【摘要】：針對桿狀類工程結(jié)構(gòu)構(gòu)件和結(jié)構(gòu)體系,本文提出了一種新的梁模型——統(tǒng)一分析梁與一種新的數(shù)值分析方法——有限節(jié)線法。利用統(tǒng)一分析梁和有限節(jié)線法不僅可以解決任意桿狀類結(jié)構(gòu)構(gòu)件或結(jié)構(gòu)體系的力學(xué)分析問題,而且當(dāng)問題的性質(zhì)與傳統(tǒng)梁理論的前提條件一致時(shí),會得出同樣精度的解答。算例計(jì)算結(jié)果也證明了統(tǒng)一分析梁的合理性與有限節(jié)線法的正確性。論文的主要工作如下:1論述了梁的發(fā)展歷史以及本文的研究意義;2引入了統(tǒng)一分析梁和有限節(jié)線法的概念,并根據(jù)最小勢能原理,推導(dǎo)出了在靜力作用下的常微分方程組及其相應(yīng)的邊界條件;3論述了統(tǒng)一分析梁和有限節(jié)線法在固體力學(xué)中實(shí)體構(gòu)件中的應(yīng)用,分別與傳統(tǒng)梁理論中的Euler梁、Timoshenko梁和自由扭轉(zhuǎn)作用時(shí)的Saint Venant梁進(jìn)行了比較,并給出了非圓非對稱厚壁截面的統(tǒng)一分析梁算例;4論述了統(tǒng)一分析梁和有限節(jié)線法在約束扭轉(zhuǎn)時(shí)薄壁桿件中的應(yīng)用,分別與Vlasov梁和Umansky梁進(jìn)行了比較,并給出了半開半閉截面薄壁桿件的統(tǒng)一分析梁算例;5指出了統(tǒng)一分析梁在解決更廣泛工程問題時(shí)需要克服的問題。
[Abstract]:In this paper, a new beam model-unified analysis beam and a new numerical analysis method-finite nodal line method are proposed for rod-like engineering structural members and structural systems. The unified analytical beam and finite nodal line method can not only solve the mechanical analysis problem of any rod-like structural member or structural system, but also obtain the same precision solution when the properties of the problem are consistent with the premise of the traditional beam theory. The calculation results also prove the rationality of the unified analysis and the correctness of the finite nodal method. The main work of this paper is as follows: 1. The history of beam development and the significance of this paper are discussed. 2 the concept of unified analysis beam and finite nodal line method is introduced, and according to the principle of minimum potential energy, The ordinary differential equations under static force and their corresponding boundary conditions are derived. The application of unified analysis beam and finite nodal line method to solid members in solid mechanics is discussed. The results are compared with that of Euler beam and Saint Venant beam under free torsion respectively in traditional beam theory. An example of unified analysis of non-circular asymmetric thick wall section is given. 4. The application of unified analysis beam and finite node line method in torsional restrained thin-walled member is discussed, which is compared with Vlasov beam and Umansky beam, respectively. The unified analysis of thin-walled members with semi-open and semi-closed section is given. 5. The problems to be overcome in solving more extensive engineering problems are pointed out.
【學(xué)位授予單位】：河南理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：TU323

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