Engineering Transactions, 48, 4, pp. 395–403, 2000

The Full Systems Method in Dynamics Problems of 3d Bodies

E.I. Bespalova
Institute of Mechanics of The National Academy of Sciences
Ukraine

A.B. Kytaygorodsky
Institute of Mechanics of The National Academy of Sciences
Ukraine

A new method is proposed to solve the problems of stationary dynamics for inhomogeneous anisotropic 3D bodies of finite sizes with arbitrary conditions on bounding surfaces. It is the reduction of the initial three-dimensional boundary problem to the system of three correlated one-dimensional boundary-value problems. Thus the increase of the number of independent variables results in the linear (but not exponential!) increase of the required computer resources. This determines the method efficiency when solving multidimensional problems. Several examples of solution for particular problems of mechanics of deformed bodies are presented.
Full Text: PDF

References

N. ALAM and N.T. ASNANI, Vibration and damping analysis of fibre reinforced composite material plates, 3. of Composite Materials, 20, 1, 2–18, 1986.

E.I. BESPALOVA, Solution of the problems of the theory of elasticity by the full systems method, Zhurnal Vichislit. Matem. and Matem. Phys., 9, 1346–1353, 1989.

E.I. BESPALOVA, A.B. KYTAYGORODSKY, Steady elasticity-theory problems with higt-gradient loads and localized mass and rigidity inhomogeneities, Int. Appl. Mech., 34, 9, 846–852, 1998.

L.V. KANTOROVICH, V.I. KRYLOV, Approximate methods of higher analysis, Phizmatgiz, Moskva – Leningrad 1962.

L. KOLLATZ, The eigenvalue problems, Nauka, Moskva 1968.

S.G. LECHNITSKY, Theory of elasticity anisotropic body, Nauka, Moskva 1977.




Copyright © 2014 by Institute of Fundamental Technological Research
Polish Academy of Sciences, Warsaw, Poland