FEM Considerations to Simulate Interlocked Bladed Disks With Lagrange Multipliers

A few structural simulation issues with constrained Finite Elements using Lagrange multipliers are described. The main difficulties associated to interlocked bladed disks are: 1. Contacts. The structural state must be calculated by the FEM solver accounting the centrifugal, thermal and pressure loads. The interlock surfaces may slide, some area will be in contact and some others will be separated. This is a nonlinear condition that needs solver iterations. 2. Interference. The blade surfaces susceptible to contact are not necessarily periodic. In many cases pretwist is needed during assembly to couple the blades. The solution for surfaces in contact require a cyclic symmetry boundary condition. Different issues related to coordinates systems will be discussed. 3. Overconstraint. The model mesh nodes may accommodate more than one boundary condition. Interlock nodes are affected for both conditions, possibility of contact and cyclic symmetry. The use of Lagrange multipliers may cope with these problems. This is a well-known method although some FEM methodology peculiarities will be derived from scratch, either in the static and modal simulations. Pros and cons of this approach will be discussed related to classical solutions to the aforementioned problems. Every algorithm described has been already implemented in a FEM code than runs with successful results.