Rado Flajs and Miran Saje
On Convergence of Affine Thin Plate Bending Element
1705 - 1713
2012
6
8
International Journal of Mechanical and Mechatronics Engineering
https://publications.waset.org/pdf/13804
https://publications.waset.org/vol/68
World Academy of Science, Engineering and Technology
In the present paper the displacementbased nonconforming quadrilateral affine thin plate bending finite element ARPQ4 is presented, derived directly from nonconforming quadrilateral thin plate bending finite element RPQ4 proposed by Wanji and Cheung 19. It is found, however, that element RPQ4 is only conditionally unisolvent. The new element is shown to be inherently unisolvent. This convenient property results in the element ARPQ4 being more robust and thus better suited for computations than its predecessor. The convergence is proved and the rate of convergence estimated. The mathematically rigorous proof of convergence presented in the paper is based on Stummels generalized patch test and the consideration of the element approximability condition, which are both necessary and sufficient for convergence.
Open Science Index 68, 2012