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James A. Liggett

Other affiliations: University of Iowa
Bio: James A. Liggett is an academic researcher from Cornell University. The author has contributed to research in topics: Boundary value problem & Finite element method. The author has an hindex of 29, co-authored 83 publications receiving 4118 citations. Previous affiliations of James A. Liggett include University of Iowa.


Papers
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Journal ArticleDOI
TL;DR: In this article, a multidomain boundary element formulation for the analysis of general two-dimensional plane strain/stress crack problems is presented, and the analyses were performed using traction singular quater-point boundary elements on each side of the crack tip(s) with and without transition elements.
Abstract: A multidomain boundary element formulation for the analysis of general two-dimensional plane strain/stress crack problems is presented. The numerical results were accurate and efficient. The analyses were performed using traction singular quater-point boundary elements on each side of the crack tip(s) with and without transition elements. Traction singular quarter-point boundary elements contain the correct √r displacement and 1/√r traction variations at the crack tip. Transition elements are appended to the traction singular elements to model the √r displacement variation. The 1/√r traction singularity is not represented with these elements. Current research studies for the crack propagation analysis of quasi-static and fatigue fracture problems are discussed.

548 citations

Journal ArticleDOI
TL;DR: In this paper, the adjoint solution of the system (generally easier than the transient analysis) to find gradient data and a Jacobian matrix are used to find a Hessian matrix, which is used in the Levenberg-Marquardt method to adjust parameters so as to minimize the difference between calculated and measured heads.
Abstract: Modern monitoring devices can inexpensively extract a huge amount of data from water-distribution systems through measurements of pressure (and sometimes flows). These data can be used in algorithms for transient analysis, time-lagged calculations, inverse calculations, and event detection to continuously determine the calibration and the general state of health of the distribution system. The last three calculations depend on the first. The most useful of those three is the inverse calculation, which can calibrate while determining leaks or unauthorized use. A key to efficient calculation is the adjoint solution of the system (generally easier than the transient analysis) to find gradient data and a Jacobian matrix. These are used to find a Hessian matrix, which is used in the Levenberg-Marquardt method to adjust parameters so as to minimize the difference between calculated and measured heads. The adjoint method is also used to compute sensitivities, which are valuable in judging the quality of the solution.

412 citations

Journal ArticleDOI
TL;DR: In this article, an inverse problem is formulated with equivalent orifice areas of possible leaks as the unknowns, and the variance of leak areas, based on the quality of system characteristics and pressure data, indicates the likely accuracy of the results.
Abstract: Leak detection in water‐distribution systems can be accomplished by solving an inverse problem using measurements of pressure and/or flow. The problem is formulated with equivalent orifice areas of possible leaks as the unknowns. Minimization of the difference between measured and calculated heads produces a solution for the areas. The quality of the result depends on number and location of the measurements. A sensitivity matrix is key to deciding where to make measurements. Both location and magnitude of leaks are sensitive to the quantity and quality of pressure measurements and to how well the pipe friction parameters are known. The overdetermined problem (more measurements than suspected leaks) gives the best results, but some information can be derived from the underdetermined problem. The variance of leak areas, based on the quality of system characteristics and pressure data, indicates the likely accuracy of the results. The method will not substitute for more traditional leak surveys but can serve...

307 citations

Journal ArticleDOI
TL;DR: In this paper, the Fourier series is used to detect, locate, and quantitatively quantify a 0.1% size leak with respect to the cross-sectional area of a pipeline, and different damping ratios of various Fourier components are used to find the location of a leak.
Abstract: Leaks in pipelines contribute to damping of transient events. That fact leads to a method of finding location and magnitude of leaks. Because the problem of transient flow in pipes is nearly linear, the solution of the governing equations can be expressed in terms of a Fourier series. All Fourier components are damped uniformly by steady pipe friction, but each component is damped differently in the presence of a leak. Thus, overall leak-induced damping can be divided into two parts. The magnitude of the damping indicates the size of a leak, whereas different damping ratios of the various Fourier components are used to find the location of a leak. This method does not require rigorous determination and modeling of boundary conditions and transient behavior in the pipeline. The technique is successful in detecting, locating, and quantifying a 0.1% size leak with respect to the cross-sectional area of a pipeline.

