Analysis of elastostatic problems using a semi-analytical method with diagonal coefficient matrices

Khodakarami, Mohammad Iman; Khaji, N.

doi:10.1016/j.enganabound.2011.06.003

Cited by 18 publications

(24 citation statements)

References 33 publications

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“…In other words, emphasis is basically devoted to those important aspects of the method which are subjected to remarkable modifications in comparison with the previous works of the authors [32][33][34][35][36][37][38]. For more details on the formulation of the method, the readers are referred to Ref.…”

Section: Fundamentals Of the Semi-analytical Methodsmentioning

confidence: 98%

“…In elastostatic problems, F i (ξ ) varies in the undertaken domain like a body force. Therefore, F i (ξ ) is defined as a linear function such as a i ξ + b i , in which a i and b i are obtained according to traction conditions in the LCO and at the boundaries [33,34]. The proposed form of force function basically provides inappropriate displacement functions u i (ξ ) for crack problems, as is not capable of producing infinite stresses at the crack tip.…”

Section: Physical Modelingmentioning

confidence: 98%

“…In other words, the present method offers an efficient procedure for solving various problems as already reported in Refs. [32][33][34][35][36][37][38]. In this section, the required procedure for solving Euler's differential equations is illustrated, and the extension of the procedure to derive the SIFs is extensively discussed in the next section.…”

Section: Solution Proceduresmentioning

confidence: 99%

“…The governing equilibrium equations for elastostatic problems may be illustrated as integrated over the problem domain Ω. It may be shown [33] that the proposed semi-analytical method results in the following set of differential equations for elastostatic problems:…”

Section: Derivation Of Formulationsmentioning

confidence: 99%

“…A new semi-analytical method has been developed by Khaji and coworkers [32][33][34][35][36][37][38]. In this method, only boundaries of problems are discretized using specific subparametric elements and higher-order Chebyshev mapping functions.…”

Section: Introductionmentioning

confidence: 99%

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Development of a new semi-analytical method in fracture mechanics problems based on the energy release rate

2016

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The existence of crack and notch is a considerable and serious subject in the failure study of solids and structures. As most of cracked domain problems do not have closed-form solutions, numerical methods are dominant approaches dealing with fracture mechanics problems. In fracture mechanics and failure analysis, cracked media energy and consequently stress intensity factors (SIFs) play a crucial and significant role. Based on linear elastic fracture mechanics, the SIFs may be estimated using the energy release rate, as an indirect approach. This study presents the development of a new semi-analytical method to model cracked media. In this method, only the boundaries of problems are discretized using specific higher-order subparametric elements and higher-order Chebyshev mapping functions. Implementing the weighted residual method and using Clenshaw-Curtis quadrature yield diagonal Euler's differential equations. Therefore, when the local coordinate origin is located at the crack tip, the geometry of crack problems is implemented directly without further processing. In order to present crack boundary conditions, a modified form of nodal force function is presented. Validity and accuracy of the proposed method is fully illustrated by four benchmark problems, whose results agree very well with those of other numerical and/or analytical solutions existing in the literature.

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