Konsol kirişlerde büyük sehim oluşumu, tek ve çok katmanlı modelleme
Large deflections of cantilever beams, single and multi layered modelling
Yazar: FATİH TEMİZ
Danışman: DOÇ. DR. CEMAL BAYKARA
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Makine Mühendisliği Ana Bilim Dalı / Konstrüksiyon ve İmalat Bilim Dalı
Derece: Yüksek Lisans, 2012
Konu: Makine Mühendisliği = Mechanical Engineering

Özet:
Son yıllarda birçok sektörde kiri? yapılarının önemi artmı?, hafif ve aynı zamanda mukavim tasarımların geli?tirilmesine yönelik ciddi çalı?malar yapılmaktadır. Özellikle makine endüstrisi, havacılık alanlarında ergonomik tasarım arayı?ları bu çalı?maların yoğunla?masında büyük rol oynamaktadır. Ayrıca in?aat sektöründe de kiri? tasarımının önemi gittikçe artmaktadır. Kiri?ler gerek malzeme yapılarının gerekse konstrüktif yapılarının geli?tirilmesi sonucunda birçok alanda kullanılabilir hale gelmi?lerdir.Kiri? türlerinin içinde en yaygın olarak kullanılan konsol kiri? türünün ?imdiye kadar lineer malzeme kabulü yapılarak modellenmesine yönelik birçok çalı?ma bulunmaktadır. Bu çalı?maların gerçeğe en uygun olmasına yönelik lineer olmayan davranı?ların incelenmesi hususu son yıllarda hızla geli?en ara?tırma alanlarında biri haline gelmi?tir. Bilhassa ankastre mesnetli konsol kiri?lerin yüksek esnekliğe sahip, büyük yer deği?im olu?umuna izin veren yapıları temelde iki adet lineer olmayan özellik içermektedir. Bunlardan ilki malzemenin klasik kabullerin aksine lineer olmayan davranı?a sahip olmasından kaynaklanmaktadır. Bu malzemelerde gerilme ve birim ?ekil deği?tirme ili?kisi üstel bir ifadeye bağlı olarak deği?mektedir. ?kincisi ise büyük yer deği?im olu?umunun getirmi? olduğu bir netice olan geometrrik lineer olmama durumudur.Bu çalı?mada büyük yer deği?im olu?umuna izin veren ve lineer olmayan ludwick tipi malzeme özelliğine sahip bir ankastre konsol kiri?in deği?ik uç momentleri uygulanarak elde edilen yatay ve dikey doğrultudaki yer deği?imler, ANSYS programı yardımı ile elde edilmi?tir. Elde edilen bu sonuçların analitik ve numerik olarak hesaplanmı? sonuçlar ile kar?ıla?tırılması yapılmı?tır.Konsol kiri? türünden yola çıkılarak yapılan çalı?mada fonksiyonel derecelendirilmi? ve tabakalı kiri? yapılarının modellenmesi ve analizi yapılmı?tır. Bir çok katmandan olu?an kiri? yapılarının ANSYS programında uygun eleman türü belirenerek modellenmesi ve bu modellerden elde edilen sonuçlar kendi aralarında kar?ıla?tırlmı?tır.Tek katmandan ve çok katmandan olu?an kiri? yapılarına gerek lineer olmayan, gerekse lineer olan malzeme özelliği kazandırılması neticesinde, uç momentleri ve uç kuvvetleri etkitilerek elde edilen modellerin davranı?ları incelenmi? ve olu?an yer deği?im değerleri kar?ıla?tırılmı?tır.Bu çalı?mada ANSYS programında kiri? yapıları modellenirken özellikle lineer olmayan davranı? kabiliyetini sağlama, malzeme davranı?ına ve olu?turulacak geometriye uygun eleman türünü seçme i?lemleri yapıldıktan sonra bu özelliklerin çe?itlendirilerek farklı kompozisyonlar meydana getirilmi? ve bu kompozisyonların uygualanan moment ve kuvvet neticesindeki durumları incelenmi?tir. Bu örneklerdenxviyola çıkılarak daha yeni modellemeler ve yakla?ımlar ortaya konulabilir, kullanılan parametrelerin çoğaltılması ile bu alandaki çalı?malar çe?itlendirilebilir.

