Numerical integration over arbitrary polygonal domains based on Schwarz-Christoffel conformal mapping

This paper presents a new numerical integration technique oil arbitrary polygonal domains. The polygonal domain is mapped conformally to the unit disk using Schwarz-Christoffel mapping and a midpoint quadrature rule defined oil this unit disk is used. This method eliminates the need for a two-level isoparametric mapping Usually required. Moreover, the positivity of the Jacobian is guaranteed. Numerical results presented for a few benchmark problems in the context of polygonal finite elements show that the proposed method yields accurate results.

Water-wave scattering by two submerged plane vertical barriers-Abel integral-equation approach

The classical problem of surface water-wave scattering by two identical thin vertical barriers submerged in deep water and extending infinitely downwards from the same depth below the mean free surface, is reinvestigated here by an approach leading to the problem of solving a system of Abel integral equations. The reflection and transmission coefficients are obtained in terms of computable integrals. Known results for a single barrier are recovered as a limiting case as the separation distance between the two barriers tends to zero. The coefficients are depicted graphically in a number of figures which are identical with the corresponding figures given by Jarvis (J Inst Math Appl 7:207-215, 1971) who employed a completely different approach involving a Schwarz-Christoffel transformation of complex-variable theory to solve the problem.

Depressed weir with two unequal sheetpiles in anisotropic soil

An analytical solution is presented, making use of the Schwartz-Christoffel transformation, for determining the seepage characteristics for the problem of flow under a weir having two unequal sheetpiles at the ends and embedded in an anisotropic porous medium of finite thickness. Results for several particular cases of simple hydraulic structures can be obtained from the general solution presented. Numerical results in nondimensional form have been given for quantity of seepage and exit gradient distribution for various conditions in the equivalent transformed isotropic section and, by making use of the physical parameters in the actual anisotropic plane and the set of transformation relations given, these quantities (seepage loss, exit gradient) can be interpreted in the actual anisotropic physical plane.

Elastic constants of triclinic copper sulphate pentahydrate crystals

Using an iterative technique to obtain the exact solutions of the cubic Christoffel equation, the 21 elastic constants of copper sulphate pentahydrate have been determined at 25°C by the ultrasonic pulse echo method. The elastic constants, referred to the IRE recommended system of axes, are c11=5·65, c12=2·65, c13=3·21, c14=−0·33, c15=−0·08, c16=−0·39, c22=4·33, c23=3·47, c24=−0·07, c25=−0·21, c26=0·02, c33=5·69, c34=−0·44, c35=−0·21, c36=−0·16, c44=1·73, c45=0·09, c46=0·03, c55=1·22, c56=−0·26 and c66=1·00 in units of 1010 N m−2.