Lesson 5

Strain Gradient Notation

Purpose of Lesson To derive the displacement interpolation polynomials that serve as the basis for the development of finite elements and finite difference operators in terms of a physically interpretable notation.

The displacements in the continuum are due to rigid body motions and deformations. The deformations can be expressed in terms of strain quantities, i.e., the strains and derivatives of the strains. In two dimensions, the strain gradient coefficients are the following: the two rigid body displacements, (Urb)0 and (Vrb)0; the rigid body rotation, (rrb)0; the three constant strain components, (εx)0, (εy)0, and (γxy)0; and derivatives of the strains, such as (εx,x)0.

The direct connection between this ...

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