Development and testing of a 9-node mesh-distortion tolerant finite element

• Main Author: R, Jerin Wesley
• Other Authors: Sellakkutti Rajendran
• Format: Final Year Project
• Language: English
• Published: 2019
• Subjects: DRNTU::Engineering::Aeronautical engineering
• Online Access: http://hdl.handle.net/10356/77496
• Institution: Nanyang Technological University

The performance of the classical isoparametric finite elements generally deteriorates when the finite mesh has distortions. The 9-noded quadrilateral element, also known as the QUAD9 element, uses the classical isoparametric shape functions for is stiffness matrix formulation. This will be referred to as the Parametric-Parametric (PP) element hereinafter. In the US-QUAD8 element proposed by Rajendran and co-researchers, the formulation of the element uses both the parametric and metric shape functions for deriving its stiffness matrix. This element is known to produce excellent results even with mesh distortions. This element is referred to as PM element (because it uses parametric and metric shape functions for its formulation) and its performance has already been compared with that of PP, MM and MP elements. A similar approach is used in this report with respect to the 9-noded quadrilateral element and the PM version of 9-node element is compared with other versions (PP, MM and MP). An existing MATLAB code for 8-node element is modified to implement these new versions. This code is used to compare the performance of new versions developed. Both the displacements and stresses are computed for the test problems using various types and extents of mesh distortions.