Sonlu eleman deplasman metodu ve sürücü kabini tavan çökme dayanımının incelenmesi
Finite element displacement method and examination of the endurance of the driver cabs roof crush
- Tez No: 21854
- Danışmanlar: DOÇ. DR. MURAT EREKE
- Tez Türü: Yüksek Lisans
- Konular: Makine Mühendisliği, Mechanical Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1992
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 118
Özet
ÖZET Bu çalışma iki temel amaçla yapılmıştır. Birincisi kafes (karoseri) hesabı için bir sonlu eleman programının geliştirilmesi, ikincisi ise bu programın kullanılması ile yerli üretilen bir traktör sürücü" kabininin Türk standartlarına uygunluğunun teorik olarak incelenmesidir. Bu çalışmada Sonlu Elemanlar Metodu hakkında temel bilgi verilmektedir. Genel tanım içersinde eleman tipleri ve özellikle deplasman metodu geniş kapsamlı olarak bir örnek kafes yapı üzerinde anlatılmaktadır. Çalışma prensibi aynı olmak üzere bazı eleman tipleri için lokal veya global katılık matrislerinin tanımları verilmektedir. Sonlu ; eleman metodu ile son olarak yöntemin karoseri tasarımında kullanımı konvansiyonel tasarımla karşılaştırılarak verilmektedir. Sonlu eleman metodu ile birlikte yuvarlanma emniyeti hakkında da temel bilgi verilmektedir. İncelenecek olan traktör emniyet kabininin devrilme sırasında (yuvarlanma ve şaha kalkma durumlarında) ezilme ve deformasyon olması nedeni ile sonlu eleman metodu ile birlikte yuvarlanma emniyeti hakkında da bilgi verilmektedir. Son olarak çalışmada Hisarlar Makina Sanayi 'nin imal ettiği traktör emniyet kabinine ait resimler üzerinden ve diğer data lar dan faydalanılarak sonlu eleman deplasman metodu prensibi ile çalışan bir bilgisayar programı yardımı ile bu emniyet kabininin de formasyonu incelenmektedir.
Özet (Çeviri)
SUMMARY FINITE ELEMENT DISPLACEMENT METHOD AND EXAMINATION OF THE ENDURANCE OF THE DRIVER CAB'S ROOF CRUSH In this study, Finite Element Method is given as a general definition. In the general definition, principle of method, types of element, and use of this method in car frame are given. In addition, a tractor safety cab is examined with finite element displacement method. Many engineering problems can not be solved with analitical way. Analitical solution are obtained in only some simplyfied conditions. Finite element method is the most important method among other numerical methods. Finite element method has become one of the most widely used way in the analysis of complex structural systems, because of the development of software-hardware. After these developments, problems which have many unknown terms can also be solved easily. This method has been formed from elements to system formulation. Hie main concept of this method is that the real structure is represented as a mathematical model, Model is divided into finite elements. Elastic properties of elements such as elasticity module are known. Finite element method has many advantages such as: - This method can be applied to structures which undergo static and dynamic loads. - This method gives enough and satisfying results. With capability of complete automation, this method is a different method than the other conventional methods. - Alternative structures, whose constructions are changed, can be examined easily and simply. - It is possible to compare different structures with da t as. VIIIOn the contrary» this method has also some disadvantages such as: The division of the main structure requires experince. - Since data numbers are too much, during the input of datas some mistakes can be made - If results are not arranged, they are just a number order and interpretation of results become difficult. Finite element method is an important auxilary component in development of vehicle representation interne of making up conventional calculation methods. When the method is used correctly and integrated into progres of vehicly improvement with special conditions of method, some advantages can be obtained. In finite element method, experts are necessary especially in programming stages, because obtained results can not be useful. Finite element method is not enough to develop the vehicle body. This method provides to form a well-built base, to shorten the developing process, and to avoid wrong developing. And so ¦ inter ms of time, material and personel expenses can be reduced. In addition, new model can be tried theorotically with new materials and so it helps new improvements. The first attempts to model whole car bodies to obtain results for cases of static bending and torsion load were often done by modelling beam type structures as beam elements, resulting in relatively coarse meshes. These attempts did not give very good results compared to the experiments and it was found out in all automotive companies doing caculations of this kind, this was mainly due to an inadequate modelling technique. One reason for this that the beam elements that were connected to others in corners by connection of their six degrees of freedom did not represent the real behaviour of such structures, which should be modelled very carefully. If such carefully modelled substructures are used within finite element models of* car bodies the results obtained approach those of experimental data. For dynamic calculations, a trimmed body model was used, taking the body in white and adding appropriate mass distribution for items such as the carpet, damping material, the seats, etc. This was done because the dynamic tests were performed on such a trimmed body. IXAfter preparing the