Response Surface Methodology Study Based On Multivariate Rational Function

In structural optimization design model, the constraint function tend to be implicit function of design variables, and it is an important part of the structure optimization design that transforming the implicit function relationship that the constraint function for design variables into the explicit function relationship by constructing an approximate function. Now, the widely used method is response surface methodology. There is a great gap between the approximation function built by the traditional polynomial-based response surface method and the true function, and the fitting accuracy is low, and the computational work is great. So, building an approximation function which is very close to the true function is a good way to improve the fitting accuracy of response surface method. For this purpose, the response surface methodology study based on multivariate rational function is carried out, and the main research work in this paper is as follows.1. The shortcomings existing in the traditional polynomial-based response surface method for beam and plate is discussed and analyzed. For beam and plate structure, some examples are analyzed to generalize the fitting accuracy issues of traditional polynomial-based response surface method by using traditional polynomial-based response surface method.2. The conjecture about the determinant of the truss structure stiffness matrix and the expression of the adjoint matrix element is demonstrated in statically indeterminate truss structure. Using the idea of splitting the structure stiffness matrix, and following the thinking of special to general, this conjecture is demonstrated from simple statically indeterminate truss structure to general statically indeterminate truss structure.3. Response surface method based on multivariate rational function for beam structure is proposed and studied. The conjecture about the determinant of the beam structure stiffness matrix and the expression of the relevant adjoint matrix element is put forward through studying the relationship between the section properties of beam and the displacement of structure, and some examples are analyzed to indirectly verify its rationality. Then according to the given expression form by conjecture, the response surface equation based on multivariate rational function for beam structure is built, and some examples are analyzed to verify its high fitting accuracy. The relationship between the product of principal diagonal elements and multivariate rational function primitives is analyzed from the point of beam structure stiffness matrix, and according to this law, the response surface equation of taking the product of principal diagonal elements as multivariate rational function primitives is built for beam structure. Likewise, on the basis of guaranteeing high fitting accuracy, to reduce the computational work, the response surface equation based on multivariate rational function for beam structure ignoring the deformation of tension and compression is built.4. Response surface method based on multivariate rational function for plate structure is proposed and studied. Using finite element method, displacement response of plate is analyzed and the analytic solution form of node displacement is got. The conjecture about the determinant of the plate structure stiffness matrix and the expression of the relevant adjoint matrix element is put forward, and some examples are analyzed to discuss its rationality. Then, according to the law between thickness property and displacement of structure, the response surface equation based on multivariate rational function for plate structure is built, and some examples are analyzed to verify its high fitting accuracy.