本文關(guān)鍵詞： MEMS 尺寸效應(yīng) 應(yīng)變梯度理論 鐵木辛柯梁單元　出處：《山東大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：隨著科技的快速發(fā)展以及制造工藝水平的不斷提升,微機電系統(tǒng)(英文縮寫為MEMS)因其具有眾多優(yōu)點而被廣泛地應(yīng)用在電子產(chǎn)品、醫(yī)療器械、汽車工業(yè)以及航空航天等眾多高精尖領(lǐng)域。因此,需要對MEMS器件進行細致地分析和研究。在MEMS的結(jié)構(gòu)設(shè)計以及分析計算過程中,可以將一些結(jié)構(gòu)簡化為微板或者微梁,這也正是MEMS器件中典型的結(jié)構(gòu)。所以,分析這類微尺寸結(jié)構(gòu)的力學(xué)性能就變得非常重要。然而微觀結(jié)構(gòu)的性能和宏觀尺寸結(jié)構(gòu)的性能有著明顯的不同,因此傳統(tǒng)理論不適用于分析微觀結(jié)構(gòu)的力學(xué)性能。許多研究學(xué)者做了相關(guān)的微米結(jié)構(gòu)的力學(xué)試驗,試驗表明復(fù)合材料、多晶硅、聚合物以及金屬材料都具有尺寸效應(yīng),即隨著微結(jié)構(gòu)尺寸的不斷縮小,其材料的力學(xué)性能在不斷的增強,而這一現(xiàn)象無法用傳統(tǒng)理論進行解釋。于是需要發(fā)展和完善一種能夠適用于研究微納米結(jié)構(gòu)力學(xué)性能的理論與模型。雖然許多學(xué)者發(fā)展了多種用于解釋尺寸效應(yīng)現(xiàn)象的理論,例如非局部理論、偶應(yīng)力理論、表面能理論以及應(yīng)變梯度理論等,但是最成功的理論之一當(dāng)屬應(yīng)變梯度理論。非局部理論更加適用于結(jié)構(gòu)軟化的研究。表面能理論只考慮了表面效應(yīng)的影響而忽略了結(jié)構(gòu)體內(nèi)部的影響,因此該理論更加適用于表面與體積之比更大的納米量級的結(jié)構(gòu)。梯度彈性理論雖然計算簡單但精度較低。偶應(yīng)力理論只考慮了一種應(yīng)變梯度項,而應(yīng)變梯度理論則考慮了三種應(yīng)變梯度項,集合了多種理論的優(yōu)點,避免了一些缺點,因此該理論得到了廣泛應(yīng)用。應(yīng)用應(yīng)變梯度理論構(gòu)造了一種適用于復(fù)雜問題的非傳統(tǒng)微納米尺度鐵木辛柯梁單元。新單元中包含三個能夠預(yù)測尺寸效應(yīng)的材料長度尺寸參數(shù),同時這個單元可以通過設(shè)置材料長度尺寸參數(shù)退化為修正偶應(yīng)力理論單元或者傳統(tǒng)單元。對于傳統(tǒng)的單元,滿足C_0型連續(xù),每個單元包含兩個節(jié)點,每個節(jié)點又有兩個自由度。但對于新構(gòu)造的單元,則滿足C_1型連續(xù),每個單元包含兩個節(jié)點,每個節(jié)點又有四個自由度。新單元采用撓度和轉(zhuǎn)角獨立差值,有限元方程、剛度矩陣和質(zhì)量矩陣通過積分弱形式可推導(dǎo)得出。為了檢驗新單元的精確性和可靠性,研究了新單元的收斂情況以及剪切鎖死問題。接著研究了鐵木辛柯梁不同邊界條件下的靜態(tài)問題和動態(tài)問題。為了精確地研究微納米結(jié)構(gòu)的尺寸效應(yīng),本文還同時考慮了表面影響和體影響。從物理角度來說,尺寸效應(yīng)不僅是由體產(chǎn)生的,還與表面有關(guān)。表面能理論和應(yīng)變梯度理論分別用于說明表面影響和體影響。本文構(gòu)造了基于應(yīng)變梯度理論以及表面能理論的伯努利-歐拉梁模型和鐵木辛柯梁模型�？刂品匠�、邊界條件和初始條件可以應(yīng)用哈密頓原理得出。兩個新模型中都包含三個材料長度尺寸參數(shù)和三個表面彈性常數(shù)。新構(gòu)造的非傳統(tǒng)模型不僅能夠退化為只考慮體影響或者只考慮表面影響的模型,還可以退化為修正偶應(yīng)力理論模型和傳統(tǒng)模型。除此之外,當(dāng)不考慮剪切變形影響時,新構(gòu)造的模型可以退化為伯努利-歐拉梁模型。為了說明新構(gòu)造的模型,研究了微納米尺度的伯努利-歐拉梁以及鐵木辛柯梁的靜態(tài)問題和動態(tài)問題。結(jié)果顯示當(dāng)梁的尺寸很小時,不同模型之間的差別很大,即尺寸效應(yīng)很明顯。隨著納米梁尺寸的不斷變大,模型之間的差別不斷減小。本文還基于應(yīng)變梯度理論研究了具有彈性支座的Kirchhoff微板模型。此模型引入了三個額外的材料參數(shù),使得新模型能夠預(yù)測彈性支撐微板結(jié)構(gòu)的尺寸效應(yīng)。通過設(shè)置一些材料參數(shù)等于零,能夠?qū)⒋四Ｐ屯嘶癁閭鹘y(tǒng)理論模型或修正偶應(yīng)力理論模型。結(jié)果討論中給出了四邊簡支的方形微板靜態(tài)彎曲問題、穩(wěn)定性問題和自由振動問題等的研究,同時比較了當(dāng)前模型和其他退化模型之間的差別,并研究了彈性支撐對板的影響。此研究可以有效地指導(dǎo)具有彈性支撐方形微板的分析與設(shè)計,因此具有很好的應(yīng)用前景。
[Abstract]:With the rapid development of technology and manufacturing level rising, microelectromechanical systems (abbreviated as MEMS English) because it has many advantages and is widely used in electronic products, medical devices, automotive industry and aerospace and other high-tech fields. Therefore, the need for detailed analysis and Research on the MEMS device. The MEMS structure design and analysis of the calculation process, can be simplified as micro plate or micro beam, which is the typical structure of the MEMS device. Therefore, the analysis of mechanical properties of micro size structures have become very important. However, the performance of microstructure and macro size structure has obvious is different, so the traditional theory is not applicable to the analysis of mechanical properties of micro structures. Many scholars have done research on mechanical test of micron structure of the relevant test results show that the composite, polycrystalline silicon, polymer And metal materials have size effect, with the size of the micro structure is shrinking, the mechanical properties of the materials in the unceasing enhancement, and this phenomenon can not use the traditional theory to explain. So we need to develop and perfect the theory and a model can be applied to the research on micro nano mechanical properties. Although many scholars have developed many used to explain the size effect of the theory, such as the non local theory, couple stress theory, surface energy theory and the strain gradient theory, but the theory is undoubtedly one of the most successful. The strain gradient theory