Sentence examples for by using the complex from inspiring English sources

Closed form solutions of elastic fields are obtained by using the complex function theory.

By using the complex modal displacement the forward and backward modes are properly identified.

Subsequently, the analyses of modal damping and frequency response for laminated composites are implemented by using the complex eigenvalue method.

This dual conceptualization leads to a holistic perspective obtained by using the complex adaptive systems framework (Dooley and Van de ven, 1999, Levin, 1998) as a lens.

In this paper, we derive the impulse response of the distributed order integrator/differentiator and its asymptotic property by using the complex path integral.

A compact analytical solution of stresses around a pin loaded hole in orthotropic plates is obtained by using the complex stress functions.

Almost all above problems were solved by using the complex-variable technique.

Smith [1] successfully solved the problem of the interaction between a screw dislocation and a circular or elliptic inclusion contained within an infinite body subject to a uniform applied shear stress at infinity by using the complex-variable function and circle theorem.

By using the aeroelastic complex modes, the aeroelastic coupled gust responses are effectively captured and interpreted.

In this Corrigendum, the singularity of the total stresses is further studied for the impermeable crack, and the intensity factors are re-derived by using the obtained complex potentials.

Proof By using the fractional complex transform (19), we obtain (22).