Method of homogeneous solutions in problems with mixed boundary conditions. (English. Russian original) Zbl 0704.73016
Sov. Appl. Mech. 25, No. 9, 899-903 (1989); translation from Prikl. Mekh., Kiev 25, No. 9, 57-61 (1989).
The method of homogeneous solutions has proven to be very effective for solving a large class of problems in the theory of elasticity. In the author’s earlier article [(*) Prikl. Mat. Mekh. 44, 957-960 (1980; Zbl 0467.73087)], the first attempt was made within the framework of the method of homogeneous solutions to significantly reduce the volume of calculation and, most important, to improve the accuracy of the result by analyzing infinite systems in a manner similar to the approach taken in the superposition method. However, the authors of (*) found the limiting value of the unknowns in the infinite system as a result of a numerical experiment. Thus, their investigation did not make it any easier to analytically obtain the value of the exponent of the asymptote from the system.
Here, we obtain a more exact equivalence relation which is used to analytically substantiate and improve an algorithm for regularization in an axisymmetric problem concerning the tension-compression of a thick plate with a rigidly fixed lateral surface.
Here, we obtain a more exact equivalence relation which is used to analytically substantiate and improve an algorithm for regularization in an axisymmetric problem concerning the tension-compression of a thick plate with a rigidly fixed lateral surface.
Keywords:
regularization; axisymmetric problem; tension-compression; thick plate; rigidly fixed lateral surfaceCitations:
Zbl 0467.73087References:
| [1] | O. K. Aksentvan, ”Features of the stress-strain state in the neighborhood of a rib,” Prikl. Mat. Mekh.,31, No. 5, 178–186 (1967). |
| [2] | G. S. Bulanov, ”Expansion of the exponents of a stress state into a series in homogeneous solutions,” Teor. Prikl. Mekh.,14, 6–13 (1983). |
| [3] | G. S. Bulanov and V. A. Shaldyrvan, ”Improving the convergence of the method of homogeneous solutions,” Prikl. Mat. Mekh.,44, No. 5, 957–980 (1980). · Zbl 0467.73087 |
| [4] | I. I. Vorovich, ”Certain mathematical aspects of the theory of plates and shells,” Transactions of the 2nd All-Union Conference on Theoretical and Applied Mechanics. Solid Mechanics, Moscow, Nauka (1966), pp. 116–136. |
| [5] | A. M. Gomilko, V. T. Grinchenko, and V. V. Meleshko, ”Methods of homogeneous solutions and superposition in static boundary-value problems for an elastic strip,” Prikl. Mekh.,22, No. 8, 84–93 (1986). · Zbl 0623.73029 |
| [6] | A. M. Gomilko, V. T. Grinchenko, and V. V. Meleshko, ”Possibilities of the method of homogeneous solutions in mixed problems of the theory of elasticity for a half-strip,” Teor. Prikl. Mekh.,18, 3–8 (1987). · Zbl 0729.73841 |
| [7] | V. T. Grinchenko, Equilibrium and Steady-State Vibrations of Elastic Bodies of Finite Dimensions [in Russian], Naukova Dumka, Kiev (1978). |
| [8] | A. S. Kosmodamianskii and V. A. Shaldyrvan, Thick Multiply-Connected Plates [in Russian], Naukova Dumka, Kiev (1978). |
| [9] | V. V. Lidskii and V. A. Sadovnichii, ”Asymptotic formulas for the roots of one class of integral functions,” Mat. Sb.,15, No. 4, 558–566 (1967). |
| [10] | V. K. Prokopov, ”Homogeneous solutions of the theory of elasticity and their application to the theory of thin plates,” Transactions of the 2nd All-Union Conference on Theoretical and Applied Mechanics. Solid mechanics, Moscow, Nauka (1966), pp. 31–46. |
| [11] | Ya. S. Uflyand, Integral Transforms in Problems of the Theory of Elasticity, Nauka, Leningrad (1967). · Zbl 0126.19901 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
