【摘要】：隨著航天事業(yè)與電子工業(yè)的快速發(fā)展,復(fù)合材料及其結(jié)構(gòu)在現(xiàn)實(shí)生活的方方面面均有應(yīng)用,超常材料作為材料科學(xué)的新興領(lǐng)域吸引了大量學(xué)者的關(guān)注,這類材料擁有自然材料不具備的性質(zhì),如負(fù)折射率、超吸收、負(fù)泊松比等超凡特性。五零能模式材料就是一種新型的人工超材料,雖屬于彈性材料,但組成其單胞的特殊構(gòu)型使其宏觀靜態(tài)表現(xiàn)為僅能承載一種受力狀態(tài),動(dòng)態(tài)表現(xiàn)為僅能傳播一種彈性波,等效彈性模量矩陣六個(gè)特征值中僅一個(gè)不為零。針對(duì)上述新興材料,對(duì)材料本身力學(xué)性能的準(zhǔn)確預(yù)測(cè)更是該材料能成功應(yīng)用的關(guān)鍵。典型預(yù)測(cè)周期性材料等效性能的方法有漸近均勻化方法和代表體元法。代表體元法力學(xué)模型清晰,操作容易,但因缺乏嚴(yán)格數(shù)學(xué)理論,對(duì)材料的性質(zhì)不能精確預(yù)測(cè),僅可作為近似估計(jì)使用。與之相反的是漸近均勻化方法,它基于數(shù)學(xué)理論基礎(chǔ)嚴(yán)謹(jǐn)?shù)臄z動(dòng)理論,在復(fù)合材料等效性質(zhì)方面算法成熟。但復(fù)雜的計(jì)算過程阻礙了該方法的應(yīng)用。本文基于ANSYS平臺(tái)實(shí)現(xiàn)代表體元法與漸近均勻化方法的有限元求解,編制兩種方法的APDL程序,實(shí)現(xiàn)復(fù)合材料等效性能的預(yù)測(cè)。本文給出多種單胞構(gòu)型,針對(duì)這些單胞桁架構(gòu)型計(jì)算得到等效彈性模量矩陣特征值,從而得到五種五零能模式材料的單胞構(gòu)型。計(jì)算材料單胞等效彈性性能,得到等效彈性矩陣及特征值,通過比較可知,這五種單胞構(gòu)型可分成兩類不同的彈性特性,其中一類材料可傳遞彈性膨脹波,另一類可傳遞彈性剪切波。計(jì)算單胞的等效彈性性能時(shí),分別采用代表體元法和漸近均勻化法兩種計(jì)算方式。研究表明對(duì)于這種低密度彈性材料的分析,從計(jì)算時(shí)間及計(jì)算精度方面考慮,代表體元法更適合。五零能模式材料的分析分為兩步更直觀,開始從單胞桁架模型入手,檢驗(yàn)單胞構(gòu)型是否滿足五零能模式的定義,然后分析單胞實(shí)體模型,比較單胞構(gòu)型參數(shù)與材料等效彈性模量的關(guān)系。
[Abstract]:With the rapid development of space industry and electronics industry, composite materials and their structures have been applied in all aspects of real life. As a new field of material science, supernormal materials have attracted a lot of scholars'attention. These materials have some special properties that natural materials do not have, such as negative refractive index, superabsorption, negative Poisson's ratio and so on. Zero-energy mode material is a new type of artificial metamaterial. Although it belongs to elastic material, the special configuration of its cell makes it show that it can only bear one stress state in macro-static state and only one elastic wave can be transmitted in dynamic state. Only one of the six eigenvalues of the equivalent elastic modulus matrix is not zero. Accurate prediction of the mechanical properties of the material itself is the key to its successful application. The typical methods for predicting the equivalent properties of periodic materials are asymptotic homogenization method and representative voxel method. On the contrary, the asymptotic homogenization method, which is based on the perturbation theory with rigorous mathematical theory, is mature in the equivalent properties of composite materials. But the complex calculation process hinders the application of this method. In this paper, the equivalent modulus matrix eigenvalues are calculated for these single cell truss structures, and then the cell configurations of five kinds of 50-energy mode materials are obtained. By comparing the eigenvalues, we can see that the five cell configurations can be divided into two kinds of different elastic properties, one kind of material can transmit elastic expansion wave, the other kind can transmit elastic shear wave. The representative voxel method is more suitable for the analysis of elastic materials in terms of calculation time and accuracy. The analysis of 50-energy mode materials is divided into two steps, which are more intuitive. Starting with the cell truss model, we examine whether the cell configuration meets the definition of 50-energy mode, then analyze the cell solid model, compare the cell configuration parameters and materials, etc. The relationship between effective elastic modulus.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：TB33

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本文編號(hào)：2236989