發(fā)布時(shí)間：2018-01-15 21:24

  本文關(guān)鍵詞：基于局部和非局部狀態(tài)空間能量等效原理的應(yīng)變局部化數(shù)值模擬　出處：《西南交通大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 應(yīng)變局部化 非局部理論 能量等效 內(nèi)尺度 剪切帶 網(wǎng)格相關(guān)性

【摘要】：很多土木工程材料在加載至接近破壞時(shí),會(huì)出現(xiàn)應(yīng)變局部化現(xiàn)象。應(yīng)用經(jīng)典連續(xù)介質(zhì)理論或一般非局部塑性理論在解決應(yīng)變局部化問(wèn)題時(shí),會(huì)得到與網(wǎng)格相關(guān)的結(jié)果,即應(yīng)變局部化區(qū)域(剪切帶)的尺寸會(huì)隨著網(wǎng)格的細(xì)化而減小。為了克服網(wǎng)格相關(guān)性的缺陷,本文基于一般非局部塑性理論,從狀態(tài)空間能量等效角度,提出了一種求解應(yīng)變局部化問(wèn)題的新方法。在本方法中,應(yīng)用狀態(tài)空間理論,對(duì)材料體的每一點(diǎn)定義了局部和非局部?jī)蓚�(gè)狀態(tài)空間,利用權(quán)函數(shù)可以將材料屈服點(diǎn)的內(nèi)變量從局部狀態(tài)空間映射到非局部狀態(tài)空間。通過(guò)熱力學(xué)第一定律,得出了材料體在非局部狀態(tài)空間中內(nèi)能的塑性部分和彈性部分與其在局部狀態(tài)空間中的對(duì)應(yīng)部分相等這一重要結(jié)論�；谶@個(gè)結(jié)論,最終導(dǎo)出了應(yīng)用本方法解決應(yīng)變局部化問(wèn)題的一般列式,并給出了有限元算法。然后,通過(guò)具體的一維和二維算例,驗(yàn)證了本文方法的可靠性。一維算例為一個(gè)有缺陷的拉桿,應(yīng)用本方法導(dǎo)出了該問(wèn)題的解析解,并給出了材料特征塑性區(qū)域(應(yīng)變局部化區(qū)域)尺寸Lcp與材料內(nèi)尺度l之間的定量關(guān)系,并且通過(guò)有限元編程給出了一維及二維算例的數(shù)值解,得到了相應(yīng)的塑性應(yīng)變分布及荷載-位移曲線。對(duì)于一維問(wèn)題,應(yīng)用本方法得到的數(shù)值結(jié)果隨著網(wǎng)格的細(xì)化穩(wěn)定地收斂于解析解。一維及二維算例的結(jié)果分析表明,應(yīng)變局部化區(qū)域的尺寸與預(yù)測(cè)值基本相符,并沒有隨著網(wǎng)格尺寸的細(xì)化而變小。這說(shuō)明本文方法較好地克服了應(yīng)變局部化模擬中的網(wǎng)格相關(guān)性的問(wèn)題。最后針對(duì)具體算例,分析了材料內(nèi)尺度對(duì)應(yīng)變局部化區(qū)域尺寸及荷載-位移曲線的影響,驗(yàn)證了本文得出的兩者之間的定量關(guān)系。本文提出的方法只要求單元之間的位移場(chǎng)具有C0連續(xù)性且無(wú)需引入新的參數(shù),比較容易嵌入到現(xiàn)有的有限元程序中。
[Abstract]:Strain localization occurs when many civil engineering materials are loaded to near failure. The classical continuum theory or general non-local plastic theory is used to solve the strain localization problem. The mesh-related results are obtained, that is, the size of the strain localization region (shear band) will decrease with the mesh refinement. In order to overcome the defect of mesh correlation, this paper bases on the general nonlocal plasticity theory. From the point of energy equivalence in state space, a new method to solve the strain localization problem is proposed. In this method, the local and non-local state spaces are defined for each point of the material body by using the state space theory. The internal variables of the yield point of materials can be mapped from the local state space to the non-local state space by using the weight function, and the first law of thermodynamics is adopted. An important conclusion is obtained that the plastic part and elastic part of the material body in the nonlocal state space are equal to their corresponding parts in the local state space. Finally, a general formula for solving the strain localization problem by using this method is derived, and the finite element algorithm is given. Then, a concrete one-dimensional and two-dimensional numerical example is given. The reliability of this method is verified. The one-dimensional example is a drawbar with defects. The analytical solution of the problem is derived by using this method. The quantitative relationship between the size Lcp of the characteristic plastic region (strain localization region) of the material and the internal scale l of the material is given, and the numerical solutions of one-dimensional and two-dimensional examples are given by finite element programming. The corresponding plastic strain distribution and load-displacement curve are obtained. The numerical results obtained by this method converge stably to the analytical solution with the mesh refinement. The results of one-dimensional and two-dimensional numerical examples show that the size of the strain localization region is basically consistent with the predicted value. It shows that the method in this paper can overcome the problem of mesh correlation in strain localization simulation. Finally, a concrete example is given. The influence of material internal scale on strain localization region size and load-displacement curve is analyzed. The proposed method only requires C0 continuity of the displacement field between the elements and does not need to introduce new parameters, so it is easy to embed in the existing finite element program.
【學(xué)位授予單位】：西南交通大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TU501

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