本文關(guān)鍵詞： 鋼框架結(jié)構(gòu) 穩(wěn)定分析 樣條無單元法 QR法 幾何非線性 材料非線性 雙重非線性 程序設(shè)計(jì)　出處：《廣西大學(xué)》2014年博士論文　論文類型：學(xué)位論文

【摘要】：鋼結(jié)構(gòu)具有眾多優(yōu)點(diǎn),在我國工程建設(shè)中的應(yīng)用越來越廣泛,已經(jīng)是我國主要的結(jié)構(gòu)體系之一。與鋼筋混凝土結(jié)構(gòu)相比,鋼結(jié)構(gòu)具有強(qiáng)度大、自重輕、抗震性能好、設(shè)計(jì)靈活、施工方便、工期短、符合產(chǎn)業(yè)化要求、符合可持續(xù)發(fā)展的要求等優(yōu)點(diǎn)。鋼框架是鋼結(jié)構(gòu)中最常用的一種結(jié)構(gòu)形式,柱網(wǎng)布置靈活,可采用較大的柱距,而且塑性變形能力強(qiáng),抗震性好,施工簡便,廣泛地用于多高層建筑。 在高層鋼框架結(jié)構(gòu)體系中,鋼材強(qiáng)度很高,具有極好的延性,鋼構(gòu)件壁薄修長,構(gòu)造輕巧。在軸壓或壓彎作用下,結(jié)構(gòu)可能出現(xiàn)局部或整體失穩(wěn),穩(wěn)定因素控制鋼框架和構(gòu)件的極限承載力。穩(wěn)定分析是對(duì)鋼框架進(jìn)行分析時(shí)不可忽略的一個(gè)重要環(huán)節(jié)。 在對(duì)結(jié)構(gòu)進(jìn)行穩(wěn)定分析的眾多方法中,有限單元法運(yùn)用較為廣泛。但是運(yùn)用傳統(tǒng)的有限元法分析高層鋼框架的穩(wěn)定問題時(shí),存在未知量多、計(jì)算量大、占用資源多等不足。目前比較常見的一些有限元軟件在很多情況下無法跟蹤結(jié)構(gòu)的加載平衡路徑,得不到真正的穩(wěn)定極限狀態(tài)。 本文旨在研究高層鋼框架結(jié)構(gòu)體系穩(wěn)定分析的樣條函數(shù)方法,主要作了以下方面工作： (1)基于Kirchhoff薄板理論,建立彈性薄板穩(wěn)定分析的樣條無單元法(SEFM)計(jì)算格式；基于Mindlin-Reissner中厚度板理論,把板的撓度和剪應(yīng)變作為獨(dú)立的場變量,建立了厚／薄板穩(wěn)定分析的通用樣條無單元法的計(jì)算格式；應(yīng)用特征值失穩(wěn)來判斷臨界力。用C語言設(shè)計(jì)相應(yīng)的通用程序,通過典型算例說明樣條無單元法適用于不同厚度、不同邊界的板的穩(wěn)定分析,且具有精度高、收斂快、自由度少、無剪切閉鎖現(xiàn)象、程序簡便等優(yōu)點(diǎn)�？捎糜诳蚣芙Y(jié)構(gòu)體系中的板的穩(wěn)定分析。 (2)采用平衡微分方程及穩(wěn)定函數(shù)推導(dǎo)了考慮幾何非線性影響的梁柱單元的剛度矩陣。建立了平而鋼框架幾何非線性性穩(wěn)定分析的QR法計(jì)算格式,用C語言編制了平面鋼框架的兒何非線性穩(wěn)定分析的QR法計(jì)算程序。通過算例分析說明幾何非線性對(duì)鋼框架結(jié)構(gòu)穩(wěn)定的影響不能忽略,而QR法的計(jì)算格式簡單,而且精度高,不但可以計(jì)算結(jié)構(gòu)整體失穩(wěn)的臨界荷載,而且跟蹤整個(gè)加載路徑,在鋼框架的穩(wěn)定分析方面很有優(yōu)勢。 (3)在幾何非線性穩(wěn)定分析的基礎(chǔ)上,同時(shí)考慮材料非線性和幾何非線性,應(yīng)用本文推導(dǎo)的梁柱單元?jiǎng)偠染仃?用荷載增量法建立結(jié)構(gòu)非線性分析的增量剛度方程,采用塑性鉸模型,建立鋼框架雙重非線性穩(wěn)定分析的QR法計(jì)算格式,采用Euler-修正的Newton法求解非線性方程組,用切線剛度法跟蹤結(jié)構(gòu)的整個(gè)非線性平衡路徑,并用C語言設(shè)計(jì)了相應(yīng)的通用計(jì)算程序。通過典型的算例分析,分析了材料非線性對(duì)結(jié)構(gòu)穩(wěn)定的影響,證明了鋼框架雙重非線性穩(wěn)定分析的QR法的可行性和優(yōu)越性。QR法計(jì)算格式簡單,未知量少,計(jì)算精度高,不會(huì)因?yàn)樗苄糟q的出現(xiàn)修正結(jié)構(gòu)的計(jì)算網(wǎng)格和自由度,以結(jié)構(gòu)的整體失穩(wěn)作為程序計(jì)算的終止條件,不會(huì)因?yàn)榫植渴Х�(wěn)破壞而影響后續(xù)的增量計(jì)算。 (4)利用本文算法編制鋼框架結(jié)構(gòu)體系穩(wěn)定性分析的軟件包,可用于平面框架及樓板的穩(wěn)定性分析。以目前廣西最高的鋼結(jié)構(gòu)商務(wù)大樓-廣西中煙工業(yè)有限責(zé)任公司研發(fā)中心辦公樓為工程實(shí)例,利用軟件包對(duì)其進(jìn)行穩(wěn)定分析,評(píng)定該結(jié)構(gòu)的穩(wěn)定性能。
[Abstract]:The steel frame is one of the main structural systems in our country . Compared with the reinforced concrete structure , the steel structure has the advantages of large strength , light weight , good aseismatic performance , flexible design , convenient construction , short construction period , meeting industrialization requirements , meeting the requirements of sustainable development , etc . The steel frame is one of the most commonly used structural forms in the steel structure , and has the advantages of high column spacing , strong plastic deformation capability , good shock resistance , simple and convenient construction , and