Response sensitivity of material and geometric nonlinear force‐based Timoshenko frame elements

Response sensitivity is an essential component to understanding the complexity of material and geometric nonlinear finite element formulations of structural response. The direct differentiation method (DDM), a versatile approach to computing response sensitivity, requires differentiation of the equations that govern the state determination of an element and it produces accurate and efficient results. The DDM is applied to a force‐based element formulation that utilizes curvature‐shear‐based displacement interpolation (CSBDI) in its state determination for material and geometric nonlinearity in the basic system of the element. The response sensitivity equations are verified against finite difference computations, and a detailed example shows the effect of parameters that control flexure–shear interaction for a stress resultant plasticity model. The developed equations make the CSBDI force‐based element available for gradient‐based applications such as reliability and optimization where efficient computation of response sensitivities is necessary for convergence of gradient‐based search algorithms. Copyright © 2016 John Wiley & Sons, Ltd.