This article develops a methodology to predict the elastic properties of long-fiber injection-molded thermoplastics (LFTs). The corrected experimental fiber length distribution and the predicted and experimental orientation distributions were used in modeling to compute the elastic properties of the composite. First, from the fiber length distribution (FLD) data in terms of number of fibers versus fiber length, the probability density functions were built and used in the computation. The two-parameter Weibull's distribution was also used to represent the actual FLD. Next, the Mori-Tanaka model that employs the Eshelby's equivalent inclusion method was applied to calculate the stiffness matrix of the aligned fiber composite containing the established FLD. The stiffness of the actual as-formed composite was then determined from the stiffness of the computed aligned fiber composite that was averaged over all possible orientations using the orientation averaging method. The methodology to predict the elastic properties of LFTs was validated via experimental verification of the longitudinal and transverse moduli determined for long glass fiber injection-molded polypropylene specimens. Finally, a sensitivity analysis was conducted to determine the effect of a variation of FLD on the composite elastic properties. Our analysis shows that it is essential to obtain an accurate fiber

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Response surface approximations are a common engineering tool, often constructed based on finite element simulations. For some design problems, the finite element models can involve a large number of parameters. However, it is advantageous to construct the response surface approximations as a function of the smallest possible number of variables. The purpose of this paper is to demonstrate that a significant reduction in the number of variables needed for a response surface approximation is possible through physical reasoning, dimensional analysis, and global sensitivity analysis. This approach is demonstrated for a transient thermal problem, but we also show how it can be applied to any finite-element-based surrogate model construction. The thermal problem considered is the design of an integrated thermal protection system for spacecraft reentry for which a response surface approximation of the maximum bottom face temperature is needed. The finite element model used to evaluate the maximum temperature depended on 15 parameters of interest for the design. A small number of assumptions simplified the thermal equations, allowing easy nondimensionalization, which together with a global sensitivity analysis showed that the maximum temperature mainly depends on only two nondimensional parameters. These were selected to be the variables of the response surface approximation for maximum temperature, which was constructed using simulations from the original nonsimplified finite element model. The major error in the two-dimensional response surface approximation was found to be due to the fact that the two nondimensional variables account for only part (albeit the major part) of the dependence on the original 15 variables. This error was checked and reasonable agreement was found. The two-dimensional nature of the response surface approximations allowed graphical representation, which we used for material selection from among hundreds of possible materials for the design optimization of an integrated thermal protection system panel.

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