Chepurnenko A.S.

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

Optimization of Rectangular and Box Sections in Oblique Bending and Eccentric Compression

https://doi.org/10.58224/2618-7183-2023-6-5-2
Abstract
The article presents a solution to the problem of finding the optimal ratio of the height of the cross-section to the width for a rectangular and box-shaped section in the case of oblique bending and eccentric compression. Optimization is performed according to the strength criterion, and for the case of oblique bending of a rectangular beam, a solution was also obtained from the condition of a minimum full deflection. For a rectangular section, the solution is made analytically, and for a box section, numerically using the MATLAB environment and the Optimization Toolbox package. As a numerical method of nonlinear optimization, the interior point method is used. To simplify the solution, the box section is assumed to be thin-walled, i.e. it is assumed that the wall thickness is significantly less than the height and width of the cross section. An estimate of the error of such an assumption is also performed. It has been established that in the case of oblique bending of a rectangular beam, when optimizing according to the strength criterion, the optimal ratio of the cross-sectional height to width is equal to the cotangent of the angle between the force plane and the vertical axis, and when optimizing according to the rigidity criterion, it is the square root of the cotangent of this angle. In the case of eccentric compression of a rectangular beam with eccentricities in two planes, the optimal ratio of the height of the cross section to the width is equal to the ratio of the eccentricity along the vertical and horizontal axes. For a box-shaped section, graphs of the change in optimal parameters depending on the angle between the force plane and the vertical axis in the case of oblique bending, as well as depending on the ratio of eccentricities along the axes in the case of eccentric compression, are plotted.
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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.
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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.
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