Buckling in inelastic regime of a uniform console with symmetrical cross section: computer modeling using Maple 18
| Autor: | Viktor V. Chistyakov, Sergey M. Soloviev |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Discrete and Continuous Models and Applied Computational Science, Vol 31, Iss 2, Pp 174-188 (2023) |
| Druh dokumentu: | article |
| ISSN: | 2658-4670 2658-7149 |
| DOI: | 10.22363/2658-4670-2023-31-2-174-188 |
| Popis: | The method of numerical integration of Euler problem of buckling of a homogeneous console with symmetrical cross section in regime of plastic deformation using Maple18 is presented. The ordinary differential equation for a transversal coordinate \(y\) was deduced which takes into consideration higher geometrical momenta of cross section area. As an argument in the equation a dimensionless console slope \(p=tg \theta\) is used which is linked in mutually unique manner with all other linear displacements. Real strain-stress diagram of metals (steel, titan) and PTFE polymers were modelled via the Maple nonlinear regression with cubic polynomial to provide a conditional yield point (\(t\),\(\sigma_f\)). The console parameters (free length \(l_0\), \(m\), cross section area \(S\) and minimal gyration moment \(J_x\)) were chosen so that a critical buckling forces \(F_\text{cr}\) corresponded to the stresses \(\sigma\) close to the yield strength \(\sigma_f\). To find the key dependence of the final slope \(p_f\) vs load \(F\) needed for the shape determination the equality for restored console length was applied. The dependences \(p_f(F)\) and shapes \(y(z)\), \(z\) being a longitudinal coordinate, were determined within these three approaches: plastic regime with cubic strain-stress diagram, tangent modulus \(E_\text{tang}\) approximations and Hook’s law. It was found that critical buckling load \(F_\text{cr}\) in plastic range nearly two times less of that for an ideal Hook’s law. A quasi-identity of calculated console shapes was found for the same final slope \(p_f\) within the three approaches especially for the metals. |
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