Notch Stress Convergence Studies for H and P Formulation Finite Elements

摘要

In the present investigation both 2D and 3D linear elastic analyses have been undertaken to assess the accuracy and computational resources associated with the use of h-element and p-element formulations. All analyses have been undertaken for a local stress-concentrating feature, which is typical of aircraft structures, namely a circular hole in a remotely loaded plate. Here highly accurate results are obtained for both element formulations, and it is found that the p-elements offer large savings in analysis times. Subsequently a relationship is developed and validated for both 2D and 3D meshes to determine an equivalent non-uniform h-element mesh density, which will yield the same accuracy as a fully converged p-element mesh. This provides a useful transferable tool for designing cost-effective h-element meshes, obviating the need for multiple mesh refinement iterations. Finally, it is demonstrated numerically that p-elements of order five and above, can be used to predict accurate through-thickness peak stresses, in a typical plate modelled with only one element through its full thickness.