Generalization of FEM Using Node-Based Shape Functions

  • W. K
  • F.T. W
  • W. S
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Abstract

This paper proposes a definition of systems thinking for use in a wide variety of disciplines, with particular emphasis on the development and assessment of systems thinking educational efforts. The definition was derived from a review of the systems thinking literature combined with the application of systems thinking to itself. Many different definitions of systems thinking can be found throughout the systems community, but key components of a singular definition can be distilled from the literature. This researcher considered these components both individually and holistically, then proposed a new definition of systems thinking that integrates these components as a system. The definition was tested for fidelity against a System Test and against three widely accepted system archetypes. Systems thinking is widely believed to be critical in handling the complexity facing the world in the coming decades; however, it still resides in the educational margins. In order for this important skill to receive mainstream educational attention, a complete definition is required. Such a definition has not yet been established. This research is an attempt to rectify this deficiency by providing such a definition.

Figures

  • Figure 1. Various Layers of Elements Around Element I to Illustrate a System of Layered DOI in a Square Mesh of Triangular Elements, and the Corresponding Kriging Shape Functions using Quadratic Basis Function, Three Element-layers, and Quartic Spline Correlation Function
  • Figure 2. Stress Contours of Cantilever Plane-stress Beam by K-FEM with Cubic Basis Function and Three Element Layers of DOI.
  • Table 1. Results Obtained from K-FEM with Different Options for the Plane-stress Model of a Cantilever Beam
  • Figure 3. Matrices of Solution Accuracy and Computational Times for h-refinement and l-refinement, all using Linear Basis Function
  • Figure 4. Cantilever Beam Modeled by Tetrahedral Solid Elements: Comparison of h-refinement vs l-refinement.
  • Figure 6. Convergence of the Cantilever Cylindrical Shell: Isoparametric Triangular r K-FEM Shell Element (with shell surface generated by the same Kriging shape functions) Versus Flat Triangular K-FEM Shell Element (with shell surface interpolated exclusively from its own 3 nodes).
  • Figure 5. Matrices of Solution Accuracy and Computational Times for h-refinement and p-refinement, all using Three Element Layers DOI.
  • Figure 7. Flow Chart of a Typical FEM Code Extended to Include K-FEM

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CITATION STYLE

APA

W., K.-N., F.T., W., & W., S. (2015). Generalization of FEM Using Node-Based Shape Functions. Civil Engineering Dimension, 17(3). https://doi.org/10.9744/ced.17.3.152-157

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