Structural analysis and solution of systems of algebraic design equations

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Abstract
A new method for expressing the structure of a system of equations is developed using a type of occurrence matrix entitled the functionality matrix. The functionality matrix indicates not only the occurrence of variables in equations but also the functional form in which they occur. Since the difficulty of solving an equation for a variable is related to its functional form, analysis of the functionality matrix provides explicit information on the difficulty of solution of the solution of the equation.A methodology for the solution of design problems by digital computers is described. This methodology operates on the functionality matrix which describes the set of design equations. Algorithms using this methodology interact and guide the designer in an efficient selection of design variables and redundant equations. Once design variables and redundant equations are selected, a computational method is presented for ordering and solving the equations.