Bir helikopter rotor palasının kompozit malzeme kullanılarak sonlu elemanlar metodu ile dizaynı - Şahin, Halim (Fen Bilimleri Enstitüsü, 1994)
Yüksek Lisans tezi olarak sunulan bu çalışmanın birinci bölümünde havacılıkta helikopter ihtiyacının ortaya çıkışı ve bu ana kadar havacılıkta meydana gelen gelişmeler anlatılmış, Helikopterin uçağa göre avantaj ve dezavantajlarından bahsedilmiştir. İkinci bölümde detaylı olarak Helikopterin çalışma prensibinin izahı ile birlikte helikopter rotor palasının ayrıntılı olarak yapısı, çalışma şekli, özellikleri ve bunların yanında helikopter rotor palasının performansı da incelenmiştir. Üçüncü bölümde Helikopter rotor palasının kiriş kabulü ile yanal, boylamasına ve dönel titreşimleri, kuvvet denklemlerinden hareket ederek genel hareket denklemleri bulunmuştur. Daha sonra bu denklemler çözülerek serbest titreşim frekansları ve modları bulunmuştur. Dördüncü bölümde sonlu eleman kavramı ve sonlu elemanlar yöntemi izah edilmiş ve getirdiği kolaylıklar örneklenmiştir. Sonlu elemanların dinamik hareket denklemi elde edilmiş, ilgili elemanların katılık ve kütle matrislerinin bilindiği taktirde titreşim frekans ve modlarının elde edilebileceği gösterilmiştir. Beşinci bölümde, Kompozit malzemeler detaylı bir şekilde anlatılıp uygulama sahası ve yapılarda sağladığı hafiflik ve mukavemet'in yanında pahada getirdiği problemlere değinilmiştir. Sonuç kısmında ise, sonlu elemanlar yöntemiyle kompozit malzemeler kullanılarak, ANSYS yazılımında bir helikopter rotor palasının dizaynı yapılmıştır.

This study which is submitted as Master Thesis, consists of six parts; 1- Introduction; An introduction to the Helicopter subject. 2- Helicopter; Besically description and work principle. 3- Vibration Analysis of the blade, Vibration Modes and Frenquencies. 4- Finite Elements Method and general equations of a dynamic structure. 5- Composite Materials and Laminate Composites. 6- Results and Suggestions. In the first part, Historical Development is told beginning from idea of taking off any aircraft without doing taxi motion to today's modern helicopters. In second part, Helicopter is basically described giving advantages and disadvantages compared to an aircraft. Also the properties of whole structure and helicopter power plant are given and how to transmite power is explained. Generation of power in Turboshaft and Turboprop Engines are compared in accordance with it's generation way. Rotor as a part of helicopter and it's properties are explained. Also the types of Rotor Motion are summarized in a short way noting it's work principle to provide essential lift to take off helicopter. Helicopter Rotor blades are generally thin, long and fairly flexible in vertical direction. So they must have good material properties. Main differences between helicopter rotor blades and a propellers can be given as follows, a- A propeller has a small diameter and high period. But Rotor has a high diameter and small period. b- A propeller exposes to air flow in axial direction. But Rotor generally exposes to air flow coming from lateral sides. c- Propeller only occurs thrust and control moment. But rotor occurs lift besides these. ÖZET Yüksek Lisans tezi olarak sunulan bu çalışmanın birinci bölümünde havacılıkta helikopter ihtiyacının ortaya çıkışı ve bu ana kadar havacılıkta meydana gelen gelişmeler anlatılmış, Helikopterin uçağa göre avantaj ve dezavantajlarından bahsedilmiştir. İkinci bölümde detaylı olarak Helikopterin çalışma prensibinin izahı ile birlikte helikopter rotor palasının ayrıntılı olarak yapısı, çalışma şekli, özellikleri ve bunların yanında helikopter rotor palasının performansı da incelenmiştir. Üçüncü bölümde Helikopter rotor palasının kiriş kabulü ile yanal, boylamasına ve dönel titreşimleri, kuvvet denklemlerinden hareket ederek genel hareket denklemleri bulunmuştur. Daha sonra bu denklemler çözülerek serbest titreşim frekansları ve modları bulunmuştur. Dördüncü bölümde sonlu eleman kavramı ve sonlu elemanlar yöntemi izah edilmiş ve getirdiği kolaylıklar örneklenmiştir. Sonlu elemanların dinamik hareket denklemi elde edilmiş, ilgili elemanların katılık ve kütle matrislerinin bilindiği taktirde titreşim frekans ve modlarının elde edilebileceği gösterilmiştir. Beşinci bölümde, Kompozit malzemeler detaylı bir şekilde anlatılıp uygulama sahası ve yapılarda sağladığı hafiflik ve mukavemet'in yanında pahada getirdiği problemlere değinilmiştir. Sonuç kısmında ise, sonlu elemanlar yöntemiyle kompozit malzemeler kullanılarak, ANSYS yazılımında bir helikopter rotor palasının dizaynı yapılmıştır. equations of equilibrium, the stres-strain relationships and the compatibility conditions at every points in the continuum, including boundaries. The finite element approach yields an approximate analysis based upon an assumed displacement field, a stress field, ör a mixture of these within each element. Since the assumption of displacement functions is the techique most commonly used, the following steps suffice to describe this approach. 1- Divide the continuum into a finite number of subregions (ör elements) of simple geometry (triangles, rectangles, and so on) 2- Select key points on the elements to serve as nodes, where conditions of equilibrium and compatibility are to be enforced. 3- Assume displacement functions vvithin each element so that the displacements at each generic point are dependent upon nodal values. 4- Satisfy strain-displacement and stress-strain relationship vvithin a typical element. 5- Determine stifness and equivalent nodal loads for a typical element using vvork ör energy principles. 6- Develop equilibrium equations for the nodes of the discretized continuum in terms of the element contributions. 7- Solve these equilibrium equations for the nodal displacements. 8- Calculate stresses at selected points within the elements. 