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Analytical Trial Function Method I — Membrane and Plate Bending Elements

  • Song Cen
  • Zhi-Fei Long

Abstract

This chapter introduces a novel finite element method, namely, the analytical trial function method. A detailed discussion on the features of the analytical trial function method is firstly given in Sect. 14.1. Then, in the next five sections, the basic analytical solutions of plane problem, thick plate problem and thin plate problem are derived and taken as the trial functions for the corresponding finite element models. It can be seen that those resulting models exhibit excellent performance. Some challenging problems, such as the trapezoidal locking and shear locking, can be avoided naturally.

Keywords

finite element analytical trial function method membrane element plate bending element 

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Copyright information

© Tsinghua University Press, Beijing and Springer-Verlag GmbH Berlin Heidelberg 2009

Authors and Affiliations

  • Song Cen
    • 1
  • Zhi-Fei Long
    • 2
  1. 1.Department of Engineering Mechanics, School of AerospaceTsinghua UniversityBeijingChina
  2. 2.School of Mechanics & Civil EngineeringChina University of Mining & TechnologyBeijingChina

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