The Experts below are selected from a list of 225 Experts worldwide ranked by ideXlab platform
J. W. Wang - One of the best experts on this subject based on the ideXlab platform.
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Thermal Stress Analysis of a Subsurface Inclined Crack Subjected to a Point Heat Source
Journal of Energy Resources Technology-transactions of The Asme, 1997Co-Authors: C. K. Chao, J. W. WangAbstract:The thermoelastic response of a subsurface inclined crack under the application of a point heat source is studied in this paper. Based on the Complex Variable Theory and the method of analytical continuation, the problem is formulated by two stress functions and a temperature function which are enforced to satisfy the interface condition. The singular integral equations for both the temperature field and thermoelastic field are derived by taking dislocation junctions along the crack border such that both the insulated condition and traction-free condition are satisfied on the crack surface. Numerical results of the thermal stress intensity factors for different geometric configurations are discussed in detail and provided in graphical form. The results obtained in this study will be helpful in understanding the problems of seismology generated by thermal loading in a cracked body.
Zhiguo Liu - One of the best experts on this subject based on the ideXlab platform.
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A three-term theta function identity and its applications
Advances in Mathematics, 2005Co-Authors: Zhiguo LiuAbstract:In this paper, we establish a three-term theta function identity using the Complex Variable Theory of elliptic functions. This simple identity in form turns out to be quite useful and it is a common origin of many important theta function identities. From which the quintuple product identity and one general theta function identity related to the modular equations of the fifth order and many other interesting theta function identities are derived. We also give a new proof of the addition theorem for the Weierstrass elliptic function ℘. An identity involving the products of four theta functions is given and from which one theta function identity by McCullough and Shen is derived. The quintuple product identity is used to derive some Eisenstein series identities found in Ramanujan's lost notebook and our approach is different from that of Berndt and Yee. The proofs are self contained and elementary.
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a theta function identity and its implications
Transactions of the American Mathematical Society, 2004Co-Authors: Zhiguo LiuAbstract:In this paper we prove a general theta function identity with four parameters by employing the Complex Variable Theory of elliptic functions. This identity plays a central role for the cubic theta function identities. We use this identity to re-derive some important identities of Hirschhorn, Garvan and Borwein about cubic theta functions. We also prove some other cubic theta function identities. A new representation for Π∞ n=1 (1-q n ) 10 is given. The proofs are self-contained and elementary.
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Some Eisenstein series identities related to modular equations of the seventh order
Pacific Journal of Mathematics, 2003Co-Authors: Zhiguo LiuAbstract:In this paper we will use one well-known modular equation of seventh order, one theta function identity of S. McCullough and L.-C. Shen, 1994, and the Complex Variable Theory of elliptic functions to prove some new septic identities for theta functions. Then we use these identities to provide new proofs of some Eisenstein series identities in Ramanujan's notebooks or lost notebook. We also derive a new identity for Eisenstein series and some curious trigonometric identities.
C. K. Chao - One of the best experts on this subject based on the ideXlab platform.
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Thermal Stress Analysis of a Subsurface Inclined Crack Subjected to a Point Heat Source
Journal of Energy Resources Technology-transactions of The Asme, 1997Co-Authors: C. K. Chao, J. W. WangAbstract:The thermoelastic response of a subsurface inclined crack under the application of a point heat source is studied in this paper. Based on the Complex Variable Theory and the method of analytical continuation, the problem is formulated by two stress functions and a temperature function which are enforced to satisfy the interface condition. The singular integral equations for both the temperature field and thermoelastic field are derived by taking dislocation junctions along the crack border such that both the insulated condition and traction-free condition are satisfied on the crack surface. Numerical results of the thermal stress intensity factors for different geometric configurations are discussed in detail and provided in graphical form. The results obtained in this study will be helpful in understanding the problems of seismology generated by thermal loading in a cracked body.
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Explicit solutions for the elastic and thermoelastic fields with a rigid circular-arc inclusion
International Journal of Fracture, 1994Co-Authors: M. H. Shen, C. K. ChaoAbstract:A general solution to the elastic and thermoelastic problems with a rigid circular-arc inclusion is presented. The proposed analysis is based upon the Complex Variable Theory dealing with sectionally holomorphic functions which is reduced to the solution of the Hilbert problem. It is indicated that both the stress and thermal stress fields near the inclusion tip possess a square-root singularity similar to that for the corresponding crack problem. In analogy to the stress intensity factors defined for crack problem, stress singularity coefficients are introduced in this paper to characterize the near tip fields. Complete stress fields and the corresponding stress singularity coefficients as the circular-arc inclusion are under uniform remote load, concentrated force and uniform heat flux are given. Failure initiation of an infinite plate embedded with a rigid arc inclusion under different loading conditions is also discussed.
Pavel Roslyakov - One of the best experts on this subject based on the ideXlab platform.
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multi parameter description of the crack tip stress field analytic determination of coefficients of crack tip stress expansions in the vicinity of the crack tips of two finite cracks in an infinite plane medium
International Journal of Solids and Structures, 2016Co-Authors: L V Stepanova, Pavel RoslyakovAbstract:Abstract The study is aimed at analytical determination of coefficients in crack tip stress expansions for two collinear finite cracks of equal lengths in an infinite plane medium. The study is based on the solutions of the Complex Variable Theory in plane elasticity Theory. Multiparametric presentation of the stress field near the crack tips in the infinite plate with two collinear cracks of finite lengths is obtained and analyzed for a full range of mixed mode loading from pure tension to pure shear. The method of analytical determination of coefficients of the complete asymptotic expansion of the stress field near the crack tip is presented. The influence of consideration of various numbers of terms of the series expansion on the stress distribution is discussed, and the significance of the multi-parameter fracture mechanics approach is emphasized.
Chun-bo Lin - One of the best experts on this subject based on the ideXlab platform.
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Magnetoelastic stresses in a three-phase composite cylinder subject to a uniform magnetic induction
International Journal of Engineering Science, 2010Co-Authors: Chun-bo Lin, Jui-lin Lee, Shin-cheng ChenAbstract:A solution of magnetoelastic stresses on a three-phase composite cylinder subjected to a remote uniform magnetic induction is derived in this study. Based upon the Complex Variable Theory and the method of analytical continuation together with alternating technique, the general expressions of both the magnetic and the magnetoelastic field quantities can be obtained. The variations of the magnetoelastic stress on various parameters are displayed in graphic form. Comparisons between the results of this work and the existing solutions in literature under special cases reveal that the present solution is correct and general.
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The magnetoelastic problem of a crack in a soft ferromagnetic solid
International Journal of Solids and Structures, 2002Co-Authors: Chun-bo Lin, Chau-shioung YehAbstract:The induced magnetoelastic stresses and Maxwell stresses generated by a uniform magnetic field in an infinite soft ferromagnetic medium containing a finite plane crack are analyzed in this paper. The soft ferromagnetic elastic solids with a finite crack are considered to be high magnetic susceptibility materials. By the use of Complex Variable Theory, the exact solutions for magnetic field quantities and both magnetoelastic stresses and Maxwell stresses can be obtained in a closed form. The singularity of stress intensity in the vicinity of crack tip and crack opening condition can also be determined.