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

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

“…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.…”

“…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.…”

“…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.…”

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

“…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.…”

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

“…}=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] …”