Sentence examples for objective derivatives from inspiring English sources

The evolution in time for the Cauchy stress, plastic part of deformation, tensorial hardening variables and elastic rotations involves the objective derivatives associated with the same elastic spin.

A new objective derivative of back stress was proposed for kinematic hardening.

It is shown here that using hypoelastic law with an objective derivative based on the warp and weft fibre rotation tensors can correctly trace the specific behaviour of the woven materials.

A hybrid-adjoint Navier Stokes method for the pressure-based computation of hydrodynamic objective functional derivatives with respect to the shape is systematically derived in three steps: The underlying adjoint partial differential equations and boundary conditions for the frozen-turbulence Reynolds-averaged Navier Stokes equations are considered in the first step.

The Nelder Mead simplex algorithm is a classical very powerful local descent algorithm, making no use of the objective function derivatives.

A trial elastic deviatoric stress state is obtained by integrating a rate equation, cast in the form of an objective (Jaumann) derivative, based on Hooke's law.

During the consecutive trials in Chebyshev approximation, a new approach is taken to renew the design points φi by plotting the graph of the objective functions derivative and taking the roots of it as new design points with two boundary points.

For this purpose, we use the extremum search method which consists of finding the zeros of the derivative of the objective function derived from the estimated orthogonal subspace, F = a H U ̃ p U ̃ p H a (4.1).

At the other boundary,, the derivative of the objective function is: This derivative is negative only when the first term in the numerator is negative, i.e., or rearranged: (9) This is the necessary and sufficient condition for the optimal allocation being to choose the maximal affordable number of subjects,, and measure on one occasion for each of these.

Next, the topological derivative of the objective functional is derived.

This paper focuses on a class of nonlinear optimization subject to linear inequality constraints with unavailable-derivative objective functions.