... and perturbed Laplace equations associated with antiplane fracture in a graded material. We present the out-of-plane displacement and the shear stress solutions for a crack in exponentially and linearly graded materials by considering the gradation of the shear modulus either parallel or perpendicular...

... and supersonic by solving the Laplace equation and the Bessel function of imaginary argument, and analyze the phenomena of wrap-around fin rolling moment generation at angle of attack zero, and discuss the reason. The flow field of a projectile with wrap-around fins is solved by numerical method to check...

... to the solution to Laplace’s equation given in Eq. 25 , the pressure distribution throughout the foam can be determined. It is recognized that each term in Eq. 25 will satisfy the free surface boundary condition given by Eq. 18a if 26 J 0 ( k n R ) = 0 Substituting Eq. 21 into Eq...

... Laplace equations integration finite element analysis flow instability flow visualisation wakes external flows During the last three decades several studies appeared concerning the representation of the Navier-Stokes equations in terms of non-primitive variables (namely the vorticity...

... Laplace equation, assuming that the thermal conductivity varies exponentially. The corresponding boundary integral equation formulation, which turns out to be somewhat different from the homogeneous media case, is also obtained, and numerical results based upon a Galerkin approximation are presented...