Euler–Bernoulli interval finite element with spatially varying uncertain properties

The formulation of an Euler-Bernoulli beam finite element with spatially varying uncertain properties is presented. Uncertainty is handled within a non-probabilistic framework resorting to a recently proposed interval field model able to quantify the dependency between adjacent values of an interval quantity that cannot differ as much as values that are further apart. Once the interval element stiffness matrix is defined, the set of linear interval equations governing the interval global displacements of the finite element model is derived by performing standard assembly procedure. Then, the bounds of the interval displacements and bending moments are determined in approximate explicit form by applying a response surface approach in conjunction with the so-called improved interval analysis via extra unitary interval. For validation purposes, numerical results concerning both statically determinate and indeterminate beams with interval Young’s modulus are presented.