M.Sc Thesis

M.Sc StudentReuveny Liron
SubjectDesign of 2D Porous Micro Structures by Using
Geometric Meshing, Finite Element Analysis (FEA)
and Topology Optimization
DepartmentDepartment of Mechanical Engineering
Supervisors PROF. Anath Fischer
Full Thesis textFull thesis text - English Version


Topology optimization is a field that is gaining momentum rapidly. Over the years it has spread from the field of engineering design to the field of bio-medical design. Basically, topology optimization answers the engineer's main question: how and where to locate minimal amounts of material along the domain so that the structure upholds the applied constraints.

An essential issue in the bio-medical field relates to design of bone implants. From the literature one can see that topology optimization can mimic natural bone structure. This knowledge can be used for designing bone implants and scaffolds that resemble the original bone.  When referring to topology optimization of bone structure, the design goal will relate to minimum weight for a given applied load and support. The decision where to locate the material is based on minimizing the domain strain energy.

The current research deals with 2D porous structures problem with bone oriented. The goal is to examine the behavior of those materials under the influence of topology optimization. The input data is micro-CT images or 2D mesh models. The image is initially geometrically represented and then meshed. In the case of micro-CT, the mesh consists of constant size square bilinear elements. In the case of 2D mesh models the representation is of quadrilateral bilinear elements and can be refined according to requirements. This research focuses on porous structure and specifically on porous structure from bones micro-CT scans. The porous structure holes can be defined by parameters of shape, size and density. During the iterations, FE analysis is performed as the basic step for the topology optimization calculation. In the FE mechanical analysis, different types of loads can be applied: uneven/even and distributed/concentrated. During the topological optimization, material might be removed or added. The structure is deformed according to weight and strength criteria. As a result, an optimized design is verified and compared to a basic topology optimization program that can be analyzed using bilinear square elements only.

In this research a method was developed for designing freeform porous structures that have similarities to bone structures. There are several advantages to this method. First, by using quadrilateral bilinear elements, the number of elements required to solve the problem was reduced. Second, an improvement was achieved by removing pre-known void areas from the mesh. Third, with the proposed approach, cracks in the structure were patched up while keeping the crack surrounding unchanged. Fourth, the program developed based on this method is not a stand-alone program, the initial structure image can be uploaded form a finite elements program or from micro-CT images giving a full coverage for the available input data.

This research can be seen as a first step for developing a design method for 3D implants that have bone micro-structures. The method can be extended for other engineering and bio-medical applications that use porous structures.