| Abstract: | In a numerical example of compromise optimization by computerized mathematical modeling (2000 realizations) for a known deterministic
solution, in the case of an isotropic spatially reinforced porous composite, certain scatter characteristics of the optimal
solution have been established, namely four standard deviations and six coefficients of linear correlation for four properties—density,
modulus of elasticity, thermal conductivity, and linear thermal expansion coefficient. Of the 17 input data (parameters of
the composite components), 10 are stochastic, the others deterministic. An equation is presented for the four-dimensional
hyperellipsoid of normal distribution with numerical values of the coefficients, as well as all invariants and roots of the
characteristic equation, the matrix of direction cosines of the principal axes of the hyperellipsoid, and the lengths of the
principal semiaxes, depending on the dimensionality of the scattering region and the assigned probability P. The four-dimensional
hyperellipsoid has been projected onto three-dimensional space and then onto a plane. A section of the scattering region has
been constructed.
Institute of Polymer Mechanics, Latvian Academy of Sciences, Riga LV-1006, Latvia. Translated from Mekhanika Kompozitnykh
Materialov, No. 5, pp. 625–635, September–October, 1996. |
