Analytic methods of study of the strength of thin-wall structures made of composite materials | Mekhanika | kompozitsionnykh | materialov i konstruktsii
> Volume 2 > №2 / 1996 / Pages: 83-90

Analytic methods of study of the strength of thin-wall structures made of composite materials


We shall examine efficient and guaranteed exact solutions of the equations describing the stress-strain state of lamellar orthotropic plates and shells of revolution. In the load application zone the stress-strain state of the subject structures has high variability. In the case of the use of the method of finite elements or the methods with the use of the procedures of numerical integration of the ordinary differential equations, the error of the calculations is not monitored and validity of the obtained results is often not guaranteed. Conversely, the analytic methods make it possible to obtain results with an apriori evaluation of the error. Still another advantage of the analytic methods is the absence of the additional computational techniques (increase of the order of the system of equations, orthogonalization of the solutions) that are characteristic for the marching methods. Therefore the effectiveness of the analytic methods is very high. For the lamellar plates and cylindrical shells the solutions are expressed through the elementary functions. In the case of lamellar conical shells we obtain the integrals of the ordinary differential equations in terms of special functions (the generalized hypergeometric function and the Mayer G-function). We obtain the algorithms for calculating the special functions with the use of expansions in power series, and also series in the orthogonal polynomials and Bessel functions, asymptotic expansions, and polynomial and rational approximations. Thus, the proposed analytic solutions of the problems of the mechanics of composite structures are very effective with regard to the volume of the calculations and the accuracy of the results obtained.