A numerical study on the thermal expansion coefficients of fiber

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51 Figure 4.1 Examples of finite elements (Trantina, & Nimmer, 1994). 4.2.3 Boundary and Loading Conditions Applying boundary conditions and the proper loading on a structure appear as a very important part of the finite element solution. For static problems, the stiffness matrix associated with the linear equations of equilibrium for the complete structure will be singular, unless all rigid body motion is prohibited. As a result, a fundamental requirement for solution of the linear equations governing a problem is that the structure must be prevented from freely translating or rotating in space. Rigid body motion is eliminated through the application of boundary conditions requiring zero
52 displacements and/or rotations at nodes. Additional displacement boundary conditions can also be applied to the structure to model the actual structural support system. It is not necessary to restrain all of the displacements and rotations at a node. For the thermal analysis problems, prescribed temperatures, conductive heat flux boundary conditions, convection boundary conditions and radiation boundary conditions may be applied to the model. Loads may be applied to a model either in the form of applied forces, displacements or thermal effects. Concentrated loads can only be applied at the node locations of the elements. Distributed loads and body loads can also be applied to finite-element surfaces and volumes, respectively. Distributed loads are usually internally translated to equivalent nodal loads within the finite-element code. 4.2.4 Defining Material Properties In addition to the geometric detail of the component and the applied loads, the material (constitutive) properties must also be defined. For simple isotropic, linearelastic stress analysis, only the material elastic modulus and Poisson's ratio need be provided. In some cases, more detailed constitutive models may be desirable. For example, for highly loaded parts, elastic-plastic behavior may be included. In some cases, properties may be functions of time, rate, temperature, or other variables. It must be emphasized that increased capability in modeling material behavior means in general that more material data must be available. In many cases, such as timedependent material models, for example, measurements to obtain such data are nonstandard in nature (Trantina, & Nimmer, 1994). It must be kept in mind that, real material properties are not dependent upon geometry and the property is only useful in the general engineering sense if it is associated with a methodology of applying it to general geometries. Many tests are carried out on materials as functions of rate and temperature to provide comparative performance values. However, in many cases these measurements do not represent true material properties because they are uniquely associated with the test geometry
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DOKUZ EYLÜL UNIVERSITY GRADUATE SC
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M.Sc THESIS EXAMINATION RESULT FORM
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A NUMERICAL STUDY ON THE THERMAL EX
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CONTENTS Page THESIS EXAMINATION RE
Page 9 and 10: 4.2.1 Geometry Creation............
Page 11 and 12: 2 coefficients of thermal expansion
Page 13 and 14: 4 coefficients coincide to give res
Page 15 and 16: 6 concentration from pure metal to
Page 17 and 18: 8 high strength-to-weight and stiff
Page 19 and 20: 10 polymers. Thermosetting polymers
Page 21 and 22: 12 Metals are strong and tough. The
Page 23 and 24: 14 Table 2.1 Properties of reinforc
Page 25 and 26: 16 2.2.2.2 Carbon Fibers Carbon is
Page 27 and 28: 18 use is in aircraft industry foll
Page 29 and 30: 20 strength and a reasonable Young
Page 31 and 32: 22 1. Processing the conventional f
Page 33 and 34: 24 (orthorhombic) of polyethylene h
Page 35 and 36: 26 Whiskers are monocrystalline sho
Page 37 and 38: 28 3.2 Factors Affecting the Coeffi
Page 39 and 40: 30 3.2.4 Thermal Cycling The primar
Page 41 and 42: 32 3.3.1 Mechanical Dilatometry Thi
Page 43 and 44: 34 absolute accuracy of about ± 0.
Page 45 and 46: 36 3.3.3 Strain Gauges This relativ
Page 47 and 48: 38 • The composite is macroscopic
Page 49 and 50: 40 3.4.1.3 Equation of Van Fo Fy In
Page 51 and 52: 42 and the thermal expansion coeffi
Page 53 and 54: 44 P P 11 33 2 A 22 − A = Det A A
Page 55 and 56: 46 • A perfect bonding exists at
Page 57 and 58: CHAPTER FOUR FINITE ELEMENT METHOD
Page 59: 50 No matter how the geometry is cr
Page 63 and 64: CHAPTER FIVE MICROMECHANICAL ANALYS
Page 65 and 66: 56 5.2 Mesh Creation 10-node tetrah
Page 67 and 68: 58 carbon fibers were assumed to ha
Page 69 and 70: 60 Figure 5.6 The displacement fiel
Page 71 and 72: 62 small differences between these
Page 73 and 74: 64 Table 6.1 Comparison of the expe
Page 75 and 76: 66 Longitudinal CTE (1/°C) 2.25E-0
Page 83 and 84: 74 Ishikava, T., Koyama, K., & Koba
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A numerical study on the thermal expansion coefficients of fiber

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