Extending PNQ6X1 to quadrilaterals with curved edges

Abstract

Extension of Quadrilateral Finite Elements for Arbitrarily Curved Edges

Abstract Introduction Two-dimensional finite elements have been in existence for almost half a century. Despite their drawbacks, they have served the engineering community well in analyzing a wide range of practical problems. Recent developments have helped overcome several shortcomings. However, curve fitting-matching object geometries with available element geometries-remains difficult.

Traditionally, one must either use a large number of small elements (leading to computational difficulties) or employ isoparametric elements, which suffer from nonlinear mapping limitations.

Proposed Technique We present a convenient method to extend quadrilateral elements to accommodate arbitrarily curved edges. The approach is based on the realization that interpolating functions can also be used to extrapolate in the neighborhood of the quadrilateral.

Case Studies The technique is demonstrated through several pathological case studies using the 8-noded quadrilateral PNQ6X1 element. Results show that the proposed method effectively handles complex geometries while reducing computational overhead.

Conclusions Introduced a novel extrapolation-based technique for extending quadrilateral finite elements.

Demonstrated applicability to curved-edge geometries.

Validated the approach using PNQ6X1 element case studies.