A numerical study on the thermal expansion coefficients of fiber
A numerical study on the thermal expansion coefficients of fiber A numerical study on the thermal expansion coefficients of fiber
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
- Page 9 and 10: 4.2.1 Geometry Creation............
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52<br />
displacements and/or rotati<strong>on</strong>s at nodes. Additi<strong>on</strong>al displacement boundary<br />
c<strong>on</strong>diti<strong>on</strong>s can also be applied to <strong>the</strong> structure to model <strong>the</strong> actual structural support<br />
system. It is not necessary to restrain all <strong>of</strong> <strong>the</strong> displacements and rotati<strong>on</strong>s at a node.<br />
For <strong>the</strong> <strong>the</strong>rmal analysis problems, prescribed temperatures, c<strong>on</strong>ductive heat flux<br />
boundary c<strong>on</strong>diti<strong>on</strong>s, c<strong>on</strong>vecti<strong>on</strong> boundary c<strong>on</strong>diti<strong>on</strong>s and radiati<strong>on</strong> boundary<br />
c<strong>on</strong>diti<strong>on</strong>s may be applied to <strong>the</strong> model.<br />
Loads may be applied to a model ei<strong>the</strong>r in <strong>the</strong> form <strong>of</strong> applied forces,<br />
displacements or <strong>the</strong>rmal effects. C<strong>on</strong>centrated loads can <strong>on</strong>ly be applied at <strong>the</strong> node<br />
locati<strong>on</strong>s <strong>of</strong> <strong>the</strong> elements. Distributed loads and body loads can also be applied to<br />
finite-element surfaces and volumes, respectively. Distributed loads are usually<br />
internally translated to equivalent nodal loads within <strong>the</strong> finite-element code.<br />
4.2.4 Defining Material Properties<br />
In additi<strong>on</strong> to <strong>the</strong> geometric detail <strong>of</strong> <strong>the</strong> comp<strong>on</strong>ent and <strong>the</strong> applied loads, <strong>the</strong><br />
material (c<strong>on</strong>stitutive) properties must also be defined. For simple isotropic, linearelastic<br />
stress analysis, <strong>on</strong>ly <strong>the</strong> material elastic modulus and Poiss<strong>on</strong>'s ratio need be<br />
provided. In some cases, more detailed c<strong>on</strong>stitutive models may be desirable. For<br />
example, for highly loaded parts, elastic-plastic behavior may be included. In some<br />
cases, properties may be functi<strong>on</strong>s <strong>of</strong> time, rate, temperature, or o<strong>the</strong>r variables. It<br />
must be emphasized that increased capability in modeling material behavior means in<br />
general that more material data must be available. In many cases, such as timedependent<br />
material models, for example, measurements to obtain such data are<br />
n<strong>on</strong>standard in nature (Trantina, & Nimmer, 1994).<br />
It must be kept in mind that, real material properties are not dependent up<strong>on</strong><br />
geometry and <strong>the</strong> property is <strong>on</strong>ly useful in <strong>the</strong> general engineering sense if it is<br />
associated with a methodology <strong>of</strong> applying it to general geometries. Many tests are<br />
carried out <strong>on</strong> materials as functi<strong>on</strong>s <strong>of</strong> rate and temperature to provide comparative<br />
performance values. However, in many cases <strong>the</strong>se measurements do not represent<br />
true material properties because <strong>the</strong>y are uniquely associated with <strong>the</strong> test geometry
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