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Mesh Quality Parameters in Finite Element Analysis
Why Element Quality Checks?
  • The shape of Elements in FE Analysis must be distorted from their Ideal shapes when meshing the irregular or complex geometric shapes.

  • Every element is designed to work properly within a certain range of shape distortion. Exactly how much distortion and what type of distortion is allowed before an element degenerates depends on factors such as element type, numerical procedures used in the element design, and so forth.

  • The Ideal shape of [2D Elements] a triangular element is an equilateral triangle and a quadrilateral, it is a square.

  • The Ideal shape of [3D Elements] a Tetrahedron element is a Regular or Isosceles Tetrahedron and a Hexahedron, it is a Cube etc.,.

  • If the actual shape that the element assumes after mapping onto model geometry differs too much from the natural shape, the element becomes degenerated and produces erroneous results.

"Result Quality α Element Quality"

  • The major types of degeneration are Aspect Ratio, Skewness, Jacobian Ratio, Warping Factor, Maximum Corner Angle, Orthogonal Quality, Parallel Deviation, Taper, Curvature distortion and mid-size node position.

  • Generally, large angles between edges (close to 180 degree) are more degenerating than small angles (close to 0 degree).

  • Each FE mesh should be run through an element quality check, and degenerated elements should be eliminated.

  • In order to get reasonably accurate results, it is always important to generate a structured mesh with good quality parameters.

  • If Elements are Degenerated  they will become too stiff and underestimate the deformations (Field Variables) and its derivatives like strain & stress values become erroneous.

2D Finite Elements
Triangular Element
Quadrilateral Element
3D Finite Elements
  • Degenerated Elements increase the inaccuracy of the finite element representation and have a detrimental effect on convergence of Finite Element Solutions.

  • Now a days most of the FE Simulation softwares are equipped with In-Built Quality Check Options and Quality Based Mesh Generation Algorithms.

  • Maintaining element quality is always a challenge for analyst during mesh convergence studies. Though element size is minimized it is of no use if they are violating quality requirements.

  • So, it is important to know how to calculate these parameters for different Element Shapes. All Element distortions are measured against Ideal shapes.

  • In the subsequent articles we are going to discus about all the Quality Parameters and their Calculation. Initially Calculation of Quality Parameters for 2D elements are discussed later it will be extended to 3D elements also with the help of 2D calculations.

  • Click on the following buttons to get the detailed information of each Quality Parameter.

Orthogonal Quality
Parallel Deviation
Warping Factor/Angle
Maximum Corner Angle
Jacobian Ratio


  1. Finite Element Analysis For Design Engineers by Paul M. Kurowski (Chapter 5.3.1).

  2. Practical Finite Element Analysis by Nitin S Gokhale, Sanjay S Deshpande, Sanjeev V Bedekar and Anand N Thite (Chapter 7.9).

  3. The Finite Element Method : Practical Course by G. R. Liu , S. S. Quek (Chapter 11.4.2).

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