טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentGreenberg Or
SubjectMaterial Morphology Design by Utilizing the Stress-Moduli
Monotonicity
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Emeritus Eli Altus
Full Thesis textFull thesis text - English Version


Abstract

Finding the optimal morphology of a mechanical structure is an important design problem. Optimal morphology means that the material properties are non-uniform and there is a way to choose the non-uniformity such that a parameter will be optimal.

With the increase in use of 3D printing and manufacturing of MEMS and nano structures it has become possible to create functionally graded materials (FGMs). Those materials have properties that depends continuously on space, thus for every point they have a different value. Krush (2013) showed that the reaction force is monotonic with the compliance at a specific point, thus the optimal morphology could be analyzed. It was found that the optimal morphology contains segments of Smax and segments of Smin, thus the search is simplified to the length of the segments only. In this research, the monotonicity proof will be generalized to other cases as multiple degree of indeterminacy beam, continuum elastic body. An analytic method of finding the length of each segment is presented and compared with the results of Krush (2013) and with Method of Moving Asymptotes (MMA)- a classical optimization process. It is important to note that the MMA is not related to our work and independent of our assumptions, thus it can be used as verification to our analysis and calculations. The comparison will reveal that the methods converge into the same core results even though they are not related. The problem of optimization of a certain internal force is generalized to the more complex min-max problem. Since Each morphology chosen determines all the forces in the structure, a trade off relation was discovered, thus simple minimization is not sufficient. Thus, a more thorough analysis and discussion will be presented about different ways to select a morphology that will yield the min-max force. It will be proved that such morphology is for equality between all forces if possible.