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Journal ArticleDOI

Weight function for an elliptic crack in an infinite medium. I. Normal loading

01 Jun 2000-International Journal of Fracture (Kluwer Academic Publishers)-Vol. 103, Iss: 3, pp 227-241
TL;DR: In this paper, an integral equation method has been used to derive the crack opening displacement of an elliptic crack in an infinite elastic medium subjected to a concentrated pair of point force loading at an arbitrary location on the crack faces.
Abstract: A recently developed integral equation method has been used to derive the crack opening displacement of an elliptic crack in an infinite elastic medium subjected to a concentrated pair of point force loading at an arbitrary location on the crack faces. These results have been used to obtain the stress intensity factor along the elliptic crack front which corresponds to the weight function for an elliptic crack under normal loading. Analytical expression of the weight function can be used to derive the stress intensity factor for both polynomial loading as well as non-polynomial loading.
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Journal ArticleDOI
TL;DR: The authors investigated 90 elementary teach- ers' ability to identify two systematic error patterns in subtraction and then prescribe an instructional focus and found that more than half of the teachers chose to address basic subtraction facts first during instruction regardless of error type.
Abstract: The present study investigated 90 elementary teach- ers' ability to identify two systematic error patterns in subtraction and then prescribe an instructional focus. Presented with two sets of 20 completed subtraction problems comprised of basic facts, computation, and word problems representative of two students' math performance, participants were asked to examine each incorrect subtraction problem and describe the errors. Participants were subsequently asked which type of error they would address first during math instruction to correct students' misconceptions. An analysis of the data indicated teachers were able to describe specific error patterns. However, they did not base their instruc- tional focus on the error patterns identified, and more than half of the teachers chose to address basic subtraction facts first during instruction regardless of error type. Limitations of the study and implications for practice are discussed.

85 citations

Journal ArticleDOI
TL;DR: In this paper, a coupled finite-volume (FV)/finite-area (FA) model was proposed to simulate the propagation of multiple hydraulically driven fractures in two and three dimensions at the wellbore and pad scale.
Abstract: This paper presents the formulation and results from a coupled finite-volume (FV)/finite-area (FA) model for simulating the propagation of multiple hydraulically driven fractures in two and three dimensions at the wellbore and pad scale. The proposed method captures realistic representations of local heterogeneities, layering, fracture turning, poroelasticity, interactions with other fractures, and proppant transport. We account for competitive fluid and proppant distribution between multiple fractures from the wellbore. Details of the model formulation and its efficient numerical implementation are provided, along with numerical studies comparing the model with both analytical solutions and field results. The results demonstrate the effectiveness of the proposed method for the comprehensive modeling of hydraulically driven fractures in three dimensions at a pad scale.

40 citations

Journal ArticleDOI
TL;DR: In this paper, a general mathematical form of point load weight function is proposed based on the properties of weight functions and the available weight functions for two-dimensional cracks for the calculation of stress intensity factors in embedded elliptical cracks.

35 citations


Cites background from "Weight function for an elliptic cra..."

  • ...Several attempts have been made to derive the weight functions for embedded elliptical crack by solving the problem analytically, see recent development in [13,14]....

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Journal ArticleDOI
TL;DR: DDSim as mentioned in this paper is a next-generation damage and durability simulator with a hierarchical, multiscale, "search and simulate" strategy, which consists of three levels: initial, reduced order, conservative screening, based on a linear finite element analysis of the uncracked component, to determine the most life-limiting locations for intrinsic material flaws.

28 citations