Development of a FETI solver for structural analysis

Nowadays, the size of finite element models used in industrial and research applications is rapidly increasing, making necessary the introduction of new computational techniques for the solution of static and dynamic analysis. One of the many fields where this problem is encountered is the turbomachinery word. Turbine blades are components subject to time dependent loads, which can cause failures due to the accumulation of fatigue damage. To dissipate energy, and consequently reduce the vibration amplitude, dampers are introduced, and their design requires the execution of nonlinear dynamic analysis of the system, given the non-linearities of the contact forces. The aim of this thesis work is the development of two solvers, in MATLAB® environment, for the solution of linear static and linear dynamic problems exploiting the FETI (Finite Element Tearing and Interconnecting) method, introduces by C. Farhat and F. X. Roux in 1991. This method is based on the decomposition of the system in small parts (called domains), assigning the computation of each of them to a processor. This thesis work is a multidisciplinary project, involving structural design (both static and dynamic), numerical methods and optimization, and programming. Considering that the FETI solvers are implemented on HPC (High Performance Computing) systems, this has requested to deepen the methodologies of parallel algorithms and their implementation. The development of the thesis is mainly divided into three parts: research on the state of art of domain decomposition methods providing a theoretical background, development of the solver for linear static analysis and development of the solver for dynamic linear analysis. In turn, each implemented solver has requested a validation phase (using ANSYS software), an optimization phase and a performance analysis, highlighting the limits of the adopted implementation.