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Chapter 7: Mapping, Shape Functions, and Numerical Integration

Chapter 7: Mapping, Shape Functions, and Numerical Integration

pp. 184-215

Authors

, University of Maryland, College Park, , University of Maryland, College Park
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In the finite element formulation, the body is divided into elements of various types. This chapter describes mapping functions for the description of element geometry in the undeformed configuration and shape functions for the description of displacement and thus deformed geometry in the 2D and 3D domains. We introduce the "isoparametric" formulation in which mapping functions and shape functions are identical. This is followed by discussions on integration in the mapped domains and numerical integration.

Keywords

  • Quadrilateral elements
  • triangular elements
  • isoparametric formulation
  • isoparametric elements
  • shape functions
  • numerical integration
  • Gauss quadrature

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