The discrete Painleveequations are nonlinear difference equations that arise as
compatibility conditions of linear systems, says Joshi, then warns that the deceptive simplicity of this statement hides deep layers of mathematical properties, which she outlines here.
The inclusion of smart materials layers will modify material properties between neighboring segments, producing discontinuities and fulfilling
compatibility conditions for the continuity of the displacement and rotation of the beam and for the equilibrium of bending moment and shear at the discontinuity points.
The basic concept in the study originated from the extension of constraints of the
compatibility conditions at free interfaces between structures and substructures.
One way in which these auxiliary equations arise is through
compatibility conditions. Moreover, an interesting result is presented by showing that there is an important link between a nonhomogeneous Schrodinger equation and a combination of surface variables which are relevant to the more physical case of space-like isothermic surfaces.
The characteristic parameters of cyclically stabilized stress-strain curves can be derived from strain-life curves using the
compatibility conditions of Equations (3) and (4):
In this methodology, the Bayesian network is pursued in two directions: (1) probabilistic surrogate modeling to estimate the output uncertainty given values of the design variables, and (2) probabilistic multidisciplinary analysis (MDA) to infer the distributions of the coupling and output variables that satisfy interdisciplinary
compatibility conditions. A copula-based sampling technique is employed for efficient sampling from the joint and conditional distributions.
It turns out that in fact additional
compatibility conditions are necessary.
Newly derived
compatibility conditions for residual deformations [[theta].sub.r] improve the quality of the mathematical model of the optimization problem and avoid a direct use of the abovementioned influence matrices.
Next, the sixth-order governing differential compatibility equations, as well as the associated end-boundary
compatibility conditions, are derived based on the virtual force principle.
The bar and elastic substrate
compatibility conditions are both enforced in the strong sense.
As emphasized in the theoretical section, the connection between a single variant of martensite and the parent austenitic phase is provided by a twinned martensitic structure, which is able to satisfy the
compatibility conditions both with the austenite (over the habit plane) and with the single variant.
satisfy the
compatibility conditions. These conditions apply to the equations (2.17) are (3ii).
