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2 Journal of Applied Mathematics and Computational Mechanics

2 2016

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Numerical studies on stability of slender supporting structures

Sokół K., Uzny S.

Journal of Applied Mathematics and Computational Mechanics

2016

Vol. 15, nr 2

157--165

In this paper the results of studies on stability of the geometrically non-linear column (slender system) composed of two rods have been presented. The supporting structure has a defect in the form of cracks which are present in each of rods. The cracks are simulated by means of rotational springs. On the basis of the total potential energy principle, the boundary problem is being formulated. The results show an influence of the crack size on the stability of the column in particular on bifurcation load magnitude.

An influence of the geometrical nonlinearity of a frame column of flat frame type Γ subjected to the follower force directed towards the positive pole on its stability

Szmidla J., Wiktorowicz J.

Journal of Applied Mathematics and Computational Mechanics

2016

Vol. 15, nr 3

155--165

The results of the theoretical and numerical research for the purpose of designation of local and global instability areas of a rectangular frame with a geometrically nonlinear frame column subjected to the follower force directed towards the positive pole are presented in this work. Taking into consideration the total potential energy of an analysed system, the equations describing transverse and longitudinal movements and the boundary conditions necessary for the problem solution are formulated. On the basis of the static criterion of the loss of stability, the influences of the variable flexural stiffness of the system and the geometrical and physical parameters of the flat frame on the value of the bifurcation load are obtained. The results of numerical computations are compared with appropriate values of critical load of the comparative system.