טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentYoely Yosef
SubjectSpline Based Topological Optimization with Curvature
Constraints
DepartmentDepartment of Mechanical Engineering
Supervisors Professor Oded Amir
Dr. Iddo Hanniel
Full Thesis textFull thesis text - English Version


Abstract

The last three decades have been characterized by a remarkable popularization of numerical simulation, including multi-physics analysis, solid design and the integration of add-on tools such as optimization packages. In the area of mechanical and structural design, many engineering application areas such as automotive, civil, naval, aerospace and others, have profited from the benefits offered by using advanced numerical tools available in commercial codes. Classical mathematical programming algorithms and heuristics-based algorithms are offered as a means for finding optimized designs, that can be classified as either local or global minima solutions.

Traditionally, structural optimization has been performed manually, with engineers analyzing and modifying designs until a satisfactory level of structural efficiency is achieved. This approach relies on the experience of the engineers involved and on refining common designs for a specific application, such as the rib, spar and stiffener internal structure of aircraft wings. However, such methods may not result in the best possible structure. Furthermore, increasing demands on resources has lead to the consideration of more radical design solutions or advanced materials that may require similarly radical and currently unknown structural solutions. Hence a robust numerical method for finding optimal structures is a valuable tool for structural design.

A structural optimization problem aims to achieve the best performance of a design while satisfying all the constraints. Specifically, the class of methods known as structural topology optimization aim to find the layout of the design by changing the shape of the boundary and the number and shape of holes. Such optimized designs ultimately lead to energy savings, efficient usage of materials, and to faster manufacturing.

Many topology optimization approaches use the finite element method to calculate the response of the structure during the optimization process and some of them, called "element based-methods", are integrated with the finite element method to use the properties of finite elements as design variables in the optimization. The solutions of such approaches are usually represented by a uniform finite element mesh that bears no relation to the final geometry and hence they do not provide an accurate or smooth representation of the design boundary. The solution from topology optimization must therefore go through further post processing stages to obtain a manufacturable design. The post processing stages, which can include smoothing and shape optimization are costly and time-consuming and may result in the structure becoming less optimal.

This work presents an optimization approach that is based on explicit B-spline representation of the design, conforming with CAD standards. This parametrization enables to incorporate explicit constraints on minimum and maximum areas of holes and on curvatures of boundaries. Therefore, practical design considerations such as avoiding stress concentrations in sharp corners, and flexibility with respect to locations and sizes of holes, can be embedded into the optimization problem.

Furthermore, control over curvatures can simplify machining processes and lead to more efficient manufacturing. The presented method is applied to several minimum compliance problems. The results demonstrate the capabilities of this approach to incorporate explicit geometric constraints in a straightforward manner.