A new semi-analytical method with diagonal coefficient matrices for potential problems

Khaji, N.; Khodakarami, Mohammad Iman

doi:10.1016/j.enganabound.2011.01.011

Cited by 31 publications

(14 citation statements)

References 23 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 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%

“…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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Section: Fundamentals Of the Semi-analytical Methodsmentioning

confidence: 98%

Section: Solution Proceduresmentioning

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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“…In addition, isogeometric analysis has successfully been fused with the SBFEM principles [27]. Finally, a novel variation of SBFEM with diagonalized and thus decoupled coefficient matrices has been developed [28], in which each node can be treated independently.…”

Section: Introductionmentioning

confidence: 99%

The Scaled Boundary Finite Element Method for the Efficient Modelling of Linear Elastic Fracture

Egger¹,

Triantafyllou²,

Chatzi³

2016

Proceedings of the 9th International Conference on Fracture Mechanics of Concrete and Concrete Structures

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Abstract. In this work, a study of computational and implementational efficiency is presented, on the treatment of Linear Elastic Fracture Mechanics (LEFM) problems. To this end, the Scaled Boundary Finite Element Method (SBFEM), is compared against the popular eXtended Finite Element Method (XFEM) and the standard FEM approach for efficient calculation of Stress Intensity Factors (SIFs). The aim is to examine SBFEM's potential for inclusion within a multiscale fracture mechanics framework. The above features will be exploited to solve a series of benchmarks in LEFM comparing XFEM, SBFEM and commercial FEM software to analytical solutions. The extent to which the SBFEM lends itself for inclusion within a multiscale framework will further be assessed.

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“…}=Q[ pL CkO w CiQ u}@ R= lQD |=yx@r |R=UpOt x@ R=}v 'CW=O u=tr= VwQ QO xm |}=Hv; R= "CU= xDi=} xaUwD Q=}U@ VwQ u}= RwQt= x@ =D w Ci=} x@ C@Uv |D=@U=Lt |=yxv}Ry^=Lr R= 'OwW|t |Ov@u=tr= xRwL RQt \ki |RQt \=kv QO =yVvD '|RQt u=tr= VwQ QO "OQ=O |Q}osWJ Vy=m [26] "CU= xOW O=yvW}B |RmQt lQD VwQ x@ u=wD|t u=}t u}= QO "Ovvm x@U=Lt = Q Rt=}r} w |QU ? }=Q[ xm Ov=xDUv=wD OwOLt <= RH= VwQ w u=tr= uwO@ |@}mQD VwQ [27] 'xOWT=}kt |RQt OwOLt <= RH= |@}mQD OwOLt <= RH= VwQ w [30w29] '|@}mQD lQD u=tr= VwQ [28] 'xOWT=}kt |RQt "Ov=xOQm x@U=Lt pw= Owt |= Q@ = Q Rt=}r} w |QU pw= |xrtH 5 xm 'OQm xQ=W= [31] 'p=Dm= Qi w |H=N \UwD xm 'CU= RHt CqO=at VwQ 'O}OH , =D@Uv |=yVwQ R= |m} "CU= xDiQo Q= Qk |UQQ@ OQwt |irDNt p=Ut pL |= Q@ w 'CU= xOW O=yvW}B u= Q=mty [32] 'p}Uv=DB p=Ut pL x@ u=wD|t = RHt CqO=at VwQ |=yOQw=DUO u} QDsyt R= "OQm xQ=W= [37] …”

mentioning

confidence: 99%

تقریب ضرایب سری ویلیامز در مسائل مکانیک شکست ارتجاعی خطی با استفاده از روش معادلات مجزا

یزدانی¹,

خاجی²

2017

مهندسی عمران

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A new semi-analytical method with diagonal coefficient matrices for potential problems

Cited by 31 publications

References 23 publications

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

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

The Scaled Boundary Finite Element Method for the Efficient Modelling of Linear Elastic Fracture

تقریب ضرایب سری ویلیامز در مسائل مکانیک شکست ارتجاعی خطی با استفاده از روش معادلات مجزا

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