Element Lagrange Multipliers

Consider wanting to move a node radially in the $x$-$y$ plane by an amount given by a proportional load value. This can be accomplished by enforcing the constraint $(X+u_{x})^{2}+(Y+u_{y})^{2}-\mathrm {prop_{value}} ^{2}=0$. To accomplish this we can create an element with one node and implement the constraint in the element.

Note that when using a mesh with this type of element in it, one needs to let FEAP know in the input file that there will be element Lagrange multipliers in the problem by setting the value of nad on the control record. Since we only have one constraint, there will be only one Lagrange multiplier per point element. Supposing we apply the point constraint element in a 3D mesh with 8-node bricks, then the control record will look like:

feap ** Point constraint example **
0 0 0 3 3 8 1

Or perhaps more clearly as

feap ** Point constraint example **
ndm = 3
ndf = 3
nen = 8
nad = 1