Bending deflection of a non-uniform bar at axial compression

Аuthors

Egorov A. V.

National Institute of Aviation Technologies, 3, Kirovogradskaya str., Moscow, 117587, Russia

e-mail: antegor177@mail.ru

Abstract

The article considers a process of deformation of a hinged-mounted non-uniform bar at the axial compression. Numerical computation was performed with ANSYS and LS-DYNA software, using 3D finite elements in elastoplastic domain. The fact of stability loss was being established through the values of bending deflections being determined.

The bar non-uniformity was specified by the three elastic insertions with elasticity modulus differing from basic material of the bar. The insertions were located along the bar superficies non-symmetrically relative to its axis. A steel bar with elasticity modulus of
E_f = 200 GPa with two types of insertions, namely, hard with elasticity modulus of
E_f = 180 GPa, and soft with elasticity modulus of E_f = 1 kPa was considered.

The insertions were of a small volume: in total 0.8% relative to the bar volume.

Based on modal analysis, forms of oscillations and natural frequencies of the non-uniform bar were obtained with ANSYS software, which were compared to the shapes and frequencies of the uniform bar.

Lateral motions (bending deflections) of an axially compressed non-uniform bar were found by computing its stress and strain state with LS-DYNA software in dynamic setting, which allowed obtaining bending deflections as a function of time. For the first five forms of stability losses of the non-uniform bar corresponding loads were calculated.

Loading of the bar bending deflection over one half-wave (per the first form) was compared to Euler’s critical load. It was shown, that the obtained critical loading exceeded it by 21%. This loading can be considered as the upper estimation, since the insertions were of small volume.

With an assumption of the bar non-destructiveness, the process of shape changing, associated with large displacements was established with LS-DYNA software, and a time instant of ultimate strain reaching in the upper thin layer on the bumpy surface of the bended bar was indicated.

Keywords:

column strut, compression, stability, modal analysis, finite elements method, mode of deformation

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