is widely used for many high - rise buildings . In the high - rise steel frame structure system , the strength of the steel is very high , it has excellent ductility , the wall of the steel member is thin and long , and the structure is light . Under the action of axial compression or bending , the structure may be locally or integrally unstable , and the stability factor controls the ultimate bearing capacity of the steel frame and the component . The stability analysis is an important link which can not be neglected in the analysis of the steel frame . The finite element method is widely used in many methods for the stability analysis of the structure . However , the traditional finite element method is used to analyze the stability of the high - rise steel frame . The purpose of this paper is to study the spline function method for the stability analysis of high - rise steel frame structure system , which mainly works as follows : ( 1 ) Based on the thin plate theory , a spline - free method ( SEFM ) method for the stability analysis of elastic thin plates is established . Based on the theory of the thickness plate , the paper establishes a general spline non - element method for the stability analysis of thick / thin plates based on the theory of the thickness plate in Minlin - Reissner . It has the advantages of high precision , fast convergence , few degrees of freedom , no shear locking , simple procedure and the like , and can be used in the stability analysis of the plates in the frame structure system . ( 2 ) The stiffness matrix of beam - column units considering geometric nonlinearity is derived by using equilibrium differential equations and stable functions . The QR method for the stability analysis of the geometrical nonlinear stability of the steel frame is established . The QR method for the nonlinear stability analysis of the plane steel frame is compiled by C language . The calculation method of QR method is simple , and the precision is high , which not only can calculate the critical load of the whole instability of the structure , but also trace the whole loading path , and has the advantage in the stability analysis of the steel frame . ( 3 ) On the basis of geometric nonlinear stability analysis , considering the nonlinear and geometric nonlinearity of materials , the stiffness matrix of the beam - column element deduced from this paper is applied , and the incremental stiffness equation of the structure nonlinear analysis is established by the load increment method . ( 4 ) A software package for stability analysis of steel frame structure system is developed by using the algorithm , which can be applied to the stability analysis of plane frame and floor .

【學(xué)位授予單位】：廣西大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類號(hào)】：TU973.13

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