Controlled Thermal Expansion: Assumptions and calculations
Assumptions used by model
In determining the calculations for the controlled thermal expansion model, the following assumptions have been made:
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The thermal expansion coefficients of the materials used for both lattices are effectively constant over the temperature range that they can be used at.
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The beams making up the lattice struts have a circular cross section.
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The materials that make up the lattices are resilient enough to undergo distortion without breaking or permanent deformation.
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The joints between the two lattices are perfect and do not experience sufficient stresses to cause failure under thermal cycling.
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The optimum offset angle can only be calculated if it is possible to achieve with the lattice geometry and materials.
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The range that can be used for the offset angle is:
Calculations used by model
- Controlled thermal expansion model - Primary properties
- Controlled thermal expansion model - Secondary properties
Controlled thermal expansion model calculations - Primary properties
The equations used by the model are summarized below. For more information on the derivation of these equations see derivation of calculations.
For a definition of the symbols used, see symbols.
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Density
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Young's modulus
Where Sh is the hydrostatic stiffness
(with an assumed Poisson's ratio of 0.3)
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Shear modulus
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Bulk modulus
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Thermal expansion coefficient
Controlled thermal expansion model calculations - Secondary properties
The following remaining properties are also calculated by the model. These properties, which are listed in the notes field at the bottom of the material, are not available for selection.
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Hydrostatic stiffness Sh
where A1, A2, l1, and l2 all have the same meanings as above, and:
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Optimum offset angle, θ, to achieve desired coefficient of thermal expansion
The model calculates the value of theta, θ, from the positive value of tan(θ)
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