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Young’s modulus for silicon

Silicon is one of the most commonly encountered materials in precision engineering (including silicon wafers and MEMS), but it poses a challenge in modeling as its material properties are anisotropic (orthotropic to be exact), meaning that the stiffness varies depending on the direction of loading relative to the crystal orientation.

A great reference for its elastic properties including when isotropic approximations are appropriate is the paper by Hopcroft et al (M. A. Hopcroft, W. D. Nix, and T. W. Kenny, “What is the Young’s Modulus of Silicon?,”
Journal of Microelectromechanical Systems, vol. 19, pp. 229-238, 2010.  link to researchgate https://www.researchgate.net/publication/224124507_What_is_the_Young%27s_Modulus_of_Silicon).  Additionally Hopcroft’s course notes are useful http://micromachine.stanford.edu/~hopcroft/Publications/Hopcroft_E_Si_v1p1.pdf

 

 

An Incomplete History of the Hindle Mount, Whiffletree, Swingletree, Swingles, and the Grubb Telescope

Mechanical supports for mirrors and other optical components and substrates to maintain their initial undeformed shape is a common engineering problem.   Ideally a mirror or similar substrate can be supported on three points if the mirror or substrate is stiff enough.  However in many cases, the deflections are too large and more support is required.  One of the earliest areas where this problem arose was for the mirrors in early telescopes.  Irishman Howard Grubb came up with a novel solution by supporting the mirror on a set of levers known as a whiffletree.  For a historical bio of Howard Grubb see Biographical Encyclopedia of Astronomers or the Museum Victoria (Australia) bio or a history of the Armagh Observatory and Grubb’s telescope.

Whiffletree mirror support developed by Howard Grubb in 1835.
Whiffletree mirror support developed by Howard Grubb in 1835.  This sort of mirror mount is also commonly known as a Hindle mount in some optomechanics literature.

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Design of Constraint Systems Based on Minimax Properties of Eigenvalues

There is a neat correspondence between the mathematical concept of a constraint and the practice of exact-constraint or kinematic machine design. This leads to some really useful insight for people designing machines with dynamics in mind. The PDF below is the extended abstract for a paper that Justin presented in Austin last week at the ASPE annual meeting.

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Thermal Expansion: CTE Definitions and Thermal Strain

This entry discusses different definitions of CTE, their relation to thermal strain, how to convert between the different forms, and how to use them in a model. The forms discussed below include instantaneous coefficient of thermal expansion (CTE), secant coefficient of thermal expansion, and direct use of a thermal strain function.

nonlinear thermal strain
Figure 1

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How to Get Part Edges to Show in Paraview or ParaFOAM

Paraview is a very powerful tool for post-processing and displaying data, especially from FE or CFD simulations. But because it typically acts on the mesh without the underlying geometry, it doesn’t inherently know about the edges of parts or volumes. In this post, I run through the steps to detect the edges and draw them as a wireframe.

solidnoedges

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