A smart displacement based (SDB) beam element with distributed plasticity

The standard displacement based inelastic beam element suffers of approximations related to the inability of the cubic polynomial interpolation functions to properly describe the displacement response of the beam when exhibiting inelastic behaviour. The increase of the number of finite elements, or the use of higher order functions with additional internal degrees of freedom, are common remedies suggested to improve the approximation leading to an unavoidable reduction of the computational efficiency. Alternatively, it has been shown that the development of force based finite elements, based on the adoption of exact force shape functions, lead to more accurate results, although requiring different and more complicated iterative solution strategies. Within this scenario, this paper proposes a new inelastic beam element, within the context of the displacement based approach, based on variable displacement shape functions, whose analytic expressions are related to the plastic deformation evolution in the beam element. The adaptive generalised displacement shape are obtained by identifying, at each step, an equivalent tangent beam, characterised by abrupt variations of flexural stiffness, as a suitable representation of the current inelastic state of the beam. The presented approach leads to the formulation of a Smart Displacement Based (SDB) beam element whose accuracy appears to be comparable to those obtained through a force based approach but requiring a reduced implementation effort and a more straightforward approach. The term 'smart' aims at emphasizing the ability of the element to upgrade the displacement field according to the current inelastic state.