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Structural Engineering and Mechanics
  Volume 10, Number 2, August 2000, pages 93-110

Completeness requirements of shape functions for higher order finite elements
Rajendran S, Liew KM

    An alternative interpretation of the completeness requirements for the higher order elements is presented. Apart from the familiar condition, Sigma(i)N(i)=1, some additional conditions to be satisfied by the shape functions of higher order elements are identified. Elements with their geometry in the natural form, i.e., without any geometrical distortion, satisfy most of these additional conditions inherently. However, the geometrically distorted elements satisfy only fewer conditions. The practical implications of the satisfaction or non-satisfaction of these additional conditions are investigated with respect to a 3-node bar element, and 8- and 9-node quadrilateral elements. The results suggest that non-satisfaction of these additional conditions results in poorer performance of the element when the element is geometrically distorted. Based on the new interpretation of completeness requirements, a 3-node element and an 8-node rectangular element that are insensitive to mid-node distortion under a quadratic displacement field have been developed.

Key Words
    finite element, completeness requirements, distortion sensitivity, shape functions, geometric distortion, higher order elements
Rajendran S, Nanyang Technol Univ, Sch Mech & Prod Engn, Ctr Adv Numer Engn Simulat, N3-B3C-10, Singapore 639798, Singapore
Nanyang Technol Univ, Sch Mech & Prod Engn, Ctr Adv Numer Engn Simulat, Singapore 639798, Singapore

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