Convergence Rate of N-sided Polygonal Node-based Strain Smoothed Finite Element for 2D Castellated Beam Analysis

Authors

  • Suthee Piyaphipat Department of Civil Engineering, Faculty of Engineering, Rajamangala University of Technology Thunyaburi
  • Boonchai Phungpaingam Department of Civil Engineering, Faculty of Engineering, Rajamangala University of Technology Thunyaburi
  • Khathapol Pinpatthanapong Department of Civil Engineering, Faculty of Engineering, Rajamangala University of Technology Thunyaburi
  • Kamtornkiat Musiket Department of Civil Engineering, Faculty of Engineering, Rajamangala University of Technology Thunyaburi

Keywords:

N-Sided Polygonal element, Node-based strain smoothed finite element, free and forced vibrations, castellated beam

Abstract

N-Sided polytype smoothed finite element based on polygonal-node for two-dimensional problem is presented. Polygonal elements obtained from different algorithms namely DistMesh and PolyMesher will be further divided into small quadrilateral shape, referred as smoothing cells or elements, around the corresponding polygonal nodes. Benchmark problem was a castellated beam punched with five holes along its longitudinal axis representing discontinuous problem domain. Its far free edge is subjected to vertical shear traction while the opposite ended is designed as fixed support. Three analyses were investigated including static, free vibration, and transient vibration, respectively. For sake of simplicity, a lumped mass matrix is assumed to avoid numerical integration for shape functions. Due to its versatile yet stability and powerful time integration tool, an implicit Newmark-Beta method is employed. For static analysis, PolyMesher has shown better performance significantly for both accuracy and convergence rate to close-to-exact solution than DistMesh. Contradictory, although the results from free and forced dynamic analyses have shown in good agreement with close-to-exact solutions, a slightly better performance on DistMesh can be observed for free vibration. It is worth noting that the differences of results between both polygonal element creation are very small and negligible but not applicable for static case.

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Published

2022-09-29

How to Cite

[1]
S. . Piyaphipat, B. . Phungpaingam, K. . Pinpatthanapong, and K. . Musiket, “Convergence Rate of N-sided Polygonal Node-based Strain Smoothed Finite Element for 2D Castellated Beam Analysis”, Eng. & Technol. Horiz., vol. 39, no. 3, pp. 29–40, Sep. 2022.

Issue

Vol. 39 No. 3 (2022): July-September

Section

Research Articles

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