Response Surface Methodology Study Of Structural Optimization

For the mathematical model of structure optimization designation, the objectivefunction is represented by a function of a series of design variable, the constraint is built onthe implicit function of design variable. To solve the problem that the constraint is theimplicit function of design variable existing in the mathematical model of structureoptimization designation, we need to make the constraint explicit through converting theconstrain to be the explicit function. The most commonly used explicit method for theresponse surface method, but there are some shortcomings for the widely used responsesurface methods, such as low fitting precision, hard work load.For the purpose of improving the solving accuracy and reducing the computationalworkload of the response surface method, what the paper described is as follows:1. The shortcomings existing in the traditional polynomial-based response surfacewere discussed and analyzed. First the basic ideas and the evaluation criteria of theresponse surface methods were briefly introduced, then we introduced a new evaluationcriterion to make up for the inadequacy of the multiple fitting coefficient evaluation, nextwe got the problems that fitting precision and computing workloads existing in solving thetruss structure explicitly equations by using the traditional polynomial-based responsesurface, finally the causes of these problems were simply analyzed.2. The response surface method based on the Taylor expansion was studied. Owingto the approximate calculation of the function value near the expand point based on theTaylor expansion, we put forward the response surface method based on the Taylorexpansion. The particular form of the response surface method based on the Taylorexpansion was given by meshing the solving area and the derivation of the differentialpartial derivative, the improvement of solution accuracy in the explicitly of implicitfunction based on the improved response surface method was verified by example.3. The response surface method based on reciprocal variable was studied. Through theliterature query and the analysis of the difference between design variables form of thepolynomial response surface and the analytical solution of structure displacement, weproposed the response surface method based on reciprocal variable, the high precision ofstatic structure displacement expression was verified by example.4. The determinant equation of structure stiffness matrix and adjoint matrix elementswas assumed. Through the analysis of the form difference between truss structure displacement and the previous various arithmetic, we assumed the determinant equation ofstructure stiffness matrix and adjoint matrix, the corresponding determinant of structurestiffness matrix and adjoint matrix elements is the same order polynomial matrix ofdesign variablesAi, each item is the product ofAi first degree, the rationality ofassumption were discussed;5. The response surface method based on multivariate rational function was putforward. We presented the response surface method based on multivariate rational functionthe based on the assumption rationality of determinant equation of structure stiffnessmatrix and adjoint matrix, and gave the concrete expression form. We proved by examplesthat this algorithm can get very high approximation accuracy and showed the applicabilityof implicit function.