Regression of the response surface of laminated composite structures

Some optimization methods have recently been developed to deal with discrete variable problems such as that involving the ply angles and stacking sequence of composite laminates. However, much calculation is still required for the algorithms. A regression equation of the response surface would allow the finite element analysis to be replaced with the regression equation, saving much time in optimization design. The response surface of composite laminated structures is estimated using regression analysis in this study. The information of the surface can be obtained quickly and accurately. Usually, simple polynomials are used as base functions in regression, but the results obtained unsatisfactory in this work. Considering the periodic and directional property of the design variables (ply angles), trigonometric functions are used as base functions in regression and they fit the surface very well. According to the characteristics of ply angle and trigonometric function, the value of variable can be chosen to smoothen the response surface, greatly increasing the accuracy of the regression. This study first establishes the regression procedure, and then applies it to examples of a marine propeller and a rotor wing. The regression is used with a genetic algorithm to search for optimum ply angles in the examples, saving much time while maintaining accuracy.