Limit analysis and optimal support of reinforced three-layer

T. P. Romanova

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 20 (2016) no. 3, pp. 508-523.

Résumé

Within the model of an ideal rigid-plastic body the limit behavior of the hybrid composite circular plates is considered. The exact solution of the problem of bending is built for three-layer reinforced circular plates having different angular structure reinforcement at the top and bottom layer. The material of the middle layer and the binder in the upper and lower layers has a yield stress in compression much greater than in tension. In this case the condition of plasticity for the main moments that are based on the structural model of the reinforced layer with one-dimensional states of stress in the fibers has the form of a rectangle of type Johansen condition. The plates are hinge supported along the internal annular contour and have the rigid circular insert in the central part. The plates are under load non-uniformly distributed over the surface of the plate. It is shown that there are a few schemes of limit deformation of the plate, depending on the location of the internal support and on distribution of load. The conditions of implementation are defined for all schemes. The main moments and the velocities of the deflections of the plate are defined at different locations of the internal support. The simple analytic expressions are obtained for the limit load. The optimal location of support is determined. The optimal support is such support, at which the plate has a maximum limit load. It is shown that the optimal position of the support corresponds to the formation of plastic hinge on it. It is obtained that with increase in the applied distributed load in several times, the limit loads will be reduced in the same times and the optimal location of the support will not change. Numerical examples are given. The solution can be useful in engineering practice to evaluate the bearing capacity of three-layer reinforced concrete plates.

Détail

Keywords: rigid-plastic model, hybrid reinforcement, different-resistant materials, corner reinforcement, three-layer plate, non-uniform loading, internal support, limit load, optimal support.

Bibliographie

[1] Dekhtyar A. S., “Point supporting of plates of complicated configuration”, Stroitel'naia mekhanika i raschet sooruzhenii, 2010, no. 2, 56–59 (In Russian)

[2] Dekhtyar A. S., “Irregular structures and expedience of unification”, Stroitel'naia mekhanika i raschet sooruzhenii, 2009, no. 5, 74–77 (In Russian)

[3] Romanova T. P., “Carrying capacity and optimization of three-layer reinforced circular plate of differently resistant materials, supported on the internal contour”, Problems of strength and plasticity, 2015, no. 3, 286–300 (In Russian)

[4] Yang W. H., “How to optimally support a plate”, J. Appl. Mech, 48:1 (1981), 207–209 | DOI

[5] Olenev G. M., “Optimal location of additional supports to rigid-plastic circular plates in case of impulse loading”, Uch. Zap. Tartu. Gos. Univ., 1983, no. 659, 30–41 (In Russian) | Zbl

[6] Dekhtyar A. S., “Optimum support of a square plate”, Prikl. Mekh., 27:6 (1991), 107–110 (In Russian)

[7] Dekhtyar A. S., “Optimal placement of columns in buildings constructed by lifting”, Stroitel'naia mekhanika i raschet sooruzheni, 1989, no. 1, 14–17 (In Russian)

[8] Koreneva E. B, Grosman V. G., “Analytical solution of unsymmetric flexure problem by circular orthotropic plate with radually varying thickness based on point supports”, International Journal for Computational Civil and Structural Engineering, 2015, no. 11, 94–100 (Russian)

[9] Lellep J., Polikarpus J., “Optimal design of circular plates with internal supports”, WSEAS Transactions on Mathematics, 11:3 (2012), 222–232

[10] Wang C. M., Liew K. M., Wang L., Aug K. K., “Optimal locations of internal line supports for rectangular plates against buckling”, Structural Optimization, 4:3 (1992), 199–205 | DOI

[11] Papkovskaya O. B., Kozin O. B., Camara D., “Construction and research of solution of antisymmetric flexion task for an orthotropic strip plate supported by the rigid support”, Trudy Odesskogo politekhnicheskogo universiteta, 2006, no. 2, 181–185 (In Russian)

[12] Romanova T. P., “The Optimal Location of the Polygonal Internal Supports to the Circular Rigid-Plastic Plates”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2014, no. 3(36), 94–105 (In Russian) | DOI | Zbl

[13] Romanova T. P., “Optimal support of rigid-plastic singly and doubly connected polygonal plates”, PNRPU Mechanics Bulletin, 2014, no. 4, 152–177 (In Russian) | DOI

[14] Nemirovsky Yu. V., Romanova T. P., “Modeling of behavior of doubly connected rigid-plastic plate of arbitrary form with the internal curvilinear support under explosive loads”, Problems of strength and plasticity, 2014, no. 2, 122–133 (In Russian)

[15] Lyakhovich L. S., Perelmuter A. V., “Some problems of building constructions optimal projecting”, International Journal for Computational Civil and Structural Engineering, 2014, no. 10(2), 14–23 (In Russian)

[16] Vokhmianin I. T., Nemirovsky Yu. V., “Features of longitudinal-transverse bending of three-layer circular plates with asymmetric structures of reinforcement”, Boundary problems and mathematical modeling, Proc. of the 8th Russian Sci. Conf., v. 1, Novokuznetsk, 2006, 25–31 (In Russian)

[17] Nemirovsky Yu. V., Romanova T. P., “Calculation of dynamic deformation of three-layer reinforced concrete circular and annular plates”, Beton i Zhelezobeton, 2011, no. 6, 26–30 (In Russian)

[18] Nemirovsky Ju. V., Resnikoff B. S., “On limit equilibrium of reinforced slabs and effectiveness of their reinforcement”, Archiwum Inżynierii Lądowej, 21:1 (1975), 57–67