Keywords: finite element method, load case oriented adaptive analysis, error estimation, parallelization, master-slave concept.

The finite element method (FEM) is probably the most widespread analysis tool for the structural analysis. During recent decades, the FEM has matured to such a state that it can be widely used in practical engineering. However, it is often applied without a good understanding of the method's background, leading potentially to incorrect results and inadequate design, possibly causing damage or failure of the structure. A good way to prevent these undesirable effects is to check the quality of the solution obtained. If the results do not meet the prescribed level of accuracy, the discretization of the problem must be adequately adjusted and the problem recalculated. This process of solution enhancement is called the adaptive analysis. One of the advantages of the adaptive finite element analysis is that it can be reliably used by designers with only limited knowledge of finite element theory and without advanced experience.

The adaptive analysis (at least its h-version) is quite commonly used in the academic environment. In commercial civil engineering design offices, however, it is applied only rarely. This is caused by the fact that design of a structure must handle (besides others) many load cases and their combinations, adaptive solution of which is time consuming and yields generally complex data structures (that results from different adaptively refined meshes) from which data relevant for dimensioning of individual bearing members must be extracted. This makes the desirable adaptive design for practical engineering rather prohibitive. As a consequence, the vast majority of civil engineering projects are performed using the standard finite element method with more or less uniform discretization (possibly very coarse to reduce the overall number of degrees of freedom) without a judgement about the accuracy of solution obtained.

The aim of this paper is to present a simple approach how to make adaptive analysis accessible also for practical engineering offices. It is based on the assumption, that the commonly used analysis software (not the narrowly specialized software) performs the dimensioning of bearing members according to the linear elastic response. This allows adaptive analyses to be performed independently for each separate load case. Moreover, this implies that the analyses of individual load cases can be run in parallel using the sequential version of the FEM code. The values of internal forces used for the dimensioning of bearing members are then obtained as the envelope of individual load cases and their combinations. However, the construction of the envelope must take into account that the processed quantities are represented on different (adaptively refined) discretizations. The proposed approach therefore assumes the existence of a reference discretization on which the results of the individual parallelly solved load cases could be represented in sufficiently accurate manner. In the present study, the reference discretization is obtained simply by generating a new mesh according to the mesh density control data collected from the last adaptive step of the adaptive analyses of individual load cases. After the reference mesh is available, the results of adaptive analyses of individual load cases are mapped on it, possibly again in parallel. Such a computational scheme requires only minimal modification of design approaches currently used by most civil engineering design offices.

The whole parallel adaptive process is suitable for the master-slave parallelization concept, in which the slaves perform the individual adaptive analyses and mapping and the master is responsible for scheduling the system and for generating the reference mesh. The proposed strategy is demonstrated on a simple example using a pilot implementation based on academic software.

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