Finite Elements and Continuum Elements

  • Andrew Y. T. Leung


Since our method is very similar to the finite element method, it is worth giving a brief introduction to these methods as applied to elastic systems. If one takes the exact solution of the governing equations for the vibrating member as shape functions, a continuum element results. After deriving the element matrices for straight beams and plates, we prove that the mass matrix for a continuum element can be obtained simply by differentiating the dynamic stiffness matrix with respect to the frequency. We then relate finite elements and continuum elements by means of Simpson’s hypothesis. Therefore, many useful frequency algorithms for the finite element method are made available to the continuum element model.


Shape Function Mass Matrix Beam Element Mass Model Dynamic Stiffness 
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Copyright information

© Springer-Verlag London Limited 1993

Authors and Affiliations

  • Andrew Y. T. Leung
    • 1
  1. 1.Department of Civil and Structural EngineeringUniversity of Hong KongHong KongChina

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