Çift yönlü evrimsel topoloji optimizasyonu yöntemi ile bir motor braketinin doğal frekanslarinin en iyileştirilmesi
Maximization of natural frequencies of an engine bracket with bidirectional evolutionary topology optimization method
Yazar: YİĞİT OKUR
Danışman: DR. ÖĞR. ÜYESİ DEMET BALKAN
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Uçak ve Uzay Mühendisliği Ana Bilim Dalı / Uçak ve Uzay Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2019
Konu: Makine Mühendisliği = Mechanical Engineering ; Uçak Mühendisliği = Aircraft Engineering
Dizin: Optimizasyon teknikleri = Optimization techniques ; Topoloji tasarımı = Topological design ; Özdeğerler = Eigenvalues

Özet:
Uçak ve uzay mühendisliği alanında kullanılan parçaların, dinamik çalışma koşulları altında yeterli dayanımı sağlaması ve mümkün olduğunca hafif olması önemlidir. Bu amaçla geliştirilen yapısal en iyileştirme yöntemlerinin en temeli, kavramsal tasarım aşamasında kullanılan yöntem olan topoloji en iyileştirilmesidir.
Motor gibi dinamik uyarımların fazla olduğu bölgelerde kullanılan parçalarda, doğal frekansların uyarım frekanslarından uzak tutulması önem arz etmektedir. Bu doğrultuda, Eleman-etkisizleştirmeli Çift Yönlü Evrimsel Topoloji Optimizasyonu (BESO) yöntemi kullanılarak doğal frekans değerlerinin, belirtilen bir tasarım uzayı ve kütle kısıtı altında en iyileştirilemesi ve sonuçların yorumlanması amaçlanmıştır. Literatürde doğal frekans amaçlı topoloji en iyileştirilmesi üzerine yazılagelmiş makaleleler sınırlıdır. Bu tez çalışmasında topoloji en iyileştirilmesi konusunda bahsedilegelmiş başlıca yöntemler, mümkün olduğunca özet bir biçimde, üstün olan ve geri kalan yönleri belirtilerek anlatılmıştır. Tez içerisinde kullanılan yöntem olan BESO ise, gerek Evrimsel Topoloji Optimizasyonunun tarihsel gelişimi, gerekse matematiksel gösterimi ile ayrıntılı bir şekilde anlatılmıştır. Ayrıca, Eleman-etkisizleştirmeli BESO yöntemine ait en iyileştirme değişkenlerinin etkisi literatürdeki çalışmalardan takip edilerek yorumlanmıştır. Bu değişkenlerden biri olan Penaltı fakötürü, doğal frekansların en iyileştirilmesinde, rijitlik amaçlı en iyileştirme yaklaşımına göre farklı bir amaçla kullanılmakta; kinetik enerjinin eleman hassasiyetine olan etkisini sınırlamaktadır. Penaltı faktörünün doğal frekans amaçlı topoloji en iyileştirilmesine etkisi literatürde bulunamadığı için ön bir çalışma ile incelenmiş ve elde edilen bulgular değerlendirilmiştir.
BESO yönteminin uygulanabilmesi için ANSYS Parametrik Tasarım Dili (APDL) üzerinde bir çalıştırma algoritması yazılmıştır. Çalıştırma algoritmasının doğrulanması, BESO yazarlarına ait bir referans makaleden seçilen bir örnekteki sonuçların elde edilmesi ile sağlanmıştır.
Çalıştırma algoritması kullanılarak, akademik inceleme amaçlı, 3 boyutlu bir motor braketi için oluşturulmuş tasarım uzayının, belirli bir kütle kısıtı altında, öncelikle birinci doğal frekans değerinin, sonrasında eş zamanlı olarak birinci ve ikinci doğal frekans değerlerinin en yüksek düzeyde tutulmasını amaçlayan, topoloji en iyileştirilmesi gerçekleştirilmiştir.
Oluşturulan tasarım uzayı, aynı amaç ve kısıtlar altında, bugün birçok ticari yazılımda kullanılmakta olan Yoğunluk (SIMP) yöntemi ile yeniden en iyileştirilmiştir. Elde edilen sonuçlar BESO yöntemi ile elde edilen sonuçlar ile karşılaştırılmıştır. Sonuçların büyük oranda benzer nitelikte olduğu gösterilmiş; BESO yöntemi ile kısmen daha verimli değerler elde edilebildiği gösterilmiştir.

Abstract:
The parts used in the aeronautical and astronautical engineering field are required to have low weight and to be durable enough under dynamic loading conditions. Structural optimization approaches such as the size and the shape optimizations are used to improve the material efficiency of the parts to be designed. The most basic type of the structural optimization methods developed for this purpose is the topology optimization which is used in the concept design process.
In the aerospace engineering field, the topology optimization applications are much limited and more recent than the automotive engineering field. One reason of this situation has been declared in the literature as due to the lately developed capability of buckling approaches in the topology optimization methods.
The developments for the additive manufacturing process are significant to produce the parts in a more proper shape which is optimized by a topology optimization method in the concept design since the topological shapes are generally away from the ability of being produced by a traditional manufacturing process. Some examples of additive manufactured products are presented in the literature search section especially for the parts used in the power units of aircraft. It is explained, much more parts will be produced by additive manufacturing for the aircraft power units in the near future due to the advantages such as decreasing the number of the parts in complex components and therefore the ease of assembly, less time required for manufacturing process, ability to produce the parts with tough materials difficult to process, reducing the waste production, and the design flexibility for the complex geometries such as designed with the topology optimization during the initial concept design process as well.
