Bounds for the solution of hyperbolic problems

This article describes a newly developed and implemented method for computing guaranteed errorbounds for the solution of hyperbolic initial value problems. The basic concepts—modified fixed point theorems and approximated operators—allow an a posteriori error-estimation automatically. Therefore, no a priori knowledge of Lipschitz constants, monotonicity properties or additional error analysis is necessary.     

Biaxiale Ermüdung reibrührgeschweißter Strukturelemente

Biaxial fatigue of friction stir welded stiffened panels Within the framework of the European WelAir project, cruciform specimens made from stiffening FSW overlap joints were fatigued in the DLR biaxial test rig. To resemble the loading situation of pressurized fuselage structures, proportional loading without any phase shift, but with different load ratios λ between the loading components in both directions was applied.Natural crack initiation and subsequent crack growth were governed by the stiffness gradient caused by introducing the stringer. Cracks initiated and propagated at run‐in and run‐out locations in a direction perpendicular to the weld seam. The shortest fatigue life was observed for uniaxial loading in welding direction (λ = 0). An additional stress component perpendicular to the joint line (λ > 0) resulted in a higher number of cycles to failure. Similar to single stringer panels, increasing the load ratio also increased the number of cycles to failure for FSW clip‐stringer structural members, but additionally gives a different location of the fatal crack.