Papers by Keyword: Conformal Mapping

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Authors: Babak Saghafi, Karen Abrinia
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.
Authors: Lu Guan
Abstract: Using the method of complex analysis, the study investigates the circular orifice problem for 2k 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.
Authors: Jun Lin Li, Hai Xia Cheng
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.
Authors: Zhu Chen
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.
Authors: Tae Hyun Baek, Seung Kee Koh, Tae Geun Park
Abstract: hybrid experimental-numerical method is presented for determining the stresses around a circular hole in a finite-width, tensile loaded plate. Calculated fringes obtained by FEA provided the information about the external boundary of the hybrid element, and those fringes on straight lines were used for hybrid analysis. In order to see the effects of varying stress field, different numbers of terms in a power-series representation of the complex type stress function were tested. Actual and reconstructed fringes were compared. The hybrid results were highly comparable with those predicted by FEA. The result showed that this approach is effective and promising because isochromatic data along the straight lines in photoelasticity can be conveniently measured by use of phase shifting photoelasticity.
Authors: Hong Li, Guang Lei Li, Da Lu Qiu
Abstract: A solving method with complex variable function which is fit for numerical calculation for stress concentration phenomena on an infinite plate where there are curvilinear holes is described in this paper. According to the method, the computer programs are made to study the stress concentration problems with curvilinear holes (hexagonal form and oblate form) that are often used in ship and other engineering structures. The maximum of the stresses at the edge of the holes and the distribution of the stresses under axial loading and pure bending moment are calculated respectively. Furthermore, the variations of factors of stress concentration with the different proportions of length and width for oblate holes are considered. The influence on factors of stress concentration due to the change of plate width is indicated. The solutions are consistent with the numerical results of boundary element method, finite element method and related articles.
Authors: Dong Yan Wang, Lian Hong Zhang
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.
Authors: Lu Guan
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.
Authors: Yu Li Shao, Yan Xiao Li, Bao Liang Wang
Abstract: For complex pavements, there are circular, elliptic and rectangular shape vehicle loads under different conditions. Treatment way of vehicle loads is studied with conformal mapping method in this paper. Approach for transformation them to uniform circular shape is also researched. Terminal goal is enable the road engineers to accommodate changes of vehicle loads in their used way to pavement design which using static loads with uniform vertical pressure distribution without any more attached difficult.
Authors: Tian Shu Song, Dong Li, Ming Ju Zhang, Yue Fa Zhou
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.
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