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In this method, joint coordinates of the solar panels, yoke and the spacecraft main-body are defined as the generalized variables.
For this reason, the material model has been developed at the macroscopic scale in terms of generalized variables, aiming at computational effectiveness.
This kinematics is suitably expressed by introducing a set of generalized variables representative of the beam midline displacement field, which become the primary variables of the problem governing equations.
The finite element method for piezoelectric materials is formulated in generalized variables and co-ordinates, and the eigenvalue problem is solved directly by treating the electrical term effectively as an extra mechanical degree of freedom.
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Obviously, both the general algorithms with the generalized variable stepsizes can solve the SFP and some special variational inequality problem better.
Furthermore, we also presented a more general KM-CQ algorithm with generalized variable stepsizes.
Section 4 presents two general KM-CQ algorithms with the generalized variable stepsizes and proves the strong convergence.
We propose two more general KM-CQ algorithms with the generalized variable stepsize (1.9) or (1.10), and they can be used to approach the minimum norm solution of the SFP that solves special variational inequalities.
For a parallel solution of the QP sub-problem at each decomposition iteration, a generalized variable projection method is proposed based on an adaptive step-length selection.
First of all, the generalized variable substitution controller is designed to establish the master slave finite-time synchronization scheme for the Lorenz Stenflo systems.
Applying this criterion, some sufficient finite-time synchronization criteria under various generalized variable substitution controllers are further derived in the algebraic form.
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