Strategies for the development of finite elements for non-prismatic frames

Resumo

Non-prismatic structural elements, often referred to as beams with variable cross-sections, constitute a special class of slender structures. These types of structures capture the interest of engineers and architects due to their ability to optimize geometry to meet specific needs, such as weight reduction, material consumption, environmental impact, and costs. Despite the advantages that engineers can gain from using non-prismatic structural elements, modeling these structures poses non-trivial challenges, resulting in inaccuracies that may compromise the benefits offered by such structures. Taking this into consideration, this work presents an innovative approach to obtain the displacement solution for non-prismatic beams, obtaining the elastic stiffness matrix through the virtual work principle, using the kinematics of Timoshenko's theory. This proposed formulation is independent of bar discretization to achieve an analytical result. This is due to the absence of considering any additional approximations beyond those already contained in the analytical idealization of bar behavior, resulting in a nearly natural discretization of the structure.