A human-computer interactive design program for a multisolution nonlinear problem

Abstract

An idea of using a human-computer interactive program for an engineering design dealing with a nonlinear multisolution problem is introduced. The example shown is a program for a design of a drainage open channel. The hydraulics and geometry equations for triangular or trapezoidal ditches are to be satisfied by the ditch parameters, which are the side slopes (S_L and S_R), the depth (d) and the width of the bottom (W_b). The data are the flow rate (Q) and maximum allowable flow velocity. After W_b and one of the slopes for a nonsymmetrical ditch (S_L) are chosen by the designer, the other slope and d may be found as a solution of two nonlinear algebraic equations. Instead of trying to solve these equations, the program displays the two curves in s-d coordinate system. If the curves intersect, the designer types in the coordinates of the point of intersection. Otherwise, new curves for decreased velocity are displayed as the indicated key is pressed. The procedure may be continued until the curves intersect. The final parameters chosen by the designer are checked by the program to verify that the actual flow rate and velocity are within the required limits.