Analysis of Structures by Quadratic Programming

The analysis of linear elastic structures having cable-like members, that is members which can take tension but not compression, is formulated as one in quadratic programming. The objective function is the total complementary energy function, a quadratic form in terms of the variables which are forces and force resultants, and the constraints are the equations of equilibrium of forces at the joints. A technique is indicated to reduce the size of the quadratic program obtained so that the number of variables in the reduced program is approximately the larger of the degree of indeterminacy and the number of the cable-like members. The formulation is performed entirely for a truss.