據悉,膜結構看臺膜面(mian)(mian)的(de)(de)展平分析主含了這些過(guo)程(cheng)(cheng)：明(ming)確裁(cai)剪式樣,即(ji)確定膜曲(qu)(qu)面(mian)(mian)上的(de)(de)裁(cai)剪線,將(jiang)膜曲(qu)(qu)面(mian)(mian)分解成若干(gan)的(de)(de)子曲(qu)(qu)面(mian)(mian),然后將(jiang)各個(ge)(ge)子曲(qu)(qu)面(mian)(mian)分別近(jin)似的(de)(de)展開成二維平面(mian)(mian)。曲(qu)(qu)面(mian)(mian)展開得到(dao)平面(mian)(mian)圖(tu)形的(de)(de)過(guo)程(cheng)(cheng)是(shi)一(yi)個(ge)(ge)近(jin)似的(de)(de)過(guo)程(cheng)(cheng),因此這一(yi)過(guo)程(cheng)(cheng)的(de)(de)一(yi)個(ge)(ge)基(ji)本的(de)(de)準則就是(shi)平面(mian)(mian)與曲(qu)(qu)面(mian)(mian)形狀(zhuang)越像,用力學方法表(biao)(biao)示可用較(jiao)小變形能原(yuan)理表(biao)(biao)示,即(ji)空間曲(qu)(qu)面(mian)(mian)的(de)(de)越優(you)展平平面(mian)(mian)是(shi)從空間曲(qu)(qu)面(mian)(mian)變形到(dao)平面(mian)(mian)圖(tu)形所需(xu)變形能較(jiao)小的(de)(de)平面(mian)(mian)圖(tu)形。

根據較(jiao)小變形(xing)能原理(li),以有(you)限(xian)(xian)元(yuan)方(fang)法來進行展(zhan)平分(fen)析。用有(you)限(xian)(xian)元(yuan)方(fang)法進行分(fen)析要先(xian)確定(ding)一(yi)個與(yu)空(kong)間(jian)曲面(mian)有(you)限(xian)(xian)元(yuan)網格的(de)劃分(fen)相(xiang)一(yi)致的(de)平面(mian)圖(tu)形(xing)有(you)限(xian)(xian)元(yuan)網格劃分(fen)。展(zhan)平過程可表示為∶①、計(ji)算平面(mian)圖(tu)形(xing)的(de)初始應(ying)(ying)力(li)與(yu)等(deng)效(xiao)結點力(li)（將(jiang)空(kong)間(jian)曲面(mian)變形(xing)到(dao)(dao)平面(mian)圖(tu)形(xing)引(yin)起的(de)平面(mian)圖(tu)形(xing)內(nei)應(ying)(ying)力(li)的(de)變化）;②、有(you)限(xian)(xian)元(yuan)計(ji)算,將(jiang)平面(mian)圖(tu)形(xing)內(nei)應(ying)(ying)力(li)釋放,得(de)到(dao)(dao)末后的(de)展(zhan)平圖(tu)形(xing);③、重復上述過程,直到(dao)(dao)得(de)到(dao)(dao)變形(xing)能較(jiao)小的(de)平面(mian)圖(tu)形(xing)。

