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By considering the j scale mth order of the BSWI scaling function as the interpolation function, an interface element was constructed, and its structure is presented in Figure 2.
Figure 2(a) shows all the scaling functions of 2D tensor products BSWI, and the wavelets of tensor products BSWI are shown in Figures 2(b), 2(c), and 2(d).
According to the Timoshenko beam theory, w([xi]) and [theta]([xi]) can be independently interpolated by BSWI scaling functions as
Taking BSWI scaling functions as interpolating function is as follows:
Submitting (16) into 14), according to the generalized variational principle, the BSWI element formulation of the solving equation can be obtained as follows:
The physical DOFs of BSWI plane rigid element in local coordinate (X, Y) are
In order to construct the BSWI plane rigid frame element the relationship between global and local coordinates should be obtained.
[[PHI].sup.T]([[xi].sub.n + 1])].sup.-T] is the BSWI element transform matrix.
This moderately deep arch is idealized with one BSWI element and analyzed for a wide range of thick to thin beams by changing the slenderness ratio of R/h.
It is noteworthy that the presence of BSWI is analogous to MFE, and the accuracy of v and d is better than MFE in a wide range of thick to thin beams, even in the thick condition.
The physical model is idealized with one BSWI element and analyzed for a wide range of thick to thin beams by changing the slenderness ratio of R/h.
Numerical results calculated by BSWI are shown in Table 2, and, as a reference, the solution given by Lee and Sin  is also shown there.
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