hp-adaptive finite element analysis of thin-walled structures with use of the numerical tools for detection and range assessment of boundary layers

The presented paper concerns the a posteriori detection of the boundary layer effect in the adaptive finite element analysis of thin- and thick-walled structures. The detection is followed by the range assessment of the layer. This assessment lies in sequential solution of the local four-element problems. In each of such problems we apply different exponential subdivision ratio. The best solution from the local problems determines the width of the boundary layer, applied in the exponential modification of the uniform initial mesh. We start the paper with the presentation of the essence of the boundary effect. The suggestions regarding effective application of the numerical tool for the assessment are formulated next. We show how to enhance the standard three-step adaptive algorithm with the proposed tool. Finally, the numerical example illustrating the significance of the range assessment, and the effective hp-adaptation in the case of the structure with boundary layer is presented.