Numerically generated tangent stiffness matrices using the complex variable derivative method for nonlinear structural analysis

Accurate tangent stiffness matrices are essential for solving nonlinear structural problems using Newton-like methods. This paper presents a numerical procedure for generating accurate tangent stiffness matrices from the derivative approximation of internal force using the complex variable derivative method (CVDM). The present procedure is suitable for problems that require complex constitutive relations and/or kinematic nonlinearities whose models are difficult to linearize, as well as for the incorporation of Newton-like solution strategies with nonlinear structural analyses.