（一）、平面圖形的初始應力(li)與等效結點力(li)的計(ji)算：

將膜結構看臺空(kong)間(jian)曲(qu)面(mian)(mian)(mian)(mian)離(li)散(san)(san)成三(san)(san)(san)(san)(san)(san)結(jie)點二角(jiao)形(xing)(xing)(xing)(xing)(xing)(xing)單(dan)(dan)(dan)元(yuan)網(wang)格,平(ping)(ping)(ping)面(mian)(mian)(mian)(mian)圖(tu)形(xing)(xing)(xing)(xing)(xing)(xing)也相應(ying)的離(li)散(san)(san)成三(san)(san)(san)(san)(san)(san)結(jie)占三(san)(san)(san)(san)(san)(san)角(jiao)形(xing)(xing)(xing)(xing)(xing)(xing)單(dan)(dan)(dan)元(yuan)網(wang)格。空(kong)間(jian)曲(qu)面(mian)(mian)(mian)(mian)變(bian)形(xing)(xing)(xing)(xing)(xing)(xing)成平(ping)(ping)(ping)面(mian)(mian)(mian)(mian)圖(tu)形(xing)(xing)(xing)(xing)(xing)(xing)用(yong)有限元(yuan)方法計算時,實際上是(shi)對(dui)應(ying)三(san)(san)(san)(san)(san)(san)角(jiao)形(xing)(xing)(xing)(xing)(xing)(xing)單(dan)(dan)(dan)元(yuan)之間(jian)的變(bian)化,空(kong)間(jian)的三(san)(san)(san)(san)(san)(san)角(jiao)形(xing)(xing)(xing)(xing)(xing)(xing)單(dan)(dan)(dan)元(yuan)變(bian)形(xing)(xing)(xing)(xing)(xing)(xing)到平(ping)(ping)(ping)面(mian)(mian)(mian)(mian)三(san)(san)(san)(san)(san)(san)角(jiao)形(xing)(xing)(xing)(xing)(xing)(xing)單(dan)(dan)(dan)元(yuan)分三(san)(san)(san)(san)(san)(san)個部分∶三(san)(san)(san)(san)(san)(san)角(jiao)形(xing)(xing)(xing)(xing)(xing)(xing)單(dan)(dan)(dan)元(yuan)在(zai)單(dan)(dan)(dan)元(yuan)所在(zai)平(ping)(ping)(ping)面(mian)(mian)(mian)(mian)內的變(bian)形(xing)(xing)(xing)(xing)(xing)(xing)、三(san)(san)(san)(san)(san)(san)角(jiao)形(xing)(xing)(xing)(xing)(xing)(xing)單(dan)(dan)(dan)元(yuan)在(zai)平(ping)(ping)(ping)面(mian)(mian)(mian)(mian)外(wai)的旋(xuan)轉及三(san)(san)(san)(san)(san)(san)角(jiao)形(xing)(xing)(xing)(xing)(xing)(xing)單(dan)(dan)(dan)元(yuan)整體的位(wei)移。在(zai)這三(san)(san)(san)(san)(san)(san)個變(bian)形(xing)(xing)(xing)(xing)(xing)(xing)之中,二角(jiao)形(xing)(xing)(xing)(xing)(xing)(xing)平(ping)(ping)(ping)面(mian)(mian)(mian)(mian)外(wai)旋(xuan)轉與整體的位(wei)移均不會產生(sheng)單(dan)(dan)(dan)元(yuan)內應(ying)變(bian)。因此(ci)在(zai)確定膜結(jie)構平(ping)(ping)(ping)面(mian)(mian)(mian)(mian)圖(tu)形(xing)(xing)(xing)(xing)(xing)(xing)的初(chu)始應(ying)力(li)與等效(xiao)結(jie)點力(li)時,可以(yi)只進行(xing)比較由空(kong)間(jian)三(san)(san)(san)(san)(san)(san)角(jiao)形(xing)(xing)(xing)(xing)(xing)(xing)單(dan)(dan)(dan)元(yuan)與平(ping)(ping)(ping)面(mian)(mian)(mian)(mian)三(san)(san)(san)(san)(san)(san)角(jiao)形(xing)(xing)(xing)(xing)(xing)(xing)單(dan)(dan)(dan)元(yuan)形(xing)(xing)(xing)(xing)(xing)(xing)狀上的差別所引起的單(dan)(dan)(dan)元(yuan)應(ying)變(bian),再根據這一應(ying)變(bian)確定單(dan)(dan)(dan)元(yuan)應(ying)力(li)。這樣由空(kong)間(jian)三(san)(san)(san)(san)(san)(san)角(jiao)形(xing)(xing)(xing)(xing)(xing)(xing)變(bian)形(xing)(xing)(xing)(xing)(xing)(xing)到平(ping)(ping)(ping)面(mian)(mian)(mian)(mian)二角(jiao)形(xing)(xing)(xing)(xing)(xing)(xing)的過(guo)程就可以(yi)等效(xiao)為(wei)兩個平(ping)(ping)(ping)面(mian)(mian)(mian)(mian)三(san)(san)(san)(san)(san)(san)角(jiao)形(xing)(xing)(xing)(xing)(xing)(xing)單(dan)(dan)(dan)元(yuan)變(bian)形(xing)(xing)(xing)(xing)(xing)(xing)過(guo)程。

