- ...step.
- Note, however, that for static
weights, the matrices become time invariant and the computational cost
is reduced significantly.
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- ...directions.
- In the case of the
D-NURBS curve, there are only two terms and two weighting functions in
the potential energy form because of the single spatial parameter
*u*:
88#88.
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- ...155#155.
- The entries of the D-NURBS curve element
stiffness matrix are 156#156, where
157#157
Given integer 148#148, we can find Gauss quadrature abscissas
152#152 and weights 150#150 such that 145#145 can be approximated as
follows: 158#158.
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- ...panels.
- At present, our software assumes uniform
mass, damping, and elasticity densities over the parametric domain,
except across trimming boundaries (see Section
7.2). This is straightforwardly generalizable to
accommodate the nonuniform density functions in our formulation,
although our user interface would have to be extended to afford the
user full control in specifying these functions.
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- ...point.
- Cross-validation
[41] provides a principled approach to choosing the relevant physical
parameters-typically the ratio of data force spring constants to
surface stiffnesses-for given data sets. For the special case of
zero-mean Gaussian data errors, optimal approximation in the least
squares residual sense results when
*c* is proportional to the inverse
variance of data errors [35].
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