Structural Engineering and Mechanics

  • 제10권2호
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  • Pages.93-110
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  • 2000
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Completeness requirements of shape functions for higher order finite elements

  • Rajendran, S. (Centre for Advanced Numerical Engineering Simulations, School of Mechanical and Production Engineering, Nanyang Technological University) ;
  • Liew, K.M. (Centre for Advanced Numerical Engineering Simulations, School of Mechanical and Production Engineering, Nanyang Technological University)
  • 발행 : 2000.08.25
⟨ 이전 논문 다음 논문 ⟩

초록

An alternative interpretation of the completeness requirements for the higher order elements is presented. Apart from the familiar condition, $\sum_iN_i=1$, 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.

키워드

참고문헌

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피인용 문헌

  1. Remedies to rotational frame dependence and interpolation failure of US-QUAD8 element vol.24, pp.11, 2008, https://doi.org/10.1002/cnm.1026
  2. Mesh-distortion immunity assessment of QUAD8 elements by strong-form patch tests vol.23, pp.2, 2007, https://doi.org/10.1002/cnm.893
  3. A quadratic plane triangular element immune to quadratic mesh distortions under quadratic displacement fields vol.195, pp.9-12, 2006, https://doi.org/10.1016/j.cma.2005.04.012
  4. A novel unsymmetric 8-node plane element immune to mesh distortion under a quadratic displacement field vol.58, pp.11, 2003, https://doi.org/10.1002/nme.836
  5. A mesh distortion tolerant 8-node solid element based on the partition of unity method with inter-element compatibility and completeness properties vol.43, pp.10, 2007, https://doi.org/10.1016/j.finel.2007.05.008
  6. Mesh distortion sensitivity of 8-node plane elasticity elements based on parametric, metric, parametric-metric, and metric-parametric formulations vol.17, pp.6, 2004, https://doi.org/10.12989/sem.2004.17.6.767
  7. A technique to develop mesh-distortion immune finite elements vol.199, pp.17-20, 2010, https://doi.org/10.1016/j.cma.2009.11.017
  8. New superconvergent points of the 8-node serendipity plane element for patch recovery vol.54, pp.8, 2002, https://doi.org/10.1002/nme.460
  9. Extension of unsymmetric finite elements US‐QUAD8 and US‐HEXA20 for geometric nonlinear analyses vol.24, pp.4, 2007, https://doi.org/10.1108/02644400710748715
  10. Development of Eight-Node Curved-Side Quadrilateral Membrane Element Using Chain Direct Integration Scheme (SCDI) in Area Coordinates (MHCQ8-DI) pp.2191-4281, 2018, https://doi.org/10.1007/s13369-018-3521-7
  11. Mesh distortion insensitive and locking‐free Petrov–Galerkin low‐order EAS elements for linear elasticity vol.122, pp.23, 2000, https://doi.org/10.1002/nme.6817