On the relationship between mesh and stress field orientations in linear stability analyses of thin plates and shells

Many problems in structural mechanics involve complex principal stress fields that are not orthogonal to the geometric axis of the structure. Such problems are often analysed with finite elements, but the quality of a finite element solution may be sensitive to the orientation of the mesh with respect to the principal axes of stress. This paper presents the outline of a procedure to generate well-structured inclined quadrilateral finite element meshes for the analysis of thin plate and shell structures. The procedure was developed using the commercial FE pre-processor ABAQUS CAE and the Python script language, though it may readily be applied in any pre-processor which supports an external scripting functionality. A set of mesh convergence studies using linear buckling analyses are presented on four benchmark problems with known analytical solutions to illustrate the effect of inclined meshes on the accuracy of the computed solution. These illustrations are intended to raise an awareness of the subtle but important relationship between mesh and stress field orientation and are presented for the benefit of practising finite element analysts in structural engineering. •.•Analysis of plate and shell structures may involve inclined principal stress fields.•Such fields may cause buckling modes that are not orthogonal to the geometric axes.•In such cases the finite element solution is sensitive to the mesh orientation.•Studies show that rectangular elements subject to pure shear converge more slowly.•Highly relevant to shell analysts modelling structures in global shear and torsion.