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The weight linear equality constraints, obtained through observations, are also implemented in the formulation to test the method.
An eight node element is developed using the full layerwise plate theory and the damage constitutive law is implemented in the formulation of a user defined element routine in Abaqus commercial software.
Hence the tangential stiffness was neglected and it was not implemented in the formulation proposed here.
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The failure criteria for the different layers of the composite material used in the PFA-TWB model have been formulated in analogy with the corresponding criteria implemented in the shell formulation.
It is found that when implemented in the weak formulation of the finite element method it can be considerably simplified.
A sequential approximate optimization approach, where approximate stochastic analyses are used during portions of the optimization process, is implemented in the proposed formulation.
In our calculations, the density functional theory (DFT) is approximated using local density approximation (LDA) and its generalized gradient corrections (GGA) as implemented in the PBE formulation [19].
However, due to the current limitations in far-field boundary conditions implemented in the original NMM formulation, NMM has not been used to carry out seismic response analysis.
An extended prediction self-adaptive control (EPSAC) approach to the multi-step predictor is implemented in the development of MPC formulation.
The formulation is implemented in the same way as conventional finite element method.
The AUSM+, HLLC, and Godunov methods are presented and implemented in the context of arbitrary Lagrangian Eulerian formulation for solving the unsteady compressible Euler equations.
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