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This evaluation can be only the lower bound estimation of the load carrying capacity.
The MILP also gives a lower bound estimation of the original non-linear problem, and the accuracy of the approximation is improved by iteratively updating the MILP.
In the presented method for lower bound estimation of the load carrying capacity of structures, it is postulated that the reduced local critical load should be determined taking into account the global pre-critical bending within the first order non-linear approximation to the theory of the interactive buckling of the structure.
where u 0 is a positive constant, and give upper bound estimation of the unknown function by integral inequality technique.
This paper gives an upper bound estimation of the spectral norm for r-circulant matrices with Fibonacci and Lucas numbers.
In [10], He et al. gave the upper bound estimation of the spectral norm for r-circulant matrices with Fibonacci and Lucas numbers.
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Hence, the upper/lower bound estimation of piezoelectric fracture parameters is of theoretical and practical importance.
In this paper, under different jump conditions, we will study the upper-bound estimation of the nonlinear inequality m'(t)leq p(t m(t)+q(t m^{alpha}(t). In this paper, let (0leq t_{0}< t_{1}< t_{2}
Moreover, an adaptive bound estimation algorithm is employed to estimate the upper bound of uncertainties.
By comparing the lower bound estimations for a wide range of cylinder dimensions and different engineering materials with the rupture times determined from accurate finite element calculations, it is shown that the lower bound estimations provide quite conservative lifetime predictions.
In addition, to relax the requirement for the bound of minimum approximation error, a simple bound estimation algorithm is investigated to control the motor-mechanism coupling system.
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