While designing the parts used in the aerospace engineering field, it is significant to keep the natural frequencies of the parts away from the excitation frequencies in the areas with high dynamic excitations, such as the regions close to the engines of an aircraft. In an opposite case, resonance effects can exaggerate the dynamic response of the parts and therefore the required life of the parts may not be achieved. For this purpose, it is aimed to study maximizing the natural frequency values of a sample engine bracket under a certain design space with a certain mass limit and to interpret the results utilizing the Soft-kill Bidirectional Evolutionary Structural Optimization (or Soft-kill BESO) method which is some heuristic, however a well known and a candidate method of the future applications or the commercial software. The evolutionary methods have been studied since the beginning of the 1990s. The first main type of these methods is Evolutionary Structural Optimization (ESO). The ESO process is related with deleting (Hard-kill) some number of the elements considered inefficient by calculating the elemental sensitivities of each one in each iteration of the optimization. The Bidirectional Evolutionary Structural Optimization (BESO) is related with not only deleting (Hard-kill) some number of the elements, but also adding
some number of the elements to the design space again, which are considered efficient by calculating the elemental sensitivities of each one, in each iteration of the optimization. The Soft-kill BESO, which is a special type of the evolutionary methods is a newer method among them. The Soft-kill process has been introduced to contribute to the structural integrity and to keep the elements which are actually the variables of the optimization and therefore to provide more realistic optimization process. In the literature, the papers of the topology optimization studies have been generally published with the aim of the compliance optimization. The topology optimization studies with the aim of optimizing the natural frequencies are limited yet. In this thesis study, the primary methods of the topology optimization mentioned in the literature are explained as briefly as possible with their advantages and disadvantages. Those methods are the well known Homogenization, Solid Isotropic Materials with Penalization (SIMP) and the Level-Set. The method used in this thesis study, the Soft-kill BESO, is explained extensively with its mathematical concept and the historical background as well. Furthermore, the effects of the optimization parameters used in the Soft-kill BESO method, such as the Evolutionary Rate, the Maximum Adding Ratio or the Filter Radius are interpreted by following the related studies in the literature. These studies are found related with the compliance optimization in the literature. The Evolutionary Rate is a parameter used to define the number of the elements whose physical properties are to be reduced during the each iteration of the optimization process. On the other hand, the Maximum Adding Ratio parameter is used to define the number of the elements whose physical properties are to be improved during the iterations of the optimization process as well. The filter radius in the Soft-kill BESO method, and also in other methods such as the SIMP, is used to define the nearest elements domain for any element to share the elemental sensitivity with its neighborhood and therefore the checkerboard problem which can be seen often in the topology optimization process can be avoided and the stabilization of the optimization can be improved. To improve the stabilization of the topology optimization process, an additional approach called Stabilization Scheme is utilized in the Soft-kill BESO method by averaging the filtered elemental sensitivity values obtained in a current iteration with their values obtained in the previous iteration. The Penalty Factor, however, one of those parameters, is used in a different way in the natural frequency optimization approach then the compliance optimization approach by limiting the contribution of the kinetic energy to the elemental sensitivities. Since the effect of the penalty factor to the topology optimization with the goal of maximizing the natural frequencies are not provided in the literature, it is examined with a simple pre-study and the obtained results are presented, discussed and interpreted to use an initial value of this parameter in the engine bracket optimization. The results showed that a certain limit of the penalty factor is necessary to supply the structural integrity and thus to keep the mode numbers unchanged.
An algorithm to implement the Soft-kill BESO process, is written in ANSYS Parametric Design Language (APDL). The verification of this algorithm is carried out by obtaining the same results with an example in a reference paper written by the authors of the Soft-kill BESO. The algorithm is formed to represent the method and to study the some parameter effects. Any approaches in the algorithm to diminish the time consumed by the optimization process is not aimed to study in the concept of this thesis.
Using the written algorithm, topology optimization of a design space formed for a 3 dimensional engine bracket with the aim of academic examination, under a certain
mass limit is carried out for the purpose of maximizing the first natural frequency at the initial study and maximizing the first and the second natural frequencies simultaneously in the following study. The results present that the material efficiency which is defined by the quantity of the natural frequency or frequencies that have been optimized, per structural mass is improved in the both cases. The material efficiencies related with the unoptimized natural frequencies, seems lower than the ones related with optimized natural frequencies.
The design space is optimized again starting with its initial situation utilizing the SIMP (Density) method which is used in the tools of various commercial software of today. The aim of using another method is to compare the methods simply and to contribute the verification of the thesis study as well. It is presented that the results related with the topological view belong to the each method are quite similar, however slightly more efficient results are obtained by utilizing the BESO method. Ofcourse, the more efficient results obtained by the Soft-kill BESO method is necessary to be presented with more examples in the future studies.
In the future studies, the effects of the parameters such as the Evolutionary Rate, the Maximum Addition Ratio and the Filter Radius can be examined extensively especially for the solving time of the optimization. Various programming approaches to diminish the solving time can be integrated with the optimization process. Some approaches such as Modal Assurance Criterion may be used to track the mode being optimized in the case of order changing of the mode numbers.