這(zhe)(zhe)一過(guo)程的(de)(de)實現目前常用的(de)(de)有兩(liang)種方(fang)法(fa)∶（1）、利用三(san)角(jiao)(jiao)(jiao)(jiao)形(xing)(xing)各邊(bian)應(ying)(ying)(ying)變(bian)(bian)(bian)(bian)與(yu)三(san)角(jiao)(jiao)(jiao)(jiao)形(xing)(xing)單(dan)(dan)元的(de)(de)應(ying)(ying)(ying)變(bian)(bian)(bian)(bian)的(de)(de)關系(xi),根據空間(jian)三(san)角(jiao)(jiao)(jiao)(jiao)形(xing)(xing)單(dan)(dan)元與(yu)平(ping)面三(san)角(jiao)(jiao)(jiao)(jiao)形(xing)(xing)單(dan)(dan)元對應(ying)(ying)(ying)邊(bian)長度的(de)(de)不同,確定對應(ying)(ying)(ying)邊(bian)的(de)(de)應(ying)(ying)(ying)變(bian)(bian)(bian)(bian)來確定三(san)角(jiao)(jiao)(jiao)(jiao)形(xing)(xing)單(dan)(dan)元的(de)(de)應(ying)(ying)(ying)變(bian)(bian)(bian)(bian);（2）、由三(san)角(jiao)(jiao)(jiao)(jiao)形(xing)(xing)之間(jian)的(de)(de)奇(qi)異值變(bian)(bian)(bian)(bian)換得出空間(jian)三(san)角(jiao)(jiao)(jiao)(jiao)形(xing)(xing)變(bian)(bian)(bian)(bian)形(xing)(xing)到平(ping)面三(san)角(jiao)(jiao)(jiao)(jiao)形(xing)(xing)過(guo)程中(zhong)單(dan)(dan)元主軸方(fang)向的(de)(de)變(bian)(bian)(bian)(bian)形(xing)(xing),根據單(dan)(dan)元應(ying)(ying)(ying)變(bian)(bian)(bian)(bian)與(yu)單(dan)(dan)元主軸方(fang)向應(ying)(ying)(ying)變(bian)(bian)(bian)(bian)的(de)(de)關系(xi)米得到單(dan)(dan)元應(ying)(ying)(ying)變(bian)(bian)(bian)(bian)。這(zhe)(zhe)兩(liang)種方(fang)法(fa)在理論上是(shi)等(deng)價(jia)的(de)(de)。

（二）、展平計算：

得到平面圖形三角形單元中的應力及等效結點力后,就可以解決平面應力問題。有計算過程并沒有對平面圖形的外部邊界加以約束,因此終算結果的邊界長度與空間曲面的邊界長度并不定然相等,這樣相鄰的兩片空間曲面的平面展平圖形在難于保持邊界長度一致,會引起安裝上的不方便。為解決這一問題,有文獻引入了有邊界約束的越小變形能原理,并根據這一原理,對膜結構看臺平面圖形的邊界(jie)增加一(yi)圈剛度相對較大(da)的桿單元,以(yi)保(bao)障邊界(jie)長度的一(yi)致性。