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  本文關(guān)鍵詞： Cosserat理論 有限元 混凝土 尺寸效應(yīng)　出處：《北京交通大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：盡管經(jīng)典連續(xù)統(tǒng)理論在工程實踐中取得了巨大的成就,但在描述材料在宏細觀等不同尺度下的力學(xué)性能有著明顯的局限性,無法解釋不同結(jié)構(gòu)尺度下所表現(xiàn)出來的尺寸效應(yīng)。Cosserat連續(xù)統(tǒng)理論是有別于傳統(tǒng)連續(xù)統(tǒng)理論的微極連續(xù)介質(zhì)力學(xué),它將物體視為連續(xù)分布并有一定尺寸的微極顆粒組成,在物理方程中引入了材料內(nèi)稟尺度,由此建立了宏觀尺度和微細觀尺度的聯(lián)系。因此Cosserat連續(xù)統(tǒng)理論在分析微米尺度或有顆粒材料組成的宏觀尺度下的力學(xué)性能時,表現(xiàn)出很高的求解精度和良好的模擬效果。本文主要研究內(nèi)容和成果如下:(1)推導(dǎo)了平面問題的一般Cosserat理論的平衡方程、幾何方程和物理方程,構(gòu)造了線位移和轉(zhuǎn)角各自獨立的四邊形八節(jié)點的Cosserat有限元模型,采用FORTRAN語言,編制并調(diào)通了有限元程序CFEM。對純彎懸臂梁進行了數(shù)值模擬分析,其數(shù)值解與基于經(jīng)典彈性理論解析解和通用有限元軟件ANSYS數(shù)值解進行了對比,驗證了 Cosserat有限元模型及程序的正確性。(2)在一般Cosserat理論基礎(chǔ)上,當忽略了微極顆粒的微觀轉(zhuǎn)角,其轉(zhuǎn)角位移不再獨立而等于宏觀轉(zhuǎn)角位移時,該理論則退化為約束轉(zhuǎn)動Cosserat理論。本文推導(dǎo)了約束轉(zhuǎn)動Cosserat理論的基本方程,并以應(yīng)力分量作為基本未知函數(shù),對矩形梁純彎構(gòu)件進行了求解并給出了解析解。(3)用有限元程序CFEM對懸臂梁純彎構(gòu)件進行了數(shù)值模擬分析,研究了不同內(nèi)稟尺寸參數(shù)和宏觀尺寸對構(gòu)件力學(xué)性能的影響。研究表明,偶應(yīng)力沿橫截面為常量,且隨著內(nèi)稟尺寸的增大,偶應(yīng)力逐漸增大,豎向位移、轉(zhuǎn)角及跨中截面正應(yīng)力則逐漸減小。當內(nèi)稟尺寸一定時,隨著構(gòu)件宏觀尺寸的增大,跨中截面下邊緣處的正應(yīng)力σx逐漸增大。(4)通過程序CFEM對混凝土抗折構(gòu)件進行了數(shù)值模擬,研究了混凝土不同強度等級的內(nèi)稟尺寸參數(shù)的取值,并確定了其合理取值范圍。(5)通過數(shù)值模擬,研究了混凝土抗折強度的尺寸效應(yīng),研究表明,混凝土構(gòu)件的最小宏觀尺寸與內(nèi)稟長度的比值越小,尺寸效應(yīng)越明顯;比值越大,尺寸效應(yīng)越弱�；炷翉姸仍礁�,尺寸效應(yīng)越明顯。
[Abstract]:Although the classical continuum theory has made great achievements in engineering practice, it has obvious limitations in describing the mechanical properties of materials at different scales such as macroscopes and meso-scopes. Cosserat continuum theory is different from traditional continuum theory in micropolar continuum mechanics. It treats the object as a continuous distribution with a certain size of micropolar particles, and introduces the intrinsic scale of material into the physical equation. Therefore, the Cosserat continuum theory is used to analyze the mechanical properties of micron scale or macroscopically composed of granular materials. The main contents and results of this paper are as follows: 1) the equilibrium equations of the general Cosserat theory for plane problems are derived. Geometric equation and physical equation, the Cosserat finite element model of quadrilateral and eight-node which is independent of linear displacement and rotation angle is constructed. FORTRAN language is used. The finite element program CFEM.The numerical simulation of pure curved cantilever beam is carried out. The numerical solution is compared with the analytical solution based on classical elastic theory and the general finite element software ANSYS. The correctness of Cosserat finite element model and program is verified. Based on the general Cosserat theory, the micro rotation angle of micropolar particles is neglected. When the angular displacement is no longer independent but equal to the macroscopic angular displacement, the theory is reduced to the constrained rotational Cosserat theory. In this paper, the basic equations of the constrained rotational Cosserat theory are derived. Taking the stress component as the basic unknown function, the pure bending member of rectangular beam is solved and the analytical solution is given. (3) the numerical simulation of the pure bending member of cantilever beam is carried out by using the finite element program CFEM. The effects of different intrinsic dimension parameters and macroscopic dimensions on the mechanical properties of the members are studied. The results show that the coupling stress along the cross section is constant and the coupling stress increases gradually and the vertical displacement increases with the increase of intrinsic size. The normal stress of rotation angle and mid-span section decrease gradually. When the intrinsic dimension is fixed, with the increase of macroscopic size of the member. The normal stress (蟽 x) at the edge of the middle section is gradually increased. (4) numerical simulation of concrete flexural members is carried out by program CFEM, and the intrinsic dimension parameters of different strength grades of concrete are studied. Through numerical simulation, the size effect of concrete flexural strength is studied. The study shows that the ratio of minimum macro size to intrinsic length of concrete member is smaller. The size effect is more obvious; The bigger the ratio is, the weaker the size effect is, and the higher the strength of concrete is, the more obvious the size effect is.
【學(xué)位授予單位】：北京交通大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TU528

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