KSCE Journal of Civil Engineering

, Volume 23, Issue 4, pp 1756–1765 | Cite as

Geometrically Non-linear Analysis of Elastic Structures by Petrov-Galerkin Natural Element Method

  • Hong-Woo Lee
  • Jin-Rae ChoEmail author
Structural Engineering


This paper is concerned with the geometrically non-linear analysis of elastic structures using the natural element method, particularly a Petrov-Galerkin Natural Element Method (PG-NEM). The geometrically non-linear problem is linearized and formulated by the Taylor series expansion and the Total Lagrangian (TL) method. The Voronoi polygon-based Laplace Interpolation (LI) functions are used to approximate the displacement increments, while the Delaunay triangle-supported Constant-Strain (CS) basis functions are adopted for the expansion of the virtual displacement. The iterative computation is performed by the Newton-Raphson method, and a set of Delaunay triangles serves as a background cell for the traditional Gauss integration rule-based numerical integration. The proposed PG-NEM is illustrated through the numerical experiments, and its numerical accuracy is compared with MSC/Marc, CS-FEM and BG-NEM.


geometrically non-linear problem PG-NEM LI function constant-strain basis function linearized total Lagrangian formulation 


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Copyright information

© Korean Society of Civil Engineers 2019

Authors and Affiliations

  1. 1.Technical Research LaboratoriesPOSCOGwangyangKorea
  2. 2.Dept. of Naval Architecture and Ocean EngineeringHongik UniversitySejongKorea

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