1911年，德國科學家Van Karman首先用最小應變能方法研究了在線亞洲日產一區二區:不銹鋼管彎管加工后的應力應變特性，之后的一些學者都以此方法為基礎，僅在級數的取舍等方面作了改進。Clark則認為彎管段為封閉環殼的一部分，通過薄殼方程并以兩個變量來表達這些方程，其解與已有解非常接近，且數學處理十分成功，但上述都僅限于彎曲半徑較大的情形。Pardue和Vigness,還有 Turner、Ford都研究了彎曲半徑較小的情形，給出了整個彎管截面的應力曲線。直到1956年，Kafla和Dunn注意到內壓對柔度系數的影響，指出了內壓可使彎管的柔度系數降低，剛度增大。Rodabaugh 和 George 利用能量方法研究了內壓的影響，給出了影響計算的理論公式。Clark等的計算公式和Rodabaugh等的內壓影響修正公式現在被各國規范所廣泛使用。

 我國(guo)在(zai)“八五”“九(jiu)五”科技(ji)攻(gong)關(guan)(guan)期間(jian)，已基本解決了(le)(le)(le)(le)(le)(le)(le)(le)壓力(li)容(rong)器(qi)、壓力(li)管(guan)(guan)道直(zhi)管(guan)(guan)段的(de)(de)(de)(de)(de)(de)(de)(de)塑性(xing)(xing)(xing)極(ji)限(xian)(xian)(xian)(xian)(xian)載(zai)(zai)(zai)(zai)荷計(ji)算(suan)及工(gong)程評估問題(ti)，但未涉及彎(wan)(wan)(wan)(wan)管(guan)(guan)等復(fu)雜結構。鑒于其(qi)對管(guan)(guan)道系統(tong)承載(zai)(zai)(zai)(zai)能力(li)的(de)(de)(de)(de)(de)(de)(de)(de)重(zhong)要(yao)影響，國(guo)家科技(ji)部將壓力(li)管(guan)(guan)道元件的(de)(de)(de)(de)(de)(de)(de)(de)安(an)全(quan)評估技(ji)術列入“十五”國(guo)家重(zhong)大科技(ji)攻(gong)關(guan)(guan)的(de)(de)(de)(de)(de)(de)(de)(de)相關(guan)(guan)項(xiang)目中。文(wen)(wen)(wen)獻(xian)(xian)(xian)給(gei)(gei)出(chu)(chu)了(le)(le)(le)(le)(le)(le)(le)(le)薄壁彎(wan)(wan)(wan)(wan)管(guan)(guan)的(de)(de)(de)(de)(de)(de)(de)(de)理論解，文(wen)(wen)(wen)獻(xian)(xian)(xian)采(cai)用(yong)(yong)(yong)(yong)(yong)(yong)數(shu)值分析(xi)的(de)(de)(de)(de)(de)(de)(de)(de)方(fang)法(fa)，對不(bu)(bu)銹鋼彎(wan)(wan)(wan)(wan)管(guan)(guan)結構在(zai)復(fu)雜載(zai)(zai)(zai)(zai)荷作(zuo)用(yong)(yong)(yong)(yong)(yong)(yong)下(xia)(xia)的(de)(de)(de)(de)(de)(de)(de)(de)極(ji)限(xian)(xian)(xian)(xian)(xian)與(yu)安(an)定分析(xi)進行(xing)了(le)(le)(le)(le)(le)(le)(le)(le)深入、系統(tong)的(de)(de)(de)(de)(de)(de)(de)(de)研(yan)究(jiu)，發展了(le)(le)(le)(le)(le)(le)(le)(le)多組(zu)載(zai)(zai)(zai)(zai)荷作(zuo)用(yong)(yong)(yong)(yong)(yong)(yong)下(xia)(xia)不(bu)(bu)銹鋼管(guan)(guan)彎(wan)(wan)(wan)(wan)管(guan)(guan)結構塑性(xing)(xing)(xing)極(ji)限(xian)(xian)(xian)(xian)(xian)上限(xian)(xian)(xian)(xian)(xian)分析(xi)的(de)(de)(de)(de)(de)(de)(de)(de)有(you)限(xian)(xian)(xian)(xian)(xian)元數(shu)學規劃方(fang)法(fa)，得出(chu)(chu)了(le)(le)(le)(le)(le)(le)(le)(le)相應的(de)(de)(de)(de)(de)(de)(de)(de)無搜索優化迭代求解算(suan)法(fa)，給(gei)(gei)出(chu)(chu)了(le)(le)(le)(le)(le)(le)(le)(le)可較好地解決復(fu)雜載(zai)(zai)(zai)(zai)荷作(zuo)用(yong)(yong)(yong)(yong)(yong)(yong)下(xia)(xia)彎(wan)(wan)(wan)(wan)管(guan)(guan)結構與(yu)安(an)定分析(xi)的(de)(de)(de)(de)(de)(de)(de)(de)數(shu)值算(suan)法(fa)。