Multivariate Rational Response Surface Approximation of Nodal Displacements of Truss Structures

Abstract

Polynomial-basis response surface method has some shortcomings for truss structures in structural optimization, concluding the low fitting accuracy and the great computational effort. Based on the theory of approximation, a response surface method based on Multivariate Rational Function basis (MRRSM) is proposed. In order to further reduce the computational workload of MRRSM, focusing on the law between the cross-sectional area and the nodal displacements of truss structure, a conjecture that the determinant of the stiffness matrix and the corresponding elements of adjoint matrix involved in displacement determination are polynomials with the same order as their respective matrices, each term of which is the product of cross-sectional areas, is proposed. The conjecture is proved theoretically for statically determinate truss structure, and is shown corrected by a large number of statically indeterminate truss structures. The theoretical analysis and a large number of numerical examples show that MRRSM has a high fitting accuracy and less computational effort. Efficiency of the structural optimization of truss structures would be enhanced.