本文選題：靜不定 + 結(jié)構(gòu)　； 參考：《中南大學(xué)學(xué)報(bào)(自然科學(xué)版)》2016年01期

【摘要】：基于材料力學(xué)、結(jié)構(gòu)力學(xué)工程中靜不定結(jié)構(gòu)內(nèi)力的求解多采用力法、位移法等方法,靜不定結(jié)構(gòu)在外載荷作用下的平衡狀態(tài)是一個(gè)穩(wěn)定的平衡狀態(tài),其應(yīng)變能存在極小值,故利用靜不定結(jié)構(gòu)的多余約束力列出其應(yīng)變能表達(dá)式,引入拉格朗日乘數(shù)并結(jié)合靜力平衡方程,構(gòu)造拉格朗日函數(shù),對(duì)拉格朗日函數(shù)求一階導(dǎo)數(shù)并令一階導(dǎo)數(shù)等于0,即可求得靜不定結(jié)構(gòu)的內(nèi)力,并通過(guò)算例予以證明。研究結(jié)果表明:此方法適用于求解平面或空間靜不定梁、弧形結(jié)構(gòu)、剛架、桁架(包括非線性材料)的約束反力、內(nèi)力及位移;采用拉格朗日乘數(shù)法求解靜不定桁架內(nèi)力的通用性較強(qiáng),不但可以克服常規(guī)方法需利用幾何關(guān)系建立協(xié)調(diào)方程的缺陷,而且具有力學(xué)概念清晰直觀、計(jì)算過(guò)程簡(jiǎn)潔、便于工程設(shè)計(jì)人員在實(shí)際中掌握和計(jì)算的優(yōu)點(diǎn);其所得結(jié)果是精確解析解,故可以用于檢驗(yàn)其他方法的計(jì)算精度。
[Abstract]:Based on the mechanics of materials, the internal forces of statically indeterminate structures in structural mechanics engineering are solved by force method and displacement method. The equilibrium state of statically indeterminate structures under external loads is a stable equilibrium state, and the strain energy of statically indeterminate structures is minimized. Therefore, the strain energy expressions of statically indeterminate structures are presented by using superfluous binding force, and Lagrange multipliers are introduced and combined with static equilibrium equations to construct Lagrange functions. If the first order derivative of Lagrange function is obtained and the first order derivative is equal to 0, the internal force of the statically indeterminate structure can be obtained and proved by an example. The results show that this method is suitable for solving the constrained reaction forces, internal forces and displacements of plane or spatial statically indeterminate beams, curved structures, rigid frames and trusses (including nonlinear materials). The Lagrange multiplier method is widely used to solve the internal force of statically indeterminate truss. It can not only overcome the defect that the conventional method needs to use geometric relations to establish the coordination equation, but also has a clear and intuitive mechanical concept and a simple calculation process. It is convenient for engineering designers to grasp and calculate the advantages in practice, and the results obtained are exact analytical solutions, so it can be used to test the calculation accuracy of other methods.
【作者單位】： 湖南文理學(xué)院機(jī)械工程學(xué)院;
【基金】：湖南省科技計(jì)劃項(xiàng)目(2011SK3145) 湖南“十二五”重點(diǎn)建設(shè)學(xué)科項(xiàng)目(湘教發(fā)[2011]76號(hào)) 湖南省自然科學(xué)基金資助項(xiàng)目(2015JJ6073)~~
【分類號(hào)】：O34
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本文編號(hào)：1854005