文(wen)(wen)(wen)獻(xian)(xian)(xian)就含(han)局(ju)部減薄彎(wan)(wan)(wan)(wan)管(guan)(guan)的(de)(de)(de)(de)(de)(de)(de)(de)極(ji)限(xian)(xian)(xian)(xian)(xian)載(zai)(zai)(zai)(zai)荷作(zuo)了(le)(le)(le)(le)(le)(le)(le)(le)研(yan)究(jiu)，得出(chu)(chu)了(le)(le)(le)(le)(le)(le)(le)(le)含(han)局(ju)部減薄彎(wan)(wan)(wan)(wan)管(guan)(guan)的(de)(de)(de)(de)(de)(de)(de)(de)極(ji)限(xian)(xian)(xian)(xian)(xian)載(zai)(zai)(zai)(zai)荷的(de)(de)(de)(de)(de)(de)(de)(de)工(gong)程計(ji)算(suan)方(fang)法(fa)；文(wen)(wen)(wen)獻(xian)(xian)(xian)對在(zai)拉、壓、彎(wan)(wan)(wan)(wan)、扭(niu)和內壓作(zuo)用(yong)(yong)(yong)(yong)(yong)(yong)下(xia)(xia)含(han)缺陷彎(wan)(wan)(wan)(wan)管(guan)(guan)的(de)(de)(de)(de)(de)(de)(de)(de)極(ji)限(xian)(xian)(xian)(xian)(xian)載(zai)(zai)(zai)(zai)荷作(zuo)了(le)(le)(le)(le)(le)(le)(le)(le)研(yan)究(jiu)，得出(chu)(chu)了(le)(le)(le)(le)(le)(le)(le)(le)彎(wan)(wan)(wan)(wan)管(guan)(guan)在(zai)組(zu)合載(zai)(zai)(zai)(zai)荷作(zuo)用(yong)(yong)(yong)(yong)(yong)(yong)下(xia)(xia)的(de)(de)(de)(de)(de)(de)(de)(de)極(ji)限(xian)(xian)(xian)(xian)(xian)載(zai)(zai)(zai)(zai)荷的(de)(de)(de)(de)(de)(de)(de)(de)計(ji)算(suan)公式，能滿(man)足一般工(gong)程的(de)(de)(de)(de)(de)(de)(de)(de)計(ji)算(suan)。文(wen)(wen)(wen)獻(xian)(xian)(xian)對環向(xiang)穿透(tou)裂紋(wen)的(de)(de)(de)(de)(de)(de)(de)(de)斜接(jie)彎(wan)(wan)(wan)(wan)管(guan)(guan)進行(xing)了(le)(le)(le)(le)(le)(le)(le)(le)有(you)限(xian)(xian)(xian)(xian)(xian)元分析(xi)，計(ji)算(suan)給(gei)(gei)出(chu)(chu)了(le)(le)(le)(le)(le)(le)(le)(le)線彈性(xing)(xing)(xing)條件下(xia)(xia)，焊制斜接(jie)彎(wan)(wan)(wan)(wan)管(guan)(guan)環向(xiang)穿透(tou)裂紋(wen)分別在(zai)內壓、彎(wan)(wan)(wan)(wan)矩(ju)載(zai)(zai)(zai)(zai)荷作(zuo)用(yong)(yong)(yong)(yong)(yong)(yong)下(xia)(xia)斷(duan)裂參量K1的(de)(de)(de)(de)(de)(de)(de)(de)工(gong)程應用(yong)(yong)(yong)(yong)(yong)(yong)解；同(tong)(tong)時以內壓、彎(wan)(wan)(wan)(wan)矩(ju)不(bu)(bu)同(tong)(tong)比例的(de)(de)(de)(de)(de)(de)(de)(de)載(zai)(zai)(zai)(zai)荷比作(zuo)用(yong)(yong)(yong)(yong)(yong)(yong)下(xia)(xia)求解出(chu)(chu)全(quan)塑性(xing)(xing)(xing)J積分值。