In this paper two different finite element formulations for frictionless large deformation contact problems with non-matching meshes are presented. Both are based on the mortar method. The first formulation introduces the contact constraints via Lagrange multipliers, the other employs the penalty method. Both formulations differ in size and the way of fulfilling the contact constraints, thus different strategies to determine the permanently changing contact area are required. Starting from the contact potential energy, the variational formulation, the linearization and finally the matrix formulation of both methods are derived. In combination with different contact detection methods the global solution algorithm is applied to different twodimensional examples.
The first stage ring segment (RS) of a Siemens large gas turbine has been redesigned for Selective Laser Melting (SLM) in order to reduce the cooling air consumption and to increase the gas turbine efficiency. The material is IN939. Cylindrical specimen for uniaxial tensile, cyclic tests and creep rupture tests have been manufactured by SLM to characterize the material by derivation of stress strain and creep rupture curves. The ring segment has been tested in a real gas turbine. The loading conditions as well as measurement data from thermocouples and dynamic strain gages have been taken as input for numerical structural integrity assessment. Permissible service life of the ring segment was evaluated in respect of low cycle fatigue (LCF), high cycle fatigue (HCF) and creep. Results have been compared with the conventional design. Furthermore the hook lock up in the engine was evaluated. The manufacturing quality was ensured through several methods including an optical 3D measuring system and computer tomography, process specimen and flow tests. Post investigations such as cut ups and metallography have also been conducted. The results show that the additive manufactured RS meets the required service lifetime.
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