Controlled Thermal Expansion: Assumptions and calculations
In determining the calculations for the controlled thermal expansion
model, the following assumptions have been made:
The thermal expansion coefficients of the materials used for
both lattices are effectively constant over the temperature range
that they can be used at.
The beams making up the lattice struts have a circular cross
section.
The materials that make up the lattices are resilient enough
to undergo distortion without breaking or permanent deformation.
The joints between the two lattices are perfect and do not experience
sufficient stresses to cause failure under thermal cycling.
The optimum offset angle can only be calculated if it is possible
to achieve with the lattice geometry and materials.
The range that can be used for the offset angle is: 
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.
Density
Young's
modulus
Where Sh is the hydrostatic
stiffness
(with an assumed Poisson's ratio of 0.3)
Shear
modulus
Bulk
modulus
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.
Hydrostatic
stiffness Sh
where A1, A2,
l1, and l2
all have the same meanings as above, and:
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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Granta Design,
Cambridge, UK