文(wen)(wen)(wen)獻(xian)(xian)(xian)對沿管(guan)(guan)向(xiang)穿透(tou)裂紋(wen)的(de)(de)(de)(de)(de)(de)(de)(de)斜接(jie)彎(wan)(wan)(wan)(wan)管(guan)(guan)在(zai)內壓、彎(wan)(wan)(wan)(wan)矩(ju)聯(lian)合作(zuo)用(yong)(yong)(yong)(yong)(yong)(yong)下(xia)(xia)的(de)(de)(de)(de)(de)(de)(de)(de)整(zheng)體應力(li)進行(xing)了(le)(le)(le)(le)(le)(le)(le)(le)分析(xi)，并利(li)用(yong)(yong)(yong)(yong)(yong)(yong)斷(duan)裂力(li)學的(de)(de)(de)(de)(de)(de)(de)(de)理論和有(you)限(xian)(xian)(xian)(xian)(xian)元方(fang)法(fa)計(ji)算(suan)了(le)(le)(le)(le)(le)(le)(le)(le)內壓、內壓與(yu)彎(wan)(wan)(wan)(wan)矩(ju)組(zu)合載(zai)(zai)(zai)(zai)荷作(zuo)用(yong)(yong)(yong)(yong)(yong)(yong)下(xia)(xia)焊制斜接(jie)彎(wan)(wan)(wan)(wan)管(guan)(guan)沿管(guan)(guan)向(xiang)穿透(tou)裂紋(wen)的(de)(de)(de)(de)(de)(de)(de)(de)線彈性(xing)(xing)(xing)斷(duan)裂參量 K1和全(quan)塑性(xing)(xing)(xing)J積分。

  從(cong)國內(nei)外(wai)的(de)(de)研(yan)(yan)(yan)究(jiu)現(xian)狀(zhuang)來看，目(mu)前(qian)對(dui)不(bu)銹(xiu)鋼(gang)管(guan)(guan)(guan)(guan)(guan)(guan)道(dao)的(de)(de)研(yan)(yan)(yan)究(jiu)多集(ji)中(zhong)在(zai)直管(guan)(guan)(guan)(guan)(guan)(guan)段，圍(wei)繞管(guan)(guan)(guan)(guan)(guan)(guan)道(dao)中(zhong)重要(yao)而薄(bo)弱的(de)(de)環(huan)節(jie)－彎(wan)(wan)管(guan)(guan)(guan)(guan)(guan)(guan)的(de)(de)研(yan)(yan)(yan)究(jiu)相對(dui)較少。由于彎(wan)(wan)管(guan)(guan)(guan)(guan)(guan)(guan)幾何中(zhong)心線(xian)(xian)(xian)是曲線(xian)(xian)(xian)，加(jia)之受制造工(gong)藝(yi)的(de)(de)影(ying)響(xiang)，管(guan)(guan)(guan)(guan)(guan)(guan)壁(bi)往往不(bu)等(deng)厚(hou)(hou)，存在(zai)截面(mian)橢圓化，外(wai)拱(gong)壁(bi)厚(hou)(hou)局部變薄(bo)，內(nei)拱(gong)壁(bi)厚(hou)(hou)局部變厚(hou)(hou)甚至出現(xian)皺(zhou)褶等(deng)缺陷，當受到內(nei)壓(ya)(ya)和(he)(he)彎(wan)(wan)矩的(de)(de)聯合作用時，幾何和(he)(he)材料的(de)(de)非線(xian)(xian)(xian)性相互作用，使得(de)彎(wan)(wan)管(guan)(guan)(guan)(guan)(guan)(guan)的(de)(de)應(ying)(ying)力(li)(li)狀(zhuang)態(tai)比直管(guan)(guan)(guan)(guan)(guan)(guan)復(fu)雜(za)，因(yin)而研(yan)(yan)(yan)究(jiu)起來也相對(dui)復(fu)雜(za)。