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