional height that varies linearly along the length is effective only if the rod is fixed in at least one of the planes according to the “pinched-free end” scheme. It has been established that the increase in the critical load when using rods with a linearly varying cross-sectional height can be up to 22%.