Finite element types

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Finite element types


Displacements (u, v) in a plane element are interpolated from nodal displacements (ui, vi) using shape functions Ni as follows:












where N is the shape function matrix, u the displacement vector and d the nodal displacement vector. Here we have assumed that u depends on the nodal values of u only, and v on nodal values of v only.


From strain-displacement relation, the strain vector is:












is the strain-displacement matrix.


Consider the strain energy stored in an element:










From this, we obtain the general formula for the element stiffness matrix:






where the constitutive matrix E is given by the stress-strain relation. The stiffness matrix k defined by the above formula is symmetric since the constitutive matrix E is symmetric.










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