of nonlocal theory is more suitable to study the structure of softening. The theory of surface energy only considering the influence of the surface effect and ignore influence of structure internal structure, so the theory is more suitable for the surface to volume ratio the greater the nanometer level. Gradient elasticity theory is simpler but more precision Low. The couple stress theory considers only a strain gradient, and the strain gradient theory is considered the three strain gradient, combines the advantages of a variety of theory, to avoid some disadvantages, so the theory has been widely applied. Non traditional application of strain gradient theory is constructed for complex problem of micro nanometer scale Timoshenko beam element. The new unit contains three material length dimensions can predict the size effect parameters, and the unit can be set through the material length parameter degradation stress theory unit or the traditional unit. The modified couple for the traditional unit, meet the C_0 continuous, each containing two nodes each. Nodes have two degrees of freedom. But for the new structure of the unit, will meet C_1 continuous, each unit contains two nodes, each node has four degrees of freedom. The new unit adopts deflection and rotation Independent difference, finite element equation, the stiffness matrix and mass matrix can be derived through integral weak form. In order to test the accuracy and reliability of the new unit, a new research unit and convergence of shear locking problem. Then study the static problem of iron Xin Keliang under different boundary conditions and dynamic problems. In order to accurately study the size effect of micro nano structure, this paper also considers the influence of the surface effect and volume. From the physical point of view, the size effect is not only by the body, but also with the surface. The surface energy theory and strain gradient theory respectively used to illustrate the influence of surface effect and volume. This paper constructed the strain gradient theory and the theory of surface energy the Bernoulli Euler beam model and Timoshenko beam model. Based on the control equations, initial and boundary conditions can be obtained using the Hamilton principle. All two new models Three material length parameters and three surface elastic constants. Non traditional model of the new structure can not only reduced to only consider the impact or only consider the surface of the model, also can be reduced to the modified couple stress theory model and traditional model. In addition, when not considering the effect of shear deformation, new structure the model can be reduced to the Bernoulli Euler beam model. In order to illustrate the new structure model of micro nano scale Bernoulli Euler beam and Timoshenko beam static problems and dynamic problems. The results show that when the beam size is very small, the difference between the different models, namely the size effect is obvious. With the development of nano the beam size becomes larger and larger, the difference between the model decreases. The strain gradient theory is studied based on the Kirchhoff micro plate with elastic support model. This model introduces three additional material The material parameters, the new model can predict the size effect of micro elastic support plate structure. By setting some material parameters is equal to zero, this model can degenerate stress theoretical model for the traditional theory model. The results are given in the discussion I simply supported square plate micro static bending, free vibration and stability studies so, at the same time were compared between the current model and other degradation model differences, and study the influence of the elastic support plate. The analysis and design of this study can effectively guide the square plates with elastic support, so it has good application prospects.

