How to know the value at the center of trilinear hexahedral element

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SUMMARY

The value at the center of a trilinear hexahedral element can be determined by averaging the field variable values at its eight nodes. This method utilizes the element shape functions and is applicable when employing a 2x2x2 Gauss quadrature rule for numerical integration. The averaging process provides a straightforward approach to finding the central value within the hexahedral element.

PREREQUISITES
  • Understanding of trilinear hexahedral elements
  • Familiarity with Gauss quadrature methods
  • Knowledge of finite element analysis (FEA)
  • Basic concepts of shape functions in numerical methods
NEXT STEPS
  • Study the implementation of Gauss quadrature in finite element analysis
  • Explore the derivation and application of shape functions for hexahedral elements
  • Learn about numerical integration techniques in FEA
  • Investigate advanced methods for interpolating values within finite elements
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Finite element analysts, mechanical engineers, and computational scientists involved in simulations using hexahedral elements.

Stacky
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Hello,
If we know the value of the field variables at the nodes of hexahedral element. How one finds the value at the center of the element. The hexahedral element is trilinear and solved using 2x2x2 gauss quadrature rule.
 
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Use the element shape functions.

The answer should be the average of the 8 nodal values.
 

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