Static and dynamic analysis of space frames with non‐linear flexible connections

This paper deals with the effect of non‐linearly flexible hysteritic joints on the static and dynamic response of space frames. It is shown that a complementary energy approach based on a weak form of the compatibility condition as a whole of a frame member, and of the joint equilibrium conditions for the frame, is best suited for the analysis of flexibly jointed frames. The present methodology represents an extension of the authors' earlier work¹⁴ on rigidly connected frames. In the present case also, an explicit expression for the tangent stiffness matrix is given when (i) each frame member, along with the flexible connections at its ends, is represented by a single finite element, (ii) each member can undergo arbitrarily large rigid rotations and only moderate relative rotations and (iii) the non‐linear bending–stretching coupling is accounted for in each member. Several examples, with both quasi‐static and dynamic loading, are included, to illustrate the accuracy and efficiency of the developed methodology.