ABSTRACT
Noncircular cylindrical shells made of orthotropic materials are widely used for construction of structure elements in modern engineering (Soldatos 1999). To estimate their strength under possible conditions of service operation, it is necessary to have information about the stress-strain state of the mechanical objects being considered (Gould 1988). Currently, to solve the problems of computational mathematics, mathematical physics, and mechanics, spline-functions are widely used (Zavialov et al. 1980, Grigorenko & Krukov 1995). It is due to advantages of the splineapproximation techniques in comparison with others. As basic advantages, the following can be referred: stability of splines in respect to local disturbances, i.e., behavior of the spline near a point does not affect the behavior of the spline as a whole as, for instance, this holds in the case of the polynomial approximation; fast convergence of the spline-interpolation in contrast to the polynomial one; simplicity and convenience in realization of algorithms for constructing and calculating splines by personal computers. The use of spline-functions in variational, projective, and other discrete-continuous methods allows us to obtain appreciable results as compared to the use of classical polynomials and to substantially simplify their numerical implementation, leading to highly accurate solutions (Grigorenko & Zakhariichenko 2004, Grigorenko & Yaremchenko 2004).
