Sentence examples for using the variational approach from inspiring English sources

Therefore, the capability of analyzing cracked symmetric laminates using the variational approach has been enhanced significantly.

Governing equations and both classical and non-classical boundary conditions of motion are obtained using the variational approach.

In the present paper, static deformation of an eccentrically stiffened plates with partial composite action was analyzed by using the variational approach.

Based on the principle of the minimum potential energy, the governing differential equations were derived by using the variational approach with taking into consideration of strain energy of connectors between plate and stiffeners and associated boundary conditions as well.

Calculations have been performed using the variational approach, developed in [27].

He has made contributions on the well-posedness and asymptotic properties (such as large deviation principle, ergodicity and random attractor) of a general class of stochastic partial differential equations using the variational approach.

In 2005, Guo and Yu [6] took the lead in using the variational approaches to study the existence of multiple periodic solutions for (1.1), and a multiplicity result was given.

Recently, using the variational approaches, the multiplicity of the periodic solutions for the following system: { u ′ ( t ) = − Λ u ( t + r ) − f ( t, u ( t − r ) ), u ( 0 ) = − u ( 2 r ), u ( 0 ) = u ( 4 r ). was studied by Wu and Wu in [7].

We use the variational approach to deduce the overall vdW coefficients C (charge dipole dipole) and D (charge dipole quadruple) [18].

In addition, in [5 7], the authors used the variational approach to study the existence, nonexistence, multiplicity, and qualitative behavior of the solutions in the semiclassical limit for the Schrödinger-Poisson system as follows: textstylebegin{cases} -Delta u +V x u =K_{1}(x phi u+ u^{p}, -Deltaphi= K_{2}(x)u^{2}, end{cases} where (1< p<5).

The work herein shows that in multiple-point constraint applications full composite action between the shear deformable layers can be recovered by using the variational multiscale approach.