本文選題：空間梁單元　切入點(diǎn)：剛度矩陣　出處：《長沙理工大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

【摘要】：梁結(jié)構(gòu)作為橋梁的重要承重結(jié)構(gòu),在工程中受到了十分廣泛的應(yīng)用。因此,對其進(jìn)行準(zhǔn)確合理的計(jì)算分析是十分必要的。本文以梁單元為主要研究對象,對梁單元理論及其在橋梁中的應(yīng)用作了較為深入的研究,對今后處理相關(guān)的計(jì)算分析問題具有一定的積極意義。主要研究內(nèi)容包括以下幾個(gè)方面：首先,構(gòu)造出了一種同時(shí)考慮軸向拉伸以及兩個(gè)方向彎曲的局部坐標(biāo)系下三結(jié)點(diǎn)空間梁單元。采用使用五次的Hermite插值函數(shù)及二次的Lagrange插值函數(shù)得到其橫向及縱向位移場,創(chuàng)建出新型的局部坐標(biāo)系下的空間梁單元。并基于有限元等相關(guān)理論,詳細(xì)推導(dǎo)了該新型局部坐標(biāo)系下的空間梁單元?jiǎng)偠染仃?并得出其顯示表達(dá)式。其次,基于局部坐標(biāo)系下的空間梁單元,利用坐標(biāo)轉(zhuǎn)換矩陣,得到了整體坐標(biāo)系下的梁單元?jiǎng)偠染仃嚰跋嚓P(guān)表達(dá)式,然后利用能量法對多種常見外荷載形式進(jìn)行了結(jié)點(diǎn)等效并得到了其相應(yīng)的結(jié)點(diǎn)等效荷載。同時(shí)總結(jié)歸納了常見邊界條件的處理方式等,并應(yīng)用該新型空間梁單元進(jìn)行了算例驗(yàn)證,結(jié)果表明該空間梁單元在計(jì)算上是可行的。最后,利用有限元軟件ANSYS的二次開發(fā)功能,基于其UPFs二次開發(fā)工具,將理論推導(dǎo)的梁單元形式通過用戶自定義單元的手段,修改相關(guān)的子程序,實(shí)現(xiàn)在ANSYS中定義與其具有相同結(jié)點(diǎn)數(shù)及相同自有度的新的單元類型,并利用該新單元對某一橋梁實(shí)例進(jìn)行了分析驗(yàn)證,同時(shí)采用橋梁專用軟件Midas Civil進(jìn)行輔助判定,說明了該新單元類型在實(shí)際分析中是可行的。
[Abstract]:Beam structure, as an important bearing structure of bridge, has been widely used in engineering. Therefore, it is necessary to calculate and analyze it accurately and reasonably. In this paper, the theory of beam element and its application in bridges are studied in depth, which has a certain positive significance for dealing with related computational and analytical problems in the future. The main research contents include the following aspects: first, In this paper, a three-node spatial beam element in a local coordinate system considering both axial stretching and two directions bending is constructed. The transverse and longitudinal displacement fields are obtained by using the Hermite interpolation function of the fifth degree and the Lagrange interpolation function of the quadratic degree. A new space beam element in local coordinate system is established. Based on the theory of finite element, the stiffness matrix of space beam element in this new local coordinate system is derived in detail, and the display expression is obtained. Based on the spatial beam element in the local coordinate system, the stiffness matrix and the related expressions of the beam element in the global coordinate system are obtained by using the coordinate transformation matrix. Then the energy method is used to calculate the nodal equivalent load and the corresponding nodal equivalent load is obtained. At the same time, the treatment methods of common boundary conditions are summarized. The results show that the spatial beam element is feasible in calculation. Finally, using the secondary development function of finite element software ANSYS, based on the second development tool of UPFs, a new type of space beam element is developed. By means of user-defined unit, the theoretically derived beam element form is modified to realize the definition of a new type of unit with the same number of nodes and the same degree of ownership in ANSYS. An example of a bridge is analyzed and verified by using the new element, and the bridge special software Midas Civil is used to judge the bridge. It is shown that the new unit type is feasible in practical analysis.
【學(xué)位授予單位】：長沙理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：U441

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