The article presents the results of statistical analysis of the orthotropy coefficient of a multilayer cylindrical shell under compressive loads. The orthotropy coefficient is defined as the ratio of the critical load for asymmetric buckling of the shell to the critical load for axisymmetric buckling of the shell. It is assumed that the structure web is formed by laying longitudinal, annular and double spiral layers. The input values ​​are the elastic characteristics of the monolayers, assuming that these characteristics are random variables subject to the normal distribution law. The output value is the orthotropy coefficient. All calculations were performed in the MAXIMA computer algebra system. Two most common shell models were investigated: equally rigid and quasi-isotropic. It was found, in particular, that for shells with a quasi-isotropic structure, the orthotropy coefficient is “determined”.

Keywords: statistical modeling, monolayer, multilayer shell, composite material, elastic properties, stability, buckling, critical load, orthotropy coefficient, MAXIMA, Monte Carlo method.

The most significant advantage of composite structures compared to structures made of traditional materials is the ability to control the characteristics of the structure in order to obtain an optimal design. In the general case, the initial physical characteristics of the material of the composite structure are random variables. Consequently, the required quantities (stresses, strains, critical loads, etc.) are also random variables. The problem of statistical modeling of a composite structure is ultimately reduced to the problem of transforming random variables. To solve this problem, the Monte Carlo method is used. The object of study is a multi-walled plate under the action of compressive loads. The purpose of this work is to construct point estimates of the coefficients of both general and local stability for a multi-walled plate, as well as to test statistical hypotheses about the equality of the stability coefficients to their theoretical values. The initial parameters are the elastic moduli in the longitudinal and transverse directions, as well as the shear modulus of the construction material. The following were used as output values: sample mean, standard deviation, skewness and kurtosis coefficients. All calculations were carried out in the environment of the MAXIMA package. It is shown that the distribution of the overall stability coefficient practically does not differ from the normal distribution. The coefficient of local stability has a slight positive asymmetry and a steeper peak compared to the normal curve. The results obtained allow us to conclude that the spread of the elastic characteristics of the material does not significantly affect the coefficients of the general and local stability of the multi-walled plate.

Keywords: statistical modeling, statistical hypothesis, multiwall plate, stability, critical load, composite material