Semiexplicit Unconditionally Stable Time Integration for Dynamic Analysis Based on Composite Scheme

انتگرال گیری مستقیم نیمه‌صریح با پایداری نامشروط بر پایه ی روش آلفای تعمیم‌یافته

“…}mQD =@ |}xrLQtxU ?mQt VwQ |OOa |=y|oS}w w CkO OwHw =@ [17] "CU= xOW O=yvW}B |v=tR |=ys=oQ}R QO pw=ODt |=yVwQ =@ xU}=kt QO Q}N= Q=mx= Q QO C=@U=Lt u=tR w sHL '?U=vt "CU= QDW}@ '|vt[ |=yxw}W R= |v} wv |xDUO 'K}QY w |vt[ |=yOQm}wQ |=y|QDQ@ ? }mQD =@ |iQat 'OvwW|t xDN=vW xR=U x@ xDU@=w |=yVwQ u=wva =@ xm '|OOa |Q}op= QoDv= |vRw |=ypt=a 'u}W}B pw=ODt |=yVwQ hqNQ@ '=yQ=my= Q u}= QO [18] "Ov=xOW QwmPt |oS} w R= xO=iDU= =@ "Ovvm|t Q}}eD xrUt =@ ?U=vDt w OvDU}v C@=F 'sD}Qwor= |OOa |Q=O}=B '|R=Ux]@= Q QO CL=QY Q@ xwqa xm OQm jrN = Q |}=yVwQ u=wD|t \UwD xR=U x@ xDU@=w s}kDUt |Q}op= QoDv= VwQ u}DUNv "OwW u}t[D R}v sD} Qwor= QO xO=iDU= hOy =@ CUNv xw}W u}= [19] [20] "CU= |=yC}tm w OQ=O |vRw pt=a l} \ki CR VwQ [21] "Ov=xO=O O=yvW}B = Q CR nv=J 'xt=O= QO "OvDUy x@U=Lt p@=k K} QY CQwY x@ u; QO CaQU w u=mtQ}}eD hqNQ@ xm 'OQm x=Q= xR=U x@ xDU@=w |=yVwQ |xO=wv=N R= Qo}O [22] "OvOQm|t ^iL ?U=vt CkO =@ w Q}}eD uwO@ 'Ovvm|t =i}= MU=B QO OvtR=}v '|m}t=v}O p}rLD s=Hv= |= Q@ w Ow@ |t=oOvJ VwQ l} nv=J VwQ 'u}= R= |Q}oxQy@ =@ '2014 Rrm} Q w 9 |qwm u} wv VwQ "CU= xOw@ u} R=e; Ov}=Qi > > > < > > > : (6) |Q}op= QoDv= ?} QkD =} |}=tvnQR@ T} QD=t |xOvyO u=Wv '?…”

“…}mQD =@ %OQw; CUO x@ = Q 6 "xDi=}s}taD |=ir; w |O=yvW}B VwQ |i}] `=aW C= Q}}eD |xU}=kt "1 pmW l} |Q=O}=B [30] "Ow@ Oy=wN \wQWt Q=O}=B VwQ 'OW=@ Q= QkQ@ =]N OWQ uOw@ Q=Ou= Qm j@=]t u; |}=tvnQR@ T} QD=t |xS}w Q}O=kt |UQQ@ =@ u=wD|t = Q |OOa sD} Qwor= %OQm |UQQ@ 17 |x]@= Q ([A]) = max i=1;2;3 j i j = max (j 1 j ; j 2 j ; j 3 j) (17) |}=tvnQR@ T} QD=t |xS}w Q=Okt u}t ) = i w |i}] `=aW ? }DQD x@ i w 'u; QO \QW "OW=@ s}_vD p@=k 'q=@ |=yOt=U@ QO w 1 x@ l}ORv 'u}}=B |=yOt=U@ QO |i}] |O=yvW}B VwQ QO 'CU= xOW xQ=W= u; x@ 5 |x]@= Q QO QDW}B xm \wQWt=v |Q=O}=B pmW QO "OvDUy j@]vt sy Q@ |i}] x=oO}O R= VwQ wO xm = QJ 'Ow@ Oy=wN Q= QkQ@ R}v =@ ' C}tm hrDNt |=yQ=Okt <= R= x@ |O=yvW}B VwQ |i}] `=aW C= Q}}eD '1 xOW xU}=kt [31] CAAM lQ=tw}v [32] "OwW|t O=} |OOa |}=Q}t u=wva x@ xO}OB u}= R= "OyO "CU= u=Uwv |k}kL ?w=vD u=tR u}tND QO |Q}op= QoDv= |=]N Qou=}@ '?w=vD u=tR |O=yvW}B VwQ |}=tvnQR@ T} QD=t =@ Q_=vDt |xYNWt |}xrtH OvJ 'u; p=@vO x@ %OwW|t G= QNDU= 13 x]@=Q CQwY x@ 3 I SSG |O= R; |xHQO OvJ x@ s}taD "5 xm 'xR=U C=YNWt x@ |O=yvW}B VwQ |O=}v@ |=yx]@= Q |oDU@=w x@ xHwD =@ umtt 'CU= |}=Q}t C@Uv w |a}@] Ot=U@ pt=W |O= R; |xHQO l} Cr=L QO |xHQO OvJ |=yxv=t=U x@ |O=yvW}B VwQ s}taD xm OUQ@ Q_v x@ xvwo u}= CU= "CU= xv=t=U |a}@] |=yOt=U@ |x@U=Lt w xS}w Q=Okt |xrUt pL OvtR=}v |O= R; |Q}otWJ C=@U=Lt 'u=tR w sHL 'T=}ktnQR@ p=Ut QO xS}w x@ 'OQm}wQ u}= pt=W ?re= =y xv=t=U xvwou}= QO xS}w |=yQ=Okt |x@U=Lt xm = QJ &O@r]|t = Q |v}}=B |}=Qosy MQv 'xrUt `wv x@ xDU@ CU= umtt xm CU= |Q= QmD |=yOv}= Qi pY= R= |Q}oxQy@ =@ [18] '2017 u= Q=mty w |JOtv [33] "OvW=@ Q@xv} Ry w xDW=O |=yT}QD=t ?UL Q@ \ki u=wD|t = Q QwmPt |=ypt=a OvO=O u=Wv =yOwt Ot=aD VwQ |DWoR=@ |=yx]@= Q 'T=U= u}= Q@ "OQm u=}@ |}=Q}t w |DNU 'sQH |va} 'xR=U u}= R= |} wHxQy@ =@ "CW=O Ovy=wNv xS}w |=yQ=OQ@ w =yQ=Okt x@ |oDU@=w xvwoI}y \@=wQ CQwY x@ |O= R; |xHQO OvJ Cr=L QO |O=yvW}B VwQ |O=}v@ \@=wQ 'pY= %OvwW|t x=Q= 22 |r= 20…”