而對(dui)超(chao)高壓(ya)(ya)彎(wan)(wan)管(guan)(guan)(guan)(guan)(guan)(guan)還要(yao)涉及(ji)彎(wan)(wan)管(guan)(guan)(guan)(guan)(guan)(guan)的(de)(de)應(ying)(ying)力(li)(li)沿壁(bi)厚(hou)(hou)分布不(bu)均勻和(he)(he)應(ying)(ying)力(li)(li)集(ji)中(zhong)的(de)(de)現(xian)象(xiang)，因(yin)而對(dui)超(chao)高壓(ya)(ya)彎(wan)(wan)管(guan)(guan)(guan)(guan)(guan)(guan)的(de)(de)研(yan)(yan)(yan)究(jiu)就更加(jia)復(fu)雜(za)，目(mu)前(qian)對(dui)超(chao)高壓(ya)(ya)彎(wan)(wan)管(guan)(guan)(guan)(guan)(guan)(guan)的(de)(de)研(yan)(yan)(yan)究(jiu)文(wen)獻資料報道(dao)得(de)很(hen)少，而現(xian)有的(de)(de)文(wen)獻資料報道(dao)得(de)最(zui)多的(de)(de)是超(chao)高壓(ya)(ya)彎(wan)(wan)管(guan)(guan)(guan)(guan)(guan)(guan)的(de)(de)加(jia)工(gong)與制造工(gong)藝(yi)，對(dui)超(chao)高壓(ya)(ya)彎(wan)(wan)管(guan)(guan)(guan)(guan)(guan)(guan)的(de)(de)受力(li)(li)分析(xi)及(ji)工(gong)程(cheng)中(zhong)的(de)(de)應(ying)(ying)用的(de)(de)研(yan)(yan)(yan)究(jiu)報道(dao)只有楊家瑞在(zai)文(wen)獻中(zhong)提到了超(chao)高壓(ya)(ya)彎(wan)(wan)管(guan)(guan)(guan)(guan)(guan)(guan)的(de)(de)極限載荷(he)的(de)(de)計(ji)算方(fang)法。2010年，毛苗等(deng)人對(dui)受內(nei)壓(ya)(ya)作用下(xia)的(de)(de)90度大(da)型厚(hou)(hou)壁(bi)彎(wan)(wan)管(guan)(guan)(guan)(guan)(guan)(guan)進行了應(ying)(ying)力(li)(li)計(ji)算分析(xi)及(ji)試驗(yan)研(yan)(yan)(yan)究(jiu)，得(de)到了彎(wan)(wan)管(guan)(guan)(guan)(guan)(guan)(guan)的(de)(de)應(ying)(ying)力(li)(li)分布規(gui)律。2011年，樂(le)增等(deng)人應(ying)(ying)用雙(shuang)剪強度理論推(tui)導(dao)出求解不(bu)銹(xiu)鋼(gang)管(guan)(guan)(guan)(guan)(guan)(guan)彎(wan)(wan)管(guan)(guan)(guan)(guan)(guan)(guan)的(de)(de)極限載荷(he)一(yi)般公式(shi)，如式(shi)（1-1)所示。

 2014年，朱(zhu)倩等人(ren)基于統(tong)(tong)一強(qiang)度(du)(du)理論，考慮中(zhong)間主應(ying)(ying)力(li)(li)(li)效應(ying)(ying)及(ji)拉壓(ya)(ya)(ya)不等特(te)(te)性(xing)，建立了等壁(bi)厚、變壁(bi)厚及(ji)局部減薄壓(ya)(ya)(ya)力(li)(li)(li)彎(wan)管的(de)極(ji)(ji)限(xian)(xian)內壓(ya)(ya)(ya)統(tong)(tong)一解，研究(jiu)了統(tong)(tong)一強(qiang)度(du)(du)理論參(can)數(shu)、拉壓(ya)(ya)(ya)比、彎(wan)曲系(xi)數(shu)和(he)不銹鋼(gang)管彎(wan)管壁(bi)厚對統(tong)(tong)一解的(de)影響特(te)(te)性(xing)，結果(guo)表(biao)明：彎(wan)曲系(xi)數(shu)、強(qiang)度(du)(du)理論參(can)數(shu)等因素(su)對極(ji)(ji)限(xian)(xian)內壓(ya)(ya)(ya)曲線(xian)的(de)影響顯(xian)著，考慮中(zhong)間主應(ying)(ying)力(li)(li)(li)效應(ying)(ying)能(neng)充分發(fa)揮材(cai)料的(de)強(qiang)度(du)(du)潛能(neng)。李建等人(ren)考慮幾何和(he)材(cai)料的(de)非線(xian)性(xing)相互(hu)作用，采用有限(xian)(xian)元(yuan)方法研究(jiu)了復雜(za)載荷(he)下不銹鋼(gang)彎(wan)管的(de)極(ji)(ji)限(xian)(xian)載荷(he)，提出了彎(wan)矩以及(ji)內壓(ya)(ya)(ya)、彎(wan)矩聯合作用下的(de)極(ji)(ji)限(xian)(xian)壓(ya)(ya)(ya)力(li)(li)(li)、極(ji)(ji)限(xian)(xian)彎(wan)矩與彎(wan)管幾何尺寸(cun)的(de)定量關系(xi)如式(shi)（1-2)。