model, the number of the degrees of the freedom had to be reduced to a master set and then an eigenvalue analysis for eigenmodes of vibration was performed, which resulted in quite good correlation with test datas. With growing interest on the part of design departments in the use of alternative materials like aluminium or plastics» there is a need for FEM calculation on structural parts made of these materials. In finite element displacement method, the calculation of nodal displacements which are examined as unknown terms, are the base of this method. Mathematical models of the main structure form elements such as beam, rod, plate etc. After elements discretization, FE model is placed on a coordinate system. Left and/or bottom node of model should be prefered when the model is placed on a coordinate system. In order to understand better we will examine tractor safety cab. Cab is examined as a two dimensional beam element Cfrom front and side point of view} and also a three dimensional rod element. But structure with rod elements, requires special support conditions. Therefore only the upper part of the cab is examined. Figure 1 and Figure 2 shows the two dimensional beam structures. For all types of elements, finite element displacement method works the same way. Only the stiffness matrixes are different. After the model is placed on a coordinate system, elements and nodes are numbered. In displacement method force balance is utilized at nodes of the element and then deformations of the. element are examined. In the structure, all elements have own local coordinates. That is, nodal forces and nodal displacements at the end of the elements have components. Direction x, y, z it depends on two or three dimensions. The relationship between force and displacement is given with the equation C1D: p = k v C1DIn this equation k is stiffness matrix of the element in local coordinates, p is force, v is displacement. These local values are transformed to global values. In order to obtain this transforming angle between the element local coordinate and the structure global coordinate is used. Sinus, cosine and tangent values of this angle give stiffness matrix. In Figure 1 and 2 for models stiffness matrix of two dimensional beam element is: K = a b d a i me trie ç e f -a -b -ç -b -d -e C e g a. b/; d ç -e C2) E § © i © i 0 Figure 2. 2D FE model of tractor cab front view XI® a û® x Figure 2. 2D FE model of tractor cab side view Here a, b, c, d» e, f, g are variables which depend on element properties. For three dimensional rod elements stiffness matrix is: K = C3) XIIHere c, s» t are cosine, sinus, tangent values of angle C between local and global coordinates!) Equation C2D and C3D are used only for one element. For the whole structure we must obtain stiffness matrix. For this, we have two choices. 1. A transformation matrix method 2. Expended matrix method A transformation matrix consist of“1”and“0”. This means;“1”: Contact between the end of the element and node“0”: No contact With A transformation matrix and transpoze of A matrix, K stiffness matrix for structure is obtained. K = AT K2 A C4D The other method works with the same logic but it does not require A matrix. Degree of freedom times the number of node form dimension of structure stiffness matrix. Every element has a matrix in this dimension and matrix fills same logic in A matrix and all these matrixes are added. And total stiffness matrix is obtained. In this method we do not nedd transformation matrix. After the structure stiffness matrix is obtained, boundry conditions are applied. According to boundry conditions, rows and cöl urns which belong to motionless nodes are thrown from the total stiffness matrix. And reduced stiffness matrix is obtained. If the displacement vector is left alone in equation C1D, we obtain: V = K_1P C5D That is, reduced stiffness matrix inversion is done and it is multiplied by force matrix and displacement matrix is obtained. XIIIWith this caculation, we can easily find the deformation of structure in load condition. Easy concept is according to conventional calculation methods. Roll -Over And Crush Conditions A finite element computer program which was written to calculate the large deformation of structures in impact situations was available at an early stage of development when the research was started. The program considered the structure as an assemblage of individual beams with external loads or displacements applied incrementally. It is a stiffness method program so arranged that the stiffness matrix is updated after each increment to allow for the nonlinear effects of large displacements both geometrically and in properties of the beams e.g. collapse hinges and Eularian buckling can be incorporated. Commercial vehicle cabs are currently designed to satisfy ECE Regulation in Europe which provides for a front impact and roof crush test as well as for an optional rear wall crash test to provide some protection from pay load shifting forward. Since in many cases the front impact is absorbed by the chasis frame regulation does not necessarily ensure a high degree of crew protection. The roof crush test involves a static vertical load and will therefore provide protection only when the cab lands vertically on its roof. Agricultural tractors have been subject to a regulation for the provision of safety cabs and roll -over protection bars for many years. In ' Turkey, we have a standard CTS 3412!) about tractor safety cabs. XIV
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