## 1 Introduction
A robust and efficient inverse stochastic method based on the non-sampling generalized polynomial chaos method is presented for identifying uncertain elastic parameters from experimental modal data [31]. That is to say, there have already been many successful studies on quantifying mechanical behaviors of composite laminates. However, it should be noted that these research studies are mainly focused on probabilistic thoughts, where available experimental data points should be sufficient or probability density functions of uncertain input parameters can be precisely modeled or known [32; 33]. In any case, many studies which report the variability in experimental observations from material characterization testing reveal clearly the need for the development of probabilistic models for characterizing these uncertainties. However, in practice, the available experimental points or sample points are always limited or insufficient. Consequently, making good use of limited experimental points to quantify the uncertain elastic parameters of composites shows great advantages, where uncertain multi-dimensional parameters of composites can be dealt with as independent or dependent interval variables, or convex-set variables. In this aspect, there also exists some important work concentrating on non-probabilistic uncertainty quantification analyses [34; 35; 36]. For example, in the literature [37], spatially-stochastic macroscopic material properties are characterized for heterogeneous composite fabrics from limited-size macro-scale experimental measurements. The author has taken good advantages of the smallest ellipsoid and the smallest hyper-rectangle to quantify elastic moduli with some limited experimental points and, further, the uncertainty propagation in vibration and buckling problems of composite shells is studied [38]. In addition, a novel non-probabilistic quantification approach based on grey mathematical theory is developed in order to perform uncertainty quantification of correlated elastic mechanical properties for composite laminates by virtue of some limited experimental points [39], where the validity of experimental points is proved. However, from the point of micro-mechanical analysis, the research on predicting elastic mechanical parameters on the basis of micro-mechanical quantification models and theoretical analysis is rare. In view of this idea, the main contribution of this paper is to carry out uncertainty quantification of macro elastic mechanical parameters for fiber-reinforced composite laminates on the basis of micro- and macro-mechanical analysis. Here, by virtue of non-probabilistic thoughts, as input variables, material elastic performance parameters of constituents, model parameters and volume fractions are treated as uncertain interval variables in this paper. The remainder of this paper is organized in detail as follows. Firstly, in Section 2, several kinds of deterministic micro- and macro-mechanical analysis models are introduced, where analytical formulas of relationships can be explicitly established between uncertain input parameters at the micro scale and elastic mechanical parameters at the macro scale. In Section 3, by taking uncertain input parameters into account at the micro scale, uncertainty quantification of multi-dimensional elastic parameters of composites can be implemented, where uncertain variables are dealt with as independent interval variables based on non-probabilistic thoughts. Furthermore, considering correlations between any two elastic mechanical parameters, a closed and bounded convex polyhedral model is proposed via some simulated sample points or experimental data points in Section 4. Dependent uncertain macro parameters can be described by some linear inequalities constraints formulations and the non-probabilistic correlation coefficients can be evaluated.