273 citations


Cited by
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Book ChapterDOI
01 Jan 1993
TL;DR: In this paper, the authors focus on the fundamentals of poroelasticity, and discuss the formulation and analysis of coupled deformation-diffusion processes, within the framework of the Biot theory of pore elasticity.
Abstract: Publisher Summary This chapter focuses on fundamentals of poroelasticity. The presence of a freely moving fluid in a porous rock modifies its mechanical response. Two mechanisms play a key role in the interaction between the interstitial fluid and the porous rock: (i) an increase of pore pressure induces a dilation of the rock; and (ii) compression of the rock causes a rise of pore pressure, if the fluid is prevented from escaping the pore network. These coupled mechanisms bestow an apparent time-dependent character to the mechanical properties of the rock. If excess pore pressure, induced by compression of the rock, is allowed to dissipate through diffusive fluid mass transport, further deformation of the rock progressively takes place. The rock is more compliant under drained conditions than undrained ones. The chapter discusses the formulation and analysis of coupled deformation–diffusion processes, within the framework of the Biot theory of poroelasticity. The Biot model of a fluid-filled porous material is constructed on the conceptual model of a coherent solid skeleton and a freely moving pore fluid.

1,056 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present the techniques, advances, problems and likely future developments in numerical modelling for rock mechanics and discuss the value that is obtained from the modelling, especially the enhanced understanding of those mechanisms initiated by engineering perturbations.

976 citations

Journal ArticleDOI
TL;DR: In this article, an approximate theory is presented for non-breaking waves and an asymptotic result is derived for the maximum runup of solitary waves on plane beaches, and a series of laboratory experiments is described to support the theory.
Abstract: This is a study of the runup of solitary waves on plane beaches. An approximate theory is presented for non-breaking waves and an asymptotic result is derived for the maximum runup of solitary waves. A series of laboratory experiments is described to support the theory. It is shown that the linear theory predicts the maximum runup satisfactorily, and that the nonlinear theory describes the climb of solitary waves equally well. Different runup regimes are found to exist for the runup of breaking and non-breaking waves. A breaking criterion is derived for determining whether a solitary wave will break as it climbs up a sloping beach, and a different criterion is shown to apply for determining whether a wave will break during rundown. These results are used to explain some of the existing empirical runup relationships.

866 citations

Journal ArticleDOI
TL;DR: In this article, a two-dimensional dual boundary element method for linear elastic crack problems is presented. But the authors focus on the effective numerical implementation of the method, and they do not address the problem of collocation at crack tips, crack kinks and crack-edge corners.
Abstract: SUMMARY The present paper is concerned with the effective numerical implementation of the two-dimensional dual boundary element method, for linear elastic crack problems. The dual equations of the method are the displacement and the traction boundary integral equations. When the displacement equation is applied on one of the crack surfaces and the traction equation on the other, general mixed-mode crack problems can be solved with a single-region formulation. Both crack surfaces are discretized with discontinuous quadratic boundary elements; this strategy not only automatically satisfies the necessary conditions for the existence of the finite-part integrals, which occur naturally, but also circumvents the problem of collocation at crack tips, crack kinks and crack-edge corners. Examples of geometries with edge, and embedded crack are analysed with the present method. Highly accurate results are obtained, when the stress intensity factor is evaluated with the J-integral technique. The accuracy and efficiency of the implementation described herein make this formulation ideal for the study of crack growth problems under mixed-mode conditions.

656 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present an overview of both historic developments and present research and practice in the field of hydraulic transients, including mass and momentum equations for one-dimensional flows.
Abstract: Hydraulic transients in closed conduits have been a subject of both theoretical stud intense practical interest for more than one hundred years. While straightforward in te of the one-dimensional nature of pipe networks, the full description of transient fluid fl pose interesting problems in fluid dynamics. For example, the response of the turbu structure and strength to transient waves in pipes and the loss of flow axisymme pipes due to hydrodynamic instabilities are currently not understood. Yet, such u standing is important for modeling energy dissipation and water quality in transient flows. This paper presents an overview of both historic developments and presen research and practice in the field of hydraulic transients. In particular, the paper cusses mass and momentum equations for one-dimensional Flows, wavespeed, nu solutions for one-dimensional problems, wall shear stress models; two-dimensional and momentum equations, turbulence models, numerical solutions for two-dimen problems, boundary conditions, transient analysis software, and future practical an search needs in water hammer. The presentation emphasizes the assumptions and tions involved in various governing equations so as to illuminate the range of applic ity as well as the limitations of these equations. Understanding the limitations of cu models is essential for (i) interpreting their results, (ii) judging the reliability of the da obtained from them, (iii) minimizing misuse of water-hammer models in both research practice, and (iv) delineating the contribution of physical processes from the contribu of numerical artifacts to the results of waterhammer models. There are 134 refrences in this review article.@DOI: 10.1115/1.1828050 #

630 citations