2D non-prismatic beam model for stiffness matrix evaluation

Variable coefficients and complex relations generally characterize the differential equations governing non-prismatic beam behaviour. This leads to employ either complex and expensive analysis or simplified (and often inaccurate) approaches. This work aims at illustrating a 2D model for the study of beams with variable cross-section, model which is accurate but, at the same time, practical enough to be used in engineering applications. Based on the Hellinger-Reissner functional and a dimensional reduction approach, the developed theory exploits the familiar Timoshenko-kinematic, while the variables assumed for the stress definition are directly correlated to the general forces. Thus, once the stresses are calculated, the Finite Element (FE) stiffness matrix is easily recovered. The efficiency of the model is tested through some examples and resulting stiffness coefficients are compared to those obtained with an accurate 2D analysis. Final considerations and results confirm the efficiency of the method