Properties constrained cost optimization of polyester-filler systems with non-linear property-composition relationships

A general procedure for the constrained optimization of components of a polyester resin-filler composite is formulated and quantitative relationships between the mechanical properties and composition are developed.

The fillers examined were clay, marble, glass microballoons, saran microspheres, wollastonite and pecan shell flour. The effects of various ratios of flexible and rigid polyester resins and styrene monomer were also studied. The augmented, extreme vertices, simplex lattice design was employed to calculate the composition of 48 experimental points.

Samples made according to the design were tested by standard methods to obtain the density, tensile, flexural and compression strengths, secant and flexural moduli and ultimate elongation. Multiple regression analysis yielded satisfactory regression coefficients for all properties except the flexural modulus and ultimate elongation. Linear regression was adequate for density only, quadratic regression being necessary for all other properties. Qualitative conclusions about the effect of each component were drawn.

A pattern search computer program was employed to optimize the composition at the minimum total cost, while satisfying all the constraints. Examples studied included various furniture applications and polyester terrazzo-type floor tiles. The effects of different constraints were evaluated.

The final cost varied inversely with the density constraint and was highly dependent on density. Other mechanical property constraints affected final cost directly but not appreciably. Non-linear constrained optimization was shown to lead to realistic, feasible solutions and applicability of this method for similar studies of other systems was established.