M.Sc Thesis
M.Sc Student Amoyal Yohay Investigating the Potential of Reducing the Weight of Ribbed Concrete Plates Using Structural Optimization Department of Civil and Environmental Engineering Professor Oded Amir

Abstract

This study deals with the potential of reducing the weight of ribbed concrete ceilings by structural optimization tools. In the framework of the research, various procedures were used in the field of optimization of structures, and a topological optimization problem was solved using sizing optimization parameters.

The research involved an engineering problem and has been solved mathematically. The engineering problem is solved by determining different mathematical variables (design variables) that receive different values ​​and are forced to comply with different design constraints while finding a minimum / maximum of the objective function. During the use of a mathematical model, different optimal configurations were obtained for different formulations. The configurations received were based on a predefined ground structure. The ground structure is a structure that defines the totality of the possibilities of a beam in space, a beam not defined in the ground structure cannot be found in the optimal structure. Each optimal structure obtained was interpreted into a finite element software model. The research uses the STRAP finite element software commonly used in the market. During the interpretation, the optimal structure underwent various design updates. The various buildings were examined in relation to a test structure that was designed according to 466 Israeli Standard.

Three different optimization problems were solved in this research:

• Minimum compliance under volume constraint.
• Minimum volume under displacement constraint.
• Minimum volume under compliance constraint.

A number of different parametrizations were performed for the various formulations, allowing for a simpler interpretation of the optimal structure. Each parametrization defines the design parameters that are solved for the optimal problem.

Parameters that correspond to the various formulations:

1. Constant beam height, variable beam width (for each beam) with penalty.
2. Variable beam height (uniform for all beams), with width beam variable (for all beam) with penalty.
3. Constant beam height, non-uniform variable beam width (for each beam) with penalty.
4. Variable beam height (uniform for all beams), non-uniform variable beam width (for each beam) with penalty.
5. Variable beam height (for each beam) with Heaviside Projection function, constant beam width.
6. Variable beam height (for each beam) with penalty, with width beam constant.

CONCLUSION: This study investigates the potential for reducing the weight of ribbed concrete ceilings by structural optimization. A number of matching formulations and parameterizations were examined and a comparison and investigation was made of the volume obtained and the displacement compared to the test structure. The results presented in this study indicate that for certain parametrizations a 15% concrete saving was obtained relative to the test structure and at displacement about 9% less relative to the test structure. It is important to note that most of the formulations performed better than the test structure in relation of the required concrete volume and displacement. Thus the research findings show the inherent potential for reducing the weight of ribbed concrete ceilings using tools from structural optimization.