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A very thin element of the non-oriented part of the sample is shown in Figure 11.
Since we use the thin element approximation to process surfaces and apply ABCD matrices to propagate light in free space, our propagation operators are paraxial.
In other regions consisting of lenses or stops (e.g. d1-d4), it is more convenient to obtain the correlation function Γ behind the element by a Fourier transform of the Wigner function, then employ the thin element approximation (Eq. 3 5).
The mass of the thin element of thickness dz at depth z in wedge BCD is given by m_{1} (z) = frac{gamma }{g}left( {H_{1} - z} right)left( {cot alpha_{1} - cot theta_{1} } right)dz (12 where γ is unit weight of the backfill soil and g is acceleration due to gravity.
Calculation was done by using the thin element approximation (TEA) in the angular spectrum approach of plane waves (ASPW) [48].
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This is not conventional frame construction, in which two by fours and other thin elements are nailed together, but more akin to building with concrete slabs.
Development of investment casting process has been always a challenge for manufacturers of complex shape parts with thin elements.
(iii) Conditioning improvement of stiffness matrix that, in general, is weakened when using very thin elements.
These thin elements can efficiently utilize the limited space of hermetically sealed compressors or small engine compartments.
In this way, the overall barrier configuration is modeled as both thickness and null-thickness bodies (the boundary thickness is neglected), as representatives of very thin elements.
The study presented here is based on full-field measurements to characterize the behavior of thin elements of a standardized beam.
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