Determination of optimal compliance and stiffness matrices from experimental data

Abstract

A linear structure can be characterized by its compliance matrix C, which is 6x6 symmetrical and positive definite and which relates a force 6-vector Fj. to a displacement 6-vector Dj. by the relation CFj = DJ. The inverse, S, of C, is called the stiffness matrix and satisfies SDj =Fj. This thesis deals with the problem of finding optimal values of such matrices C and S from experimental determinations of a sufficient number of vector-pairs (Fj,Dj)which are presumed to contain random errors. J. E. Brock has introduced' this problem area, suggested several different criteria of optimality, and solved some of the corresponding specific problems. This thesis completes the solution to a previously unsolved specific problem of this group and contributes computationally convenient new solutions to another. Moreover, a computer program, originally written for the CDC 1604 has been rewritten, in FORTRAN IV Language, as two programs for the IBM System 360 computer, and the capability has been significantly augmented.