Papers by Keyword: Conformal Mapping

Abstract: Using the method of complex analysis, the paper investigates the plane elasticity problem of circular orifices with four-cracks through conformal mapping, and provides an exact analytical solution for the crack-tip stress intensity factor (SIF). From this we have simulated circular orifices with three-cracks, symmetrical four-cracks, asymmetrical collinear double-cracks, and symmetrical collinear double-cracks; as well as the crack problems of asymmetrical cross-shaped cracks, symmetrical cross-shaped cracks, and T-shaped cracks.

Abstract: Using the method of complex analysis, the study investigates the circular orifice problem for 2^k periodic radial cracks through constructing conformal mapping, and provides an analytical solution for the crack-tip stress intensity factor (SIF). From this we have simulated the circular orifice problems of cross-shaped cracks, symmetrical eight-cracks, single cracks, symmetrical double-cracks, and symmetrical four-cracks.

Abstract: Using the method of complex analysis and by constructing conformal mapping, the study investigates the plane elasticity problem of star-shaped cracks and provides an analytical solution for the stress intensity factor (SIF) of crack-tip type I and II. Problems of the classic Griffith crack, the cross-shaped crack, concurrent uniformly distributed three-cracks and symmetrical eight-cracks are also simulated.

Abstract: Using the complex variable function method and the technique of conformal mapping, the fracture mechanics of two symmetric collinear cracks originating from an elliptical hole in a one-dimensional (1D) hexagonal piezoelectric quasicrystals (QCs) are investigated under anti-plane shear loading and electric loading. The crack is assumed to be either electrical impermeable or permeable. The exact solutions in closed-form of the stress intensity factors (SIFs) of the phonon field and the phason field, and the electric displacement intensity factors (EDIFs) are obtained. In the limiting cases, the new results such as Griffith crack, a circular hole with equal two edge cracks and cross crack can be obtained from the present solutions. In the absence of the phason field, the obtainable results in this paper match with the classical results.

Abstract: Material flow pattern in extrusion is an important part of the forming process. Understanding and formulating the material flow helps to determine the optimum shape of the die and important details of the process. In this paper, physical modelling of forward extrusion of non-symmetric L-shape section has been carried out to obtain an experimental understanding of the material flow pattern. A theoretical formulation using the conformal mapping theory has also been presented to predict the material flow pattern. The conformal mapping function was set up to translate the non-circular cross-section region of special-shaped products into unit dish. The results for the material flow pattern for the forward extrusion of L shaped profile from circular billets are presented here. In the physical modelling tests plasticine was used as the model material and different coloured layers of plasticine were used to build up the billet. Experimental and theoretical results were compared and good agreements were observed.

Abstract: At present, only the flat ground surface problem is investigated in most studies on ground effect, which is not effective for practical applications due to the universal existence of curved ground surface. In this paper, the lift calculation of a two-dimensional flat plate airfoil placed near a curved ground surface is investigated. In order to calculate the complex velocity in the flow field, the complex variable function theory is employed. The conformal mapping method is applied to transform the flat plate airfoil to a cylinder in the uniform flow. Moreover, the discrete vortices method is modified to convert the curved ground surface to a series of discrete boundary elements. Two kinds of curved ground surfaces are considered: semicylindrical hollows and semicylindrical hills. It is shown that the lift fluctuation of flat plate airfoil located near a hollow or a hill is considerably serious, which should be considered during the design of flight vehicles flying near the ground surface.

Abstract: Dynamic anti-plane behaviors are studied on two dissimilar piezoelectric media with an interfacial non-circular cavity subjected to time harmonic incident anti-plane shearing. Based on Greens function and conformal mapping method, the dynamic stress concentration factors at the edge of the non-circular cavity are obtained by applying the orthogonal function expansion technique. Numerical cases about two dissimilar piezoelectric media with an elliptic cavity are provided with different elliptic axial length ratio, different wave number and different piezoelectric characteristic parameter. The calculating results show that dynamic analyses are of importance at lower frequencies and larger piezoelectric characteristic parameters.

Abstract: According to the structure of the crank arm, the conformal mapping method was adopted to transform the elliptical section map of it to the round. Then by the slab method an analytical model for final upsetting force of the crank arm was established, which is a derivation based on assumptions of axisymmetric plastic forming status. Finally, a simulation was implemented in case of the second crank of crankshaft 6G32. Accordance to it the accuracy of the analytical model was examined. Further more the causes of the data deviation from the model and the simulation were analyzed in this thesis.

Abstract: The paper presents the magnetic field distribution from the armature winding currents in the slotted air gap of surface-mounted permanent magnet (SMPM) motors using the Schwarz- Christoffel(SC) mapping. With the method, a slotted structure of SMPM motors is transformed into a geometrically simpler domain. Compared with the result from the finite element method, the accuracy of the method is verified. The presented work can be a basic tool for optimizing design and performance analysis of permanent magnet motors.

Abstract: Fracture problem about anisotropic composite plate of curved crack is researched with the help of appropriate conformal mapping. The crack curve is transformed into a unit circle by the quoted conformal mapping function. Based on the stress boundary conditions, the special stress function is found and the expressions for the stress field and the stress intensity factor near the parabolic crack tip are obtained.