טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentSpicer Matthew
SubjectReducing Computational Effort in Structural Topology
Optimization using Reanalysis with a Stiff
Reference Matrix
DepartmentDepartment of Civil and Environmental Engineering
Supervisor Professor Oded Amir
Full Thesis textFull thesis text - English Version


Abstract

Topological optimization for continuum structures is a computational method that strives to obtain the optimal material distribution in a given design space, usually discretized using the finite element method. The method is based on the distribution of material so that high stress areas will receive more material, while reducing material in low stress areas, aiming eventually to obtain a final structure that will be more efficient. As a result of significantly increasing progress in computational and 3D printing capabilities that enable the construction of complex structures, the method has become a central part of the design process in the automotive and aviation industries. One of the main challenges of topology optimization is managing to provide results in a reasonable time for nonlinear cases and large-scale problems. The computational effort in structural optimization is influenced by 3 main factors: the complexity of the model, the type of analysis and the optimization formulation. In the nested formulation of topology optimization where the state variables are "nested" in the design variables, the analysis of the structure will cost the most computational effort. In complex structures where the model is discretized into a large-scale finite element model, the analysis is the most influential factor in the computational effort and can consume over 95\% of the CPU time. Reanalysis methods were developed for this exact reason. The Combined Approximation (CA) reanalysis method developed by Kirsch was found to be applicable for topology optimization methods and significant computer effort can be reduced. The research focuses mainly on the attempt of reducing the number of matrix factorizations required for the solution and the advantage of stiff preconditioning formulation. Essentially, the research refers to nonlinear cases, such as geometrical nonlinearity and buckling eigenvalue problems. This work adds more insights on the subject and brings additional tools to reduce the computational effort. The research was carried out using original MATLAB codes, including the finite element analysis, nonlinear solutions, and all reanalysis methods.