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This paper aims to present an algorithm for local mesh refinement of finite elements in a two‐dimensional compressible fluid flow.

The algorithm works on a principle of maximum gradient of fluid variables, e.g. pressure, velocity and density. The simulation of two‐dimensional, transient, viscous, compressible, adiabatic flow of turbulent fluid through a De Laval nozzle was performed by the finite element method. The pressure gradient was used as a condition for mesh refinement.

With the gradient method faster numerical calculations can be obtained. Boundary layer separation and locations of normal shock waves can be described on locally refined mesh.

Further development of the algorithm is required, especially the determination of the gradient criterion.

The paper provides a new approach to mesh refinement. The mesh is refined automatically. Calculation time and required computer memory are decreased.

The purpose of this paper was to investigate and evaluate the influence of geometrical and structural design changes in order to reduce shear-lag and increase specific strength and stiffness of thin-walled composite I-beam wing spars.

A detailed FEM model of a cantilevered I-beam spar was used to investigate the influence of increased transition fillet radius and increased web sandwich core thickness on the shear-lag effect at different width to thickness ratios of flanges. Evaluation functions were used to assess specific strength and stiffness of different spar configurations.

Increased web core thickness has greater influence on normal stress distribution and the reduction of the shear-lag than fillet size. Additional weight of thicker core is not compensated enough through reduction of stress concentration. Increased transition fillet and web core thickness increase optimum flanges width to thickness ratio. Shear-lag reduces the strength of the spar more than the stiffness of the spar.

Findings in this study and detailed insight in the shear-lag effect are important for aircraft design when minimum weight of the airframe is of supreme importance.

This combined shear-lag and weight optimization study deals with composite I-beams and loads that are specific for aerospace engineering. This study does not only evaluate the shear-lag phenomena, but primarily analyses fine structural details in order to reduce it, and increases specific strength and stiffness of I-beam spars.