טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentShakour Emad
SubjectTopology Optimization of Reinforced Concrete Elements Using
Continuum Damage Models
DepartmentDepartment of Civil and Environmental Engineering
Supervisor Professor Oded Amir
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


Abstract

The subject of topology optimization has been studied extensively recently. This discipline has proven itself as a useful tool at various engineering topics in general, and at automobile and aviation engineering in particular. However, this subject is still considered novel in the field of civil engineering. This is despite the obvious motivation of minimizing the utilized construction materials, concrete in particular, due to its severe environmental damage. The investigations presented in this thesis will develop a useful and powerful tool for the design of reinforced concrete structures based on topology optimization, by considering a more realistic model of concrete damage. In particular, this method will define the optimal design of structures classified as a ‘D - region’, such as corbels, walls or deep beams.


This research studies topology optimization for reinforced concrete elements. The focus of the investigation is integrating finite element models for constructional reinforced concrete elements with topology optimization procedures, for attaining constructional structures with effective weight-stiffness ratio and material reduction and conservation. The concrete was modelled as a continuum two dimensional structure combined with a non-linear material model taking into consideration the quasi-brittle behavior attributed to the concrete. This model is based on the non - local damage theory and takes into account the varying concrete strength during tension and compression. The steel elements were modelled as elastic linear bars embedded into the concrete, and attached to it at the finite element's mesh intersections.

Compared with the existing studies in this context, the proposed solution utilizes an advanced material model of concrete which takes into account tension and compression failure of concrete, a topic not yet to be studied in this context.

During this research study, two main structural optimization problems were addressed. The first structural optimization problem is solely for steel bars distribution. The second problem is for concrete and steel bars distribution simultaneously. In addition, special techniques were developed  for the purpose of taking into consideration industrial application aspects.

In addition, during this research investigation, an idea for prestressed concrete elements optimization was brought forward. This topic was not originally in the research goal. During the prestressed concrete elements optimization, the concrete distribution inside a constructional element is conducted simultaneously with the shape of the prestressing cable embedded into the concrete. For achieving this, topology optimization for continuous structures was combined with shape optimization for concrete distribution and prestressed cable shape, respectively. The concrete was modelled as a two dimensional continuum with linear elastic behavior, which is acceptable in prestressed elements design.

And so, for conclusion, this thesis investigation deals with combining and integrating optimization techniques for structures in two main fields in civil engineering, which are reinforced concrete structures and prestress concrete structures. Several optimization problems were tested at these two different fields with thorough investigation regarding the influence of numerous design parameters and their effect on the outcome solutions. The research conclusions indicate on the high potential embodied in the combination of topology optimization with design problems from the field of civil engineering.