本文選題：有限元 + 應變局部化��； 參考：《西南交通大學》2014年碩士論文

【摘要】：在許多工程材料(如混凝土、巖石和沙土等)的破壞過程中,可以觀察到剪切帶局部化的現(xiàn)象.伴隨剪切帶局部化現(xiàn)象發(fā)生的同時是材料承載能力的逐漸喪失直致完全破壞。剪切帶局部的數(shù)值模擬對于分析材料和結構的破壞機理、預測混凝土和巖土結構破壞行為以及正確估計建筑物地基承載能力都具有重要意義。本文分析了古典連續(xù)介質(zhì)力學理論進行剪切帶局部化的有限元數(shù)值模擬的缺陷,通過一維和二維數(shù)值算例驗證了古典連續(xù)介質(zhì)力學模型所導致的數(shù)值結果的網(wǎng)格相關性,論述了其產(chǎn)生的根本原因是控制微分方程喪失強橢圓性導致彈塑性邊值問題不適定,進而導致計算結果的不唯一。從物理的角度分析,基于古典連續(xù)介質(zhì)力學理論的控制微分方程喪失橢圓性的原因是其本構關系模型中沒有引入材料內(nèi)尺度的概念。本文總結分析了已有的用于矯正網(wǎng)格相關性的各種理論和模型,并在此基礎上提出了一個非局部塑性模型用于剪切帶局部化的有限元分析。所提的模型基于積分形式的非局部塑性理論和代表性體積元(RVE)的概念,在本構關系方程中引入了材料內(nèi)尺度,通過被積函數(shù)的泰勒展開建立了積分形式的非局部模型和其近似等效的微分方程之間的關系。本文導出了耦合的增量塑性一致性方程和增量平衡方程的變分形式,并基于伽遼金近似方法(Galerkin's Method)得出了有限元列式,并提出了用于本構方程積分的非局部有限元和移動邊界技術。將本文提出的非局部模型用于一維和二維問題的變形局部化的有限元分析結果表明,本文提出的非局部模型能夠得出客觀的模擬結果,剪切帶的厚度與網(wǎng)格大小無關,而是取決于材料內(nèi)尺度。當材料內(nèi)尺度趨近于零時,非局部理論的模擬結果接近于局部理論的結果。本文還提出了將來需要進一步研究的問題。
[Abstract]:In many engineering materials (such as concrete, rock and sand etc.) the destruction process, can be observed in the shear band localization phenomenon. With simultaneous shear band localization phenomenon is the carrying capacity of the material lost gradually until completely destroyed. The numerical simulation for the local shear failure mechanism analysis of material and structure, prediction of failure the soil structure of rock and concrete behavior and correct estimation plays an important role in building foundation bearing capacity. This paper analyzes the classical continuum mechanics theory of finite element simulation of shear band localization numerical grid defects, through correlation of one-dimensional and two-dimensional numerical examples to verify the numerical results of classical continuum mechanics model which, discusses the the basic reason is the loss of strong ellipticity control differential equation leads to the problem of ill posed elastoplastic boundary value, which leads to the results Not only the analysis. From the physical point of view, the reason of loss of control of elliptic differential equation from classical continuum mechanics theory is based on the concept of not introducing constitutive material scale relationship model. This paper summarizes and analyzes the existing correction for various mesh correlation theory and model, and put forward a a non local plasticity model for finite element analysis of shear band localization. The proposed model based on the integral form of the non local plasticity theory and the representative volume element (RVE) concept, in the material constitutive relation equation into the inner scale, the Taylor integrand started to establish the relationship between integral form the non local model and its approximate equivalent differential equations. In this paper, the coupling of the incremental plastic consistency equation and the incremental equilibrium equation of variational form is derived, and based on the Galerkin approximation method (Galer Kin's Method) the finite element formulation, and puts forward the integral constitutive equation for nonlocal finite element and moving boundary technique. The proposed nonlocal model for finite element deformation localization of 1D and 2D problem analysis showed that can non local model proposed in this paper the results of objective. The thickness of the shear band and the mesh size, but depends on the material scale. When the material scale tends to zero, the simulation results are close to the non local theory of local theory results. This paper also put forward the future needs further study.

【學位授予單位】：西南交通大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：TU43

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本文編號：1754924