h-adaptative strategy proposal for Finite Element Method applied in structures imposed to multiple load cases

Resumo

This paper proposes an h-adaptive strategy for structures subjected to multiple load cases to evaluate
and control intrinsic discretization errors of the Finite Element Method. The proposed strategy consists of an
iterative process (i) initially, for each loading case, the ideal size of each finite element is determined by an
estimation of its error; (ii) then, an intersection of the size results is conducted, and a new mesh is generated by
using the Bidimensional Anisotropic Mesh Generator. These two steps are repeated until the relative global error,
based on energy, is less than a previously arbitrated value, considering all load cases separately. The computational
routine implementation is carried out in Matlab®. A posteriori error estimator based on stress recovery,
considering superconverged points, is used for evaluating the discretization errors. Besides that, the definition of
the new finite element mesh is achieved by applying two classical h-adaptive techniques (named in this work as
ZZ and LB) whose results are compared via an evaluation of local and global quality parameters. Both techniques
are underpinned on the equidistribution criterion of the error based on energy norm and depend on a relationship
of these discretization errors comparing two subsequent meshes. A Michell’s structure is considered and the results
obtained show that the proposed h-adaptive strategy results in a mesh with a relative global error below the
allowable value for all loads. Finally, comparing both h-adaptive techniques, LB presents a smaller variation of
the number of elements between iterations, leading to a more stable process with meshes that have better local and
global quality parameters.