An influence of a non-prismatic rod as a part of a geometrically nonlinear system under generalized load with a force directed towards the positive pole on the value of the bifurcation load

Abstract eng:
The article presents the theoretical considerations and results of the numerical computations regarding the issue of stability of the geometrically nonlinear column with the non-prismatic rod under the generalized load with the force directed towards the positive pole (case of L. Tomski's load). The boundary problem was formulated on the basis of minimum potential energy principle and solved using the small parameter of amplitude method (perturbation method). It was proved that appropriate selection of the shape of the rod of the cross-section variable along the axis results in an increase in the value of the bifurcation load of the column compared to the reference system (built of prismatic rods of the same volume) and thus have an influence on the range of local loss of rectilinear form of static equilibrium.

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