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Numerical studies on stability of slender supporting structures

Sokół K., Uzny S.

Journal of Applied Mathematics and Computational Mechanics

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2016

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Vol. 15, nr 2

157--165

EN

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.

2

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

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2016

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Vol. 15, nr 3

155--165

EN

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.

3

Długości wyboczeniowe krzyżulca wieży w skratowaniu typu X

Rykaluk K.

Inżynieria i Budownictwo

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2015

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R. 71, nr 4

201--204

PL

Główny problem jest skupiony na wyznaczeniu długości wyboczeniowej w kierunku prostopadłym do ściany wieży, gdy obydwa pręty są ciągłe. W artykule został rozwiązany za pomocą wyznaczenia obciążenia bifurkacyjnego krzyżulca ściskanego, który jest sprężyście stabilizowany przez krzyżulec rozciągany lub ściskany siłą mniejszą niż krzyżulec pierwszy. Przedstawiono przykłady obliczeniowe.

EN

The main problem is focused on determination the buckling length in a direction perpendicular to the wall of the tower when both members are continuous. The paper have been solved by a designation of the load bifurcation for the largest compressive diagonal, which is elastically stabilized by a second diagonal. The second member can be stretched or compressed less force than the first member. Example calculations are presented.

4

The Stability of Geometrically Nonlinear Column Loaded by a Generalized Force Directed to Positive Pole at Stepped Variable of Flexural Rigidity

Szmidla J., Cieślińska-Gąsior I., Wiktorowicz J.

Machine Dynamics Research

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2014

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Vol. 38, No. 1

65-72

EN

The results of theoretical and numerical research that aims at determining areas of local and global instability of geometrically non-linear column loaded by a generalized force directed towards a positive pole at stepped variable of flexural rigidity are presented in the paper. Taking into account total potential energy of column, equations of transverse displacements and boundary conditions necessary to solve the issue were obtained. On the basis of the static criterion of stability an influence of variable flexural stiffness and geometrical and physical parameters of system on the value of the bifurcation load of considered structure was determined. The results of numerical calculations were referred to value of critical load of relevant linear column (a comparative column).