“…xvwoQy Ok=i w |t=olD K} QY VwQ l} xm [21] %CR Rrm} Q w uJ VwQ "CU= |OOa |}=Q}t |}=Q}t Ok=i w |t=owO K} QY VwQ l} xm [25] %Pajand u=}tW=y w OvSB VwQ "CU= |OOa "|Oqwi |WtN ?=k |Q=PoQ=@ w xUOvy "7 pmW w 0/0015 ? }DQD x@ xR=U ?w=vD u=tR u} QDW}@ w u} QDtm 'x}=B u}= Q@ "CU= xOW w |DNU w sQH =@ ?U=vDt 'GRr |}=Q}t T} QD=t "CU= xOt; CUO x@ x}v=F 0/519 =B Q@ '|r}Q |wor= R= |wQ}B =@ 'swU w pw= |=yOwt |= Q@ |}=Q}t C@Uv 1 ZQi =@ MU=B w xOW l} QLD wQDvUr= |xrRrR |x}=B ?=DW p=ta= =@ 'Qw@Rt ?=k [1] "CU= xOW CUO x@ x}v=F 0/025 |v=tR s=o =@ xOW|UQQ@ |=yVwQ R= xO=iDU= =@ u; |OOa |xrRrR |x}=B ?=DW \UwD xm 'xk@] 15 |Oqwi |WtN ?=k l} '|vwvm VN@ QO , q@k xm 'QwmPt ?=k |Q=PoQ=@ w xUOvy "CU= xOW p}rLD xOW l} QLD wQDvUr= "CU= 7 pmW j@=]t 'CU= xOW xar=]t [18] '2017 Tv=Q=mty w |JOtv \UwD |Q=PoxQ=tW |x}=B Q@ 'Q}N= |xR=U QO xDiQ Q=m x@ |=yuwDU w =yQ}D `]=kt ?} Q[ "Ov= xOW ?=NDv= [18] '2017 Vv=Q=mty w |JOtv Q=DWwv j@=]t '7 pmW sQowr}m 7850 w p=mU=B=o}o 200 ?…”

“…}DQD x@ xR=U ?w=vD u=tR u} QDW}@ w u} QDtm 'x}=B u}= Q@ "CU= xOW w |DNU w sQH =@ ?U=vDt 'GRr |}=Q}t T} QD=t "CU= xOt; CUO x@ x}v=F 0/519 =B Q@ '|r}Q |wor= R= |wQ}B =@ 'swU w pw= |=yOwt |= Q@ |}=Q}t C@Uv 1 ZQi =@ MU=B w xOW l} QLD wQDvUr= |xrRrR |x}=B ?=DW p=ta= =@ 'Qw@Rt ?=k [1] "CU= xOW CUO x@ x}v=F 0/025 |v=tR s=o =@ xOW|UQQ@ |=yVwQ R= xO=iDU= =@ u; |OOa |xrRrR |x}=B ?=DW \UwD xm 'xk@] 15 |Oqwi |WtN ?=k l} '|vwvm VN@ QO , q@k xm 'QwmPt ?=k |Q=PoQ=@ w xUOvy "CU= xOW p}rLD xOW l} QLD wQDvUr= "CU= 7 pmW j@=]t 'CU= xOW xar=]t [18] '2017 Tv=Q=mty w |JOtv \UwD |Q=PoxQ=tW |x}=B Q@ 'Q}N= |xR=U QO xDiQ Q=m x@ |=yuwDU w =yQ}D `]=kt ?} Q[ "Ov= xOW ?=NDv= [18] '2017 Vv=Q=mty w |JOtv Q=DWwv j@=]t '7 pmW sQowr}m 7850 w p=mU=B=o}o 200 ? }DQD x@ '?=k Kr=Yt |tHL sQH w |v=UWm xO=iDU= =@ "CU= QDt Q@ uDw}vwr}m 50 'w |rkF Q=@ COW "Ov=xOW ZQi ?amtQDt Q@ =B Q@ ?=k OwOLt <= RH= pOt [8] 'Q=oR=U sQH T} QD=t w uwDU Q}D OwOLt <RH R= "CU= p}rLD R= s=o Qy QO xmr@ 'OwW|tv xO=O C@Uv x]@=Q l} x@ uOw@K}QY xt}v |oS} w xm OwRi= O}=@ "CU= xDU@=w CaQU w u=mtQ}}eD |O=}v@ |=yx]@= Q pt=W 'sD}Qwor= |xawtHt x@ w R=}Dt= xm 'CU= K} QY , qt=m |x]@= Q…”