9- Determine support reactions at restrained nodes if desired. in this technique, it is also possible to discretize a structure into a mixture of different types of elements. in this part also the dynamic equations of motion has been obtained follovving sonıe steps. Essentially in dynamic problems. Displacements velocities, strains, stresses and loads depend on time. After some steps, using auxiliary equations. The main equation of motion of a body ör structure has been obtained as follovvs. [M]ö(0 + [#]Ö(0 = 0 Where 0(0 is the accelaration vector of nodal points in global system, Q(t) is the displacement vector of nodal points in global system, either can be solved by using known differanüal equation solution methods.[M] is the mass matrix of the system, [K] is the stifness matrix of the system. The equation above can be solved for desired body using it's mass [M] and stifness [K] matrices by substituting these matrices in to viii general equation of motion. After doing that, next step will be to solve equation using knovvn differential equation solution methods. in the fifth part, Composite materials have been described giving what fiber and matrices were told giving material properties and then in vvhich areas Composite materials are used. it is knovvn that technological developments, especially in the last century depend on development in material science. So researchers, desing-Engineers have tried to find new materials which may posses good mechanical and strength properties. So the idea of composite material came into sight and was interested in. in fact, Nature also has some many kind of composite materials. Wood is a fibrous composite, Also Bone is yet another example of a natura! composite that supports the weight of various members of the body. in the sixth part, Results and suggestions are given. in obtaining results ANSYS softvvare was used. ANSYS softvvare consist of three main phases. These phases that an engineering problem is usually solved in are prepocessing, solution and postprocessing. Also this master thesis was solved in three phases as an engineering problem.Each phase consists of a variety number of subphases. ANSYS softvvare enables to make analysis given in follovving : 1- linear and Nonlinear Static Analysis. 2- Buckling Analysis 3- Modal Analysis 4- Full Harmonic Response Analysis. 5- Nonlinear Transient Dynamic Analysis. 6- Linear Transient Dynamic Analysis. 7- Reduced Harmonic Response Analysis. 8- Substructuring Analysis. 9- Heat Transfer Analysis. in this analysis, we used Shell91 from the shell family of the ANSYS. Shell91 has six degrees of freedom at each node: translations in the nodalx,y and z directions and rotation about the nodal x,y,z axis. This element may be used for layered applications of a structural shell.The element is defıned by eight nodes,various layer thicknesses,various layer material direction angles and various orthotropic material properties.Midside nodes may not be removedfrom this element. The geometric locations of midside nodes ix are automatically calculated The material properties of each layer may be orthotropic in the plane of the element.Each layer of the laminated shell element may have variable thickness.The thickness is assumed to vary linearly över the area of the layer There are some assumptions and restrictions for this element.For nonlinear materials,no layer can be thicker than 1/3 of the average element thickness.All nodes are assumed to be at the mid-thickness of the element.Shear deflections are included in the element ; however, normals to the center plane before deformation are assumed to be straight after deformation.The stress varies linearly through the thickness of the each layer. in our structure there are two types load, Inertia load about Y axis and surface loads affecting on finite elements created in Y direction.ANSYS softvvare facilities enable to enter and see what type is needed and select. Also in this thesis STRESS STIFFENING concept was used.Stress stiffening (Also called geometric stiffening,Incremental stiffening,Initial stress stiffening, ör differential stiffening) is the stiffening (ör \veakening) of a structure due to its stress state.This stiffening effect couples the in-plane and transverse displacements,and normally needs to be considered for thin structures with bending stiffness very small compared to axial stiffness,such as cables,thin beams,and shells. This effect also augments the regular nonlinear stiffness matrix produced by large strain ör large deflection effects.The effect of stress stiffening is accounted for by generating and then using an additional stiffness matrix called "Stress Stiffness Matrix". The stress stiffness matrix is added to the regular stiffness matrix in order to obtain total stiffness.Stress stiffening may be used for static analysis. The stress stifness matrix is computed based on the stress state of the previous equilibrium iteration. Thus, to generate a valid stress stiffened problem, at least two iterations are normally required,with the first iteration being used to determine the stress state that will be used to generate the stress stiffness matrix of the second iteration.If the additional stifness affects the stresses, more iterations need to be done to obtain a converged solution. in some analyses.The static (ör initial) stress state may be large enough that the additional stiffness effects must be included for accuracy.Modal,reduced harmonic,reduced transient and substructure analyses are linear analyses for vvhich the prestressing effects can be included.If it is noted that in these cases the stress stifness matrix is constant.As a result using stress stiffening x effects, itiş possible to obtain high strength thin structures as mentioned above.
A Helicopter rotor blade design from composite material using finite element method
Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1994
Keywords: uçak mühendisliği; helikopter; kompozit malzemeler; rotor kanadı; sonlu elemanlar yöntemi; tasarım; Aircraft Engineering; Helicopter; Composite materials; Rotor blade; Finite element method; Design