Structural Computation of an Assembly of Rigid Links, Frictionless Joints, and Elastic Springs

The aim of the paper is to set up a scheme for efficient computation of the small-displacement response of a plane assembly of rigid links, frictionless joints, and elastic springs to static external forces applied at the joints. The particular assembly of Fig. 1 is used as an example. The conventional “stiffness method”-which becomes singular when, as here, the links are rigid-is abandoned in favor of a method which describes the current state of the assembly in terms of the amplitudes of m (here = 3) independent infinitesimal modes of inextensional deformation of the assembly; and the calculation boils down to the solving of an m x m (here 3 x 3) set of algebraic equations. The method is particularly straightforward if the inextensional modes (as here) may be obtained by inspection; but a general algorithm is presented for obtaining the inextensional modes of an arbitrary assembly of the same general kind. A major advantage over the conventional stiffness method-which requires, of course, the replacement of rigid links by (stiff) elastic members is that the number of variables may be reduced substantially. This can be very important for large assemblies.