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
Famous quotes containing the words shape and/or functions:
“How shall my animal
Whose wizard shape I trace in the cavernous skull,
Vessel of abscesses and exultation’s shell,
Endure burial under the spelling wall....”
—Dylan Thomas (1914–1953)
“In today’s world parents find themselves at the mercy of a society which imposes pressures and priorities that allow neither time nor place for meaningful activities and relations between children and adults, which downgrade the role of parents and the functions of parenthood, and which prevent the parent from doing things he wants to do as a guide, friend, and companion to his children.”
—Urie Bronfenbrenner (b. 1917)