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Engineering | Finite Element Analysis | Stress

Value Design

Consulting

Stress can be described as a measurement of intensity of force. As all engineers know, if this intensity increases beyond a limit known as yield, the component's material will undergo a permanent change in shape or may even be subjected a to dramatic failure. Three conditions have to be met in any stress analysis, equilibrium of forces (or stresses), compatibility of displacements and satisfaction of the state of stress at continuum boundaries. These conditions, which are usually described mathematically in good undergraduate strength of material texts, are also applicable to non-linear analyses.

Linear Analysis :

1) It all starts off with the formulation of the components stiffness' matrix. This square matrix is formed from details of the material properties, the model geometry & any assumptions of the stress-strain field (plane stress or strain).

2) Once the stiffness matrix is created, it may be used with the knowledge of the forces to evaluate the displacements of the structure (hence the term displacement analysis).

3) On evaluation of the displacements, they are differentiated to give six strain distributions, 3 mutually perpendicular direct strains & 3 corresponding shear strains.

4) Finally six stress distributions are determined via the stress/strain relationships of the material.

5) Commercial packages calculate a range of more usable stress fields from the six stress components such as the principal stresses & a host of failure prediction stresses as described by the most common yield criteria (Von Mises/Maxwell/Heckney, Guest/Tresca, Heubner/Thornton, etc.). The displacements can be used in conjunction with the element stiffnesses to determine the reaction forces & the forces internal to each element .

6) A point to note is that at least one of the displacements must be known before the rest can be determined. These known displacements are referred to as boundary conditions.