**Author details**

24 Nonlinearity, Bifurcation and Chaos – Theory and Applications

positive direction goes toward the center of curvature

of the degree not exceeding the number of approximation.

**8. Conclusions** 

further theoretical justification.

**Figure 13.** The deformation of the shell with ovality and taper. Solid curves correspond to the middle of panels: black – large curvature, gray – small curvature, dash – forming at the junction of the panels;

The change of / *<sup>Н</sup> a b* from 0.96 to 0.84 significantly (1.2-1.4 fold) increases compliance of the membranes, while maintaining the overall picture of the distribution of displacements in the circumferential direction and increasing heterogeneity in the longitudinal direction.

The field of displacements was explained semi-automatically on the basis of the above algorithm. The forms of the radial deflection of some shell generatrixes are shown in Fig. 13.

A modified method of the parameter continuation (MMPC) is proposed. This method enables simplification of the calculations both at the stage of constructing the model, and also within its continued use due to precise values of the Taylor coefficients for the solution

The expression to calculate approximations by the MMPC in the general case and with the

The application of fractional-rational transformation for the polynomial approximation in the form of the 1-D and 2-D PAs used for increasing the degree of convergence and for the analytical continuation of the approximation in the region of its meromorphy was analyzed. It was concluded that such a transformation is justified if it is applied to polynomials which depend on the variable of integration. We used 2-D PAs for the independent variable and for the artificial parameter applying the scheme proposed by V. Vavilov. In this paper it is shown that this transformation provides a satisfactory quality for the approximation behavior and minimizes its error, in spite of the fact that the use of 2-D PAs requires a

The estimation of stability using MMPC approximation is also proposed. A study of numerical results was conducted by applying the methods for three model examples which

nonlinearity type of products and squares of the desired functions is presented.

Igor Andrianov *Institute of General Mechanics, RWTH Aachen University, Templergraben, Aachen, Germany* 

Jan Awrejcewicz *Lodz University of Technology, Department of Automation and Biomechanics, Stefanowski Str., Lodz, Poland* 

Victor Olevs'kyy *Ukrainian State Chemistry and Technology University, Gagarina av., 8, UA-49070, Dnipropetrovs'k, Ukraine* 
