Chepurnenko A.S.

Candidate of Engineering Sciences (Ph.D.), Associate Professor, Don State Technical University (DSTU), Russia

FLAT BENDING SHAPE STABILITY OF RECTANGULAR CROSS-SECTION WOODEN BEAMS WHEN FASTENING THE EDGE STRETCHED FROM THE BENDING MOMENT

https://doi.org/10.58224/2618-7183-2022-5-4-5-18
Abstract
The article presents the solution to the problem of calculating the lateral buckling of wooden beams with a narrow rectangular section, taking into account intermediate point fixing in the edge stretched from the bending moment. The structure is considered as an orthotropic plate, the calculation is performed by the finite element method (FEM). To obtain a result that is valid for any beam geometry, the system of FEM equations is reduced to a dimensionless form. The dimensionless parameter that determines the value of the critical load is calculated based on the solution of the generalized eigenvalue problem. The numerical calculation algorithm is implemented in the MATLAB environment. The developed technique is verified by comparison with calculations in the LIRA and ANSYS software systems using flat and volumetric finite elements. A comparison is also made with the calculation formula presented in the Russian design standards for wooden structures SP 64.13330.2017 for the coefficient, taking into account intermediate fixing, with pure bending. It has been established that this dependence rather roughly takes into account the fastening from the bending plane of the edge stretched from the bending moment. Using the package Curve Fitting Toolbox of the MATLAB environment, we have selected refined formula for the coefficient, which can be used in engineering calculations.
PDF

DETERMINATION OF RHEOLOGICAL PARAMETERS OF POLYMERIC MATERIALS USING NONLINEAR OPTIMIZATION METHODS

https://doi.org/10.34031/2618-7183-2020-3-5-15-23
Abstract
The article is devoted to the problem of processing the experimental creep curves of polymers. The task is to determine their rheological characteristics from tests for any of the simplest types of deformation. The basis for the approximation of the experimental curves is the nonlinear Maxwell-Gurevich equation.
The task of finding the rheological parameters of the material is posed as a nonlinear optimization problem. The objective function is the sum of the squared deviations of the experimental values on the creep curve from the theoretical ones. Variable input parameters of the objective function are the initial relaxation viscosity and velocity modulus m*. A theoretical creep curve is constructed numerically using the fourth-order Runge-Kutta method. The nonlinear optimization problem is solved in the Matlab environment using the internal point method. The values m* and are found for which the objective function takes the minimum value.
To test the technique, the inverse problem was solved. For given values of the rheological parameters of the material, a theoretical curve of creep under bending was constructed, and the values m* and were found from it. The technique was also tested on experimental stress relaxation curves of secondary polyvinyl chloride and creep curves of polyurethane foam with a pure shear.
A higher quality approximation of experimental curves is shown in comparison with existing methods. The developed technique allows us to determine the rheological characteristics of materials from tests for bending, central tension (compression), torsion, shear, and it is enough to test only one type of deformation, and not a series, as was suggested earlier by some researchers.
PDF