Tangent Stiffness Matrix for Space Frame Members

TLDR: In this paper, the authors derived a 12 by 12 tangent stiffness matrix for a space frame member with constant cross-section, where the member end forces are expressed in the coordinate axes of the deformed geometry of the member in terms of the total end displacements.

Abstract: This presentation is concerned with the derivation of a 12 by 12 tangent stiffness matrix for a space frame member with constant cross-section. At first, the member end forces are expressed in the coordinate axes of the deformed geometry of the member in terms of the total end displacements. Then, in accordance with the Taylor expansion method, the stiffness influence coefficients are obtained as the partial derivatives of the force vector with respect to each one of the twelve member end displacements. It is believed that when this tangent stiffness matrix is used in connection with the Newton-Raphson iteration scheme in analyzing geometrically nonlinear structures, both the speed of convergence and the accuracy of the results are substantially increased. Numerical results are included to demonstrate the efficiency of the tangent stiffness matrix presented.