טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentOzer Rami
SubjectGeometrical optimization of a Beam by the Fully
Stress Design Approach
DepartmentDepartment of Mechanical Engineering
Supervisors Professor Emeritus Eli Altus
Dr. Amnon Shirizly
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


Abstract

Additive Manufacturing (AM) is a breakthrough form of technology for manufacturing and metals processing, which expands the manufacturer’s abilities, allowing new possibilities to design complicated structures, process that often difficult or impossible for those utilizing conventional methods. There has been a strong need to design a more optimal part, maximal strength and minimal weight, which practicable to manufacture due to technological proficiencies of AM technology.

In this work we emphasis on analytical solution for optimal geometry for cantilever beam and following and compare it with experimental work. The production of optimal geometry is simplified by AM technology.

Tensile round specimens produced and tested according to ASTM E8 standards examine the mechanical properties of the printed Ti6Al4V. The specimens were fabricated using the AM technology via DMLS methods, the experimental results were compared to similar conventional specimens. Comparison was performed according to AMS 4911 standard. The mechanical properties of the AM specimens match the requirement defined by the standard. The strength and yield stress of the printed Ti6Al4V were found to be higher than the forging Ti6Al4V by 20%.

Within the analytical part of this research, cantilever beam optimization was developed for uniform Von Mises stress distribution i.e., Fully Stress Design (FSD) approach under geometrical constraints.

The innovation of this work was to find analytically an optimal beam-based geometry. Specifically, under the Bernoulli assumptions the beam cross section is described by two functions: cross-section shape and width. Accordingly, the main problem was divided into three sub-problems:

1.      The cross-section thickness was found for a given shape

2.      The cross section shape was found for constant thickness

  1. Both cross-section profile and thickness were found for a given relation between them.

Beam specimens having optimal and standard (ASTM A6) geometries were tested. External load for initial yield were received and the mass of the optimal beam was found to be 25% lower than the standard beam. The experimental results were validated by numerical analysis using finite element method.

Although the analytical solutions were composed of simple forms, they represent families of alternative shapes; some of them may be very complex. This result may explain the very complicated shapes obtained by commercial packages, based on Finite Element solutions.

Based on the experimental results, we found it feasible to design and achieve optimum complicated structures in terms of maximum strength and minimum weight, while still complying with the analytical model.