【學(xué)位授予單位】：山東大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O342

【相似文獻】

相關(guān)期刊論文 前10條

1 周仁賢;康翠萍;;論技術(shù)的梯度理論與技術(shù)市場、轉(zhuǎn)移(流通)規(guī)律[J];科學(xué)管理研究;1985年03期

2 徐紀敏;;梯度理論與形勢法則[J];科學(xué)管理研究;1985年04期

3 潘照東;;論我國對外開放的目標(biāo)與政策——與夏禹龍等同志“開放的梯度理論”商榷[J];科學(xué)管理研究;1985年04期

4 汪翔;;也談梯度理論與我國的科技發(fā)展戰(zhàn)略原則——兼與徐紀敏同志商榷[J];科學(xué)管理研究;1985年06期

5 張明忠;;關(guān)于“梯度理論”的異議[J];科學(xué)管理研究;1986年03期

6 馬希良;;梯度劃分與“城鄉(xiāng)梯度論”淺析[J];科學(xué)管理研究;1986年03期

7 尚國森;論科學(xué)技術(shù)發(fā)展的“新序”[J];學(xué)會;1993年06期

8 李雷;周毅英;李文杰;謝水生;;應(yīng)變梯度理論及其數(shù)值方法研究進展[J];河南理工大學(xué)學(xué)報(自然科學(xué)版);2009年01期

9 魏悅廣,王學(xué)崢,武曉雷,白以龍;微壓痕尺度效應(yīng)的理論和實驗[J];中國科學(xué)(A輯);2000年11期

10 趙杰;陳萬吉;冀賓;;關(guān)于兩種二階應(yīng)變梯度理論[J];力學(xué)學(xué)報;2010年01期

相關(guān)會議論文 前6條

1 趙前前;;梯度理論視角下西部政府大部制改革推進研究[A];“中國特色社會主義行政管理體制”研討會暨中國行政管理學(xué)會第20屆年會論文集[C];2010年

2 劉剛;張旺民;;基于梯度理論的中部現(xiàn)代服務(wù)業(yè)的發(fā)展研究[A];中部崛起與現(xiàn)代服務(wù)業(yè)——第二屆中部商業(yè)經(jīng)濟論壇論文集[C];2008年

3 余壽文;王剛鋒;;應(yīng)變梯度理論在界面力學(xué)中的應(yīng)用[A];“力學(xué)2000”學(xué)術(shù)大會論文集[C];2000年

4 陳少華;馮彪;;單軸拉伸下剪切帶的應(yīng)變梯度理論預(yù)測[A];塑性力學(xué)新進展——2011年全國塑性力學(xué)會議論文集[C];2011年

5 李雷;賀睿;謝水生;;應(yīng)變梯度理論的無網(wǎng)格數(shù)值方法研究[A];中國力學(xué)學(xué)會學(xué)術(shù)大會'2009論文摘要集[C];2009年

6 解海鷗;魏悅廣;;顆粒增強復(fù)合材料的界面效應(yīng)[A];第16屆全國結(jié)構(gòu)工程學(xué)術(shù)會議論文集（第Ⅰ冊）[C];2007年

相關(guān)重要報紙文章 前1條

1 本報記者 朱嘉俊;產(chǎn)業(yè)轉(zhuǎn)移：寧波的梯度理論[N];中國企業(yè)報;2010年

相關(guān)博士學(xué)位論文 前3條

1 馬旭;偶應(yīng)力/應(yīng)變梯度理論及其雜交應(yīng)力元分析[D];大連理工大學(xué);2014年

2 趙杰;偶應(yīng)力/應(yīng)變梯度理論的精化不協(xié)調(diào)元分析[D];大連理工大學(xué);2010年

3 冀賓;細觀偶應(yīng)力/應(yīng)變梯度彈塑性理論的幾個基本問題[D];大連理工大學(xué);2010年

相關(guān)碩士學(xué)位論文 前4條

1 張龍;微納米結(jié)構(gòu)的力學(xué)行為及其有限單元方法研究[D];山東大學(xué);2017年

2 王艷飛;基于梯度理論的農(nóng)村社會發(fā)展的實證研究[D];西北農(nóng)林科技大學(xué);2010年

3 李凱銳;深部圍巖分區(qū)破裂梯度模型的數(shù)值研究[D];北京建筑大學(xué);2014年

4 秦楊;基于梯度理論的重慶市區(qū)域科技發(fā)展差異及對策分析[D];重慶大學(xué);2014年

，

本文編號：1445409