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STABILITY ANALYSIS OF ORTHOTROPIC RECTANGULAR PLATES USING THE FORM FACTOR

Vestnik MGSU 12/2017 Volume 12
  • Savin Sergey Yur’evich - South-West State University (SWSU) Сandidate of Technical Sciences, Associate Professor, South-West State University (SWSU), 94 50 let Oktyabrya str., Kursk, 305040, Russian Federation.
  • Ivlev Ivan Andreevich - Orel State University named after I.S. Turgenev Post-graduate Student, Orel State University named after I.S. Turgenev, Orel State University named after I.S. Turgenev, 95 Komsomol’skaya str., Orel, 302026, Russian Federation.

Pages 1333-1341

The article describes the problem of stability of elastic orthotropic rectangular plates for the case when two opposite sides are simply supported, and two other sides have boundary with either simple supports or fixed supports, which are arbitrarily combined. The plate that is simply supported all over the contour is not considered in the article since the authors described it in the earlier publication. The external load is uniformly distributed along the side and is applied to the shorter side of the plate. To solve the stability problem, the authors use an approximate analytical method - the form factor interpolation method, which is based on the functional relationship between an integral geometric parameter of the mid-plane surface (the form factor) and an integral mechanical parameter (the critical force of buckling). Subject: stability of elastic orthotropic rectangular plates for the case when two opposite sides are simply supported and two other sides have combination of simple supports and fixed supports arbitrarily combined. Materials and methods: the form factor interpolation method (FFIM) is used to solve the stability problem of elastic orthotropic rectangular plates. The solutions which were obtained by the FFIM method were compared with the results of calculations by FEM (the program SCAD Office 11.5). Results: for orthotropic rectangular plates with combined boundary conditions, we obtained analytical expressions for critical force surfaces and they depend on an integral geometric parameter - form factor and flexural stiffness ratio. To the authors’ knowledge, these expressions are obtained for the first time. The critical force surface for orthotropic rectangular plates constitutes one of the boundaries of this integral physicomechanical parameter for the entire set of orthotropic plates with arbitrary convex contour. Therefore, this surface can be used for obtaining reference solutions by the form factor interpolation method. We demonstrated how to obtain the solution of the stability problem for orthotropic rectangular plates by the form factor interpolation method using the results obtained from the aforementioned analytical expressions as the reference solutions. The solutions obtained by the form factor interpolation method are compared with the results of calculations by the finite element method and show a good accuracy. Conclusions: the analytical expressions for critical loads presented in this work can be used directly for the stability analysis of orthotropic rectangular plates loaded in one direction as well as to obtain one of the reference solutions by the form factor interpolation method for plates with arbitrary convex contour and combined boundary conditions. The proposed approach can be extended to other forms of plates, boundary conditions and loading types.

DOI: 10.22227/1997-0935.2017.12.1333-1341

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DYNAMICALLY LOADED BAR:STABILITY AND KINEMATIC EQUATIONS OF MOTION

Vestnik MGSU 6/2013
  • Manchenko Maksim Mikhaylovich - St.Petersburg State University of Architecture and Civil Engineering (SPbGASU) postgraduate student, Department of Theoretical Mechanics; +7 (812) 296-20-22., St.Petersburg State University of Architecture and Civil Engineering (SPbGASU), 4 2nd Krasnoarmeyskaya st., 190005, St.Petersburg; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 71-76

Differential equations of motion for a bar are provided in this paper. The bar is exposed to the applied force that intensifies as the time progresses. The condition substantiating the trans-versal inertia force is identified using the equations. On top of the emerging inertia force, brief high-speed stress increases the yield stress of the material.The external force is accompanied by the eccentricity. Therefore, linear dimensions of the bar and its eccentricity make plastic behaviour possible both in compressed and stretched areas of the rod sections. Patterns of distribution of plastic deformations (one-sided and double-sided yield) are generated using the equations of motion for each case. Cauchy problems are supple- mented by the incoming conditions according to the principle of continuity of displacement and velocity.The criterion of stability loss is a condition when the variation of the exterior torque equals to the variation of the interior torque. At the same time, the variation of a longitudinal force must be equal to zero. Having completed a series of transformations, the author obtains the stability loss functional. It is calculated simultaneously with the motion equation. When the functional is equal to zero, the bearing capacity is exhausted.Moreover, there is a simplified method of identifying the critical force. The comparison of values with the testing findings demonstrates the efficiency of employment of the approximate method.

DOI: 10.22227/1997-0935.2013.6.71-76

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  6. Nazaruk A.V. Issledovanie ustoychivosti szhatykh sterzhney, rabotayushchikh v uprugoplasticheskoy stadii pri dinamicheskikh nagruzkakh [Research into Stability of Elasto-plastic Behaviour of Compressed Rods Exposed to Dynamic Loads]. Leningrad, 1977, 23 p.
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