Abstract:
In recent years there is great increase in importance of beam structures and studies to design light also durable strucures are in progress. Since, especially machine industry, aerospace and related fields had always been searching for ergonmic design these studies are becoming more substantial. Besides for civil engineering the importance of beam constructions is inrceasing. The develoment of metallugical engineering and also design principles, beams are now such a framework in use of many applications and fields.Cantilever beams are which are the most common beam type used to built the constructions have many application fields. For instance for aeroplane industry the weight of the aircraft and the relation between weight and the strength is so important. So today composite tyoe beams are commonly used for construction of aerospace vehicles.The most common type of beams is the cantilever beams which many studies developed on until recent years sustaining linear behaving material modelling. On the other hand in recent years the non-linear behaving material type with beam structures is investigating for having solutions which are more familiar with the real applications. Especially cantilever beams which let large deflections and have high level of flexibility have two main non-linearity features. The first feature which causes non-linearity is that on the contrary of classic approaches, non-linear behaving material used to built the beam structure. Second feature which causes non-linearity is the geometric non-linearity come into existence with the large deflection.Bernoulli-Euler law which is the exact expression of the curvature of theelastic curve are used in order to formulate the problems which involve large deflection of beams. Formulating of the large deflections thin beams is one of difficulty about the mathematical issues, and in very special cases a closed form solution is obtained.There are curvatures for explaining the linear shape of a beam structure after force or moment applied. This method is not valid for the real material behaviour, thus real material does not have linear relationship between stress and strain. This is the fact that makes the solution difficult. For analysing such conditions numerical and approximate methods should be applied.The curve for the load deflection has an elastic portion and a distriction zone for transition from elastic to the plastic behaviour. After transition to the plastic zone the slope of the curvature decreases that means with the small increase in load deflection increases greatly. For the real structures behaviour is always non-linear.xviiiThis study involves analyse of large deflections of cantilever beam with the material of ludwick type subjected to various end moment values by using ANSYS software. The solution and the values which attain after this computerized analyze are compared with the results of analytical and numerical approaches.The non-linear behaviour of the beam deflection problems involves some extra difficulties than the liner beam deflection problems. For obtaining right results right adjustements should be done. The selection of element type should be available for non-linear applications. Also for the large deflection situations. Modelling approach has to be done taking in consideration of element type features. Non-linear analyse options are also complicated. ?t involves many options. ?teration number is one of the important option adjusts the sensitivity of the results. Time stepping is one of the other important option. The non-linear behaviour occurs when transition point is introduced to the software. The transition point is the yield strength point, which is a stress value. The software works with the linear elastic elasticity modulus and poisson ratio. After introducing linear elastic features, non-linear part can be introduced by selecting the right option. Non-linear isotropic hardening is the best option for introducing ludwick type material. Cause the material property given has exponential behaviour. Stress and strain relationship is built on a formula which is convenient for non-linear isotropic hardening. The lement type which selected for modelling is a three dimensional element type consisting of three nodal points. Each nodal point has seven dergrees of freedom. Suitable for non-linear applications and non-linear isotropic hardening. Large deflection properties are also suitable for this element type.For the analyses of stubby, thick beams ?beam 189? element is convenient. Timoshenko beam theory is the basic calculating method of ?beam 189?. This element is also suitable for large strain, large rotation and for non-linear applications.After analyse of large deflection of a cantilever beam with non-linear material type under various end moment values, functionally graded material and laminated structures modelling and analysing are done. The laminated structures which consist of many layers are modelled with convenient type of ANSYS modules and the results sustained from these structures are compared with each other.Sinle and also multi layered cantilever beam structures consisting of linear and non-linear material type, are modelled and differnet values of end moments and end forces are applied in order to seek for deflection properties. Also deflection results obtained from the analyses are compared.The element type for modelling functionally graded and laminated material is ?solid shell 190? which is similar to the elemnt type ?solid 185? which is a newer hybrid type element. This element builds and meshes like clinker. This element has the capability of large deflection. For functionally gaded material iti is the most suitable elemnt type of software. It is an eight node solid element. For modelling functionally graded beams do loop can be used. By dividing the thickness of the model into very thick parts and applying changing modulus of elasticity for every layer can be done by a do loop. Tihs method is convenient for modelling and analyzing laminated and functionally graded material.This study involves multi layered and single layered structures and their non-linearand also linear solutions. For the multi layered structure, each layer has its own linear elasticity modulus and poisson ratio but these values are not the same for all layers. Elasticity modulus for eeach layer increses from the upper layer to the lower.xixAfter modelling and defining the material propereties, force is applied to the free end nodes and deflection in horizontal and vertical directions analyzed.Geometric issues are also substantial to vary the large beam deflection templates. On the purpose of detecting geometric affect on the beam structures, first a traingle like shape is modelled and subjected to an end force. This rectangular like model was constructed of five layers. Each layer has its own elasticity modulus and poisson ratio. Elasticty modulus for each layer is constant and the same. Since linear elastic behaviour is assumed. Secondly parabolic shaped beam structure is modelled as the same principle with the triangle shaped model. While modelling the structures node generation option of the ANSYS software is used. After deciding the geometric properties of the model, thickness is considered to cretae the very first nodes on the active coordinate system. Two nodes are defined along the longitude and between these two nodes are filled with other nodes. The number of nodes which fills the gap between starting and the ending node is determined. After cretaing the first line with the nodes, by giving deflections along the y axis, the other part of the beam structure is modelled in two dimensions. Z axis is also used to cretae the structure in three dimensions as before. Defining elements through the longitude and generating them ends the modelling phase.Choosing the right element type is also crucial. The elemnt type which the model is based on should have available properties and convenient for the problem and suitable for goal. After this phase end force is applied on the nodes which are located on the first layer. Larger values of deflections occur on the triangle shaped beam structure than the paarabolic shaped beam structure.The modelling features of beam structures, selecting the right type of component related with the geometric condition of the model and to let the structure to behave non-linear material properties, are investigated and tried to find solutions. Also these features are diversified in order to have different compositions and related force or moment values are applied to search for the deflections. Based on these modelling attributes, the parameters can be varified and also be extended to search for other combinations.