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Investigation and analysis of periodic problem for layered composite structure on periodic foundation by means of non-smooth argument transformation method

Starushenko G., Krulik N., Tokarzewski S.

International Journal of Applied Mechanics and Engineering

2003

Vol. 8, no spec.

169-177

The solution of the periodic problem for layered composite structure on the discretely located linear-elastic bearings has been obtained in the paper (Starushenko, 2000). The general case of the problem is considered in this paper. The structure that is located on the combined continuous and discrete elastic foundation is examined. The foundation rigidity is periodically changed in the composite phase limits. The structure is fortified by elastic supports in the component part junction. The problem is solved for general problem statement. It is supposed that physical and geometrical characteristics of the body and elastic foundation can accept any value. The periodic solution of the problem has been obtained in components of displacement function by means of saw-tooth argument transformation method in the paper. Analysis of obtained solution has been carried out. The flexure functions of the elastic foundation depending of the structure rigidity and geometric factors have been found.

About representation of theory tasks periodic solutions on basis of non-smooth argument transformation

Starushenko G., Krulik N., Tokarzewski S.

Applied Mechanics and Engineering

1999

Vol. 4, no spec.

115-120

The analytical method of solving periodic tasks of elasticity theory for layered composites has been suggested in papers (Starushenko et al., 1998). The method based on introduction of special non-smooth argument transformation so-called saw-tooth transformation (t-transformation). The advantage of saw-tooth argument transformation method is connected with possibility of mathematical description in limits of unanimous approach of different nature functions: continuous, piece continuos, with local specialties. Besides its combination with average theory and a lot of scale decomposition method extends opportunities of t-transformation technique application considerably. Solution of elasticity theory for layered composite massive in case of distributed massif forces has been built in paper (Starushenko et al., 1998). In present paper case of general load (acting of periodic distributed and concentrated load in common) is examined.