Interpolation or Shape Functions
Let be the vector of nodal displacements of a typical element. The displacements at any point of the element may be found by interpolation functions as, symbolically:
where
- = vector of displacements at any point {x,y,z} of the element.
- = matrix of shape functions serving as interpolation functions.
Equation (6) gives rise to other quantities of great interest:
- Virtual displacements consistent with virtual nodal displacements:
- Strains in the elements:
- where = matrix of differential operators that convert displacements to strains using linear elasticity theory. Eq.(7) shows that matrix B in (4) is
- Virtual strains consistent with element's virtual nodal displacements:
Read more about this topic: Finite Element Method In Structural Mechanics
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