i have a question about a FE problem im working on. I made a finite element model of an linear elastic block of material (double striped block) attached with a rigid connection to the environment (colored block). A force is applied in the bottom right node.
The nodal displacements are calculated according to the Direct Stiffness Method. The system of equations is simply KU = F or U = CF with C=K^-1.
The displacement of the top right node needs to be constrained to a specified trajectory. By adding lagrange multipliers to the global stiffness matrix i have succesfully constrained the possible displacements of the top right node to a line. To be clear the force is the input, the displacement is the output.
The new system of equations is:
I want to extend the problem and therefore it is needed for me to specify a nonlinear trajectory. As far as i know the direct stiffness method with lagrange multipliers does not work in this case for it only allows to add constraints of the form y = a*x+b.
What is the best method to add a nonlinear displacement constraint to this system of linear equations?
I have been searching and reading papers in the subject but so far i have not found a sound answer.
I hope you guys can help me and i am lloking forward to your answer,