臺灣博碩士論文加值系統

對於褶皺的生成，一向是對構造有興趣者所關心的課題之一。而接續前人的研究，雖在一般均質材料之拱彎褶皺理論上已有相當基礎，對於更接近實際地質材料的非等向性材料卻較少著墨。本研究的主要目的即在於以數值模擬的方式，並根據前人已有的彈性岩層褶皺理論為基礎，來對非等向性岩層受拱彎褶皺行為做初步觀察，並期望最終能與實際野外情形比較。
本研究使用美國HKS公司所發展的ABAQUS軟體，採用有限元素法進行數值分析。拱彎褶皺的模擬技巧採用張逎楨（1999）所建立的預壓縮擾動法。所研究之材料使用完全彈性的假設。模型方面採用硬層上下包圍介質之二維平面應變模型，規劃不同的邊界條件（不同預壓縮量）配上不同的材料性質（完全等向性、硬層橫等向性、介質橫等向性、硬層與介質皆為橫等向性、不同異向性強度、橫等向性對稱軸對應座標軸不同方向……等等）來模擬。
當考慮一等向性彈性岩層上下方有介質束制時，可導出欲使其褶皺所需施加之外力與所產生的褶皺波長之間的關係式，當力小於一臨界值，於褶皺生成瞬間褶皺會形成振幅衰退波型；大於此臨界值，則會形成雙頻褶皺波型。當介質材料在褶皺振幅加強方向的彈性模數減弱時，對褶皺波型有明顯影響；硬層材料在岩層縮短方向的彈性模數減弱時，對褶皺波型有明顯影響；而以介質在振幅加強方向，與硬層在岩層縮短方向上的這兩個彈性模數代入褶皺理論公式之中所得到的等效式，和數值模擬結果相當符合。由此種方法模擬之褶皺，其最大伸張應變方向的情形，符合受到切縱應變與岩層平行剪切的情形；在等向性材料與非等向性材料案例間，最大伸張應變方向並無明顯差異。應變量R則會受到材料之非等向性，以及褶皺最終波型的共同影響。當最終的波數相同時，介質在振幅加強方向彈性模數減弱的情形所得到的R值，會比等向性材料的情形所得到的R值高。

The mechanics of folding has long been an important issue for those interested in structural geology. Although the theoretical model about the buckle of homogeneous isotropic materials has been established, few have concerned about anisotropic materials, which are more realistic. This thesis aims to study the buckle fold composed of anisotropic materials through numerical simulation.
This thesis uses ABAQUS developed by H.K.S. Inc., a finite element progrom, and the end-rotational method developed by Chang (1999). I constructed this model that is a two dimensional plane strain model, where the competent layer is surrounded by matrix, and the materials in this model are linear elastic. The factors, including material properties (degree of anisotropy, direction of the axis of symmetry of rotation… etc.), and boundary conditions were considered.
The relation between the force to buckle an isotropic elastic layer surrounded by matrix and its subsequent wavelength has been discussed. When the force is smaller than a critical value, the amplitude of the fold will be attenuated. On the contrary, the waveform comprises of two frequencies when the force is bigger than that critical value. The change of Young’s modulus in matrix in the direction normal to layer parallel shortening, and in competent layer in the direction of layer parallel shortening, affects waveform significantly. If we replace the Young’s modulus in the theoretical buckle formula by the Young’s modulus mentioned above, the theoretical formula fits the simulation results well. The largest strain elongation direction pattern corresponds to the description of folds with combined tangential longitudinal strain and layer parallel shear. The largest strain elongation directions are almost the same whether the models are comprised by isotropic or transversely isotropic material. But the aspect ratio R of the strain ellipse is affected by the anisotropy of material and the final waveform of the fold. The R of the transversely isotropic matrix model is larger than isotropic model if the final wave number of the two model are the same.

誌謝……………………………………………………………………I
摘要……………………………………………………………………II
Abstract………………………………………………………………IV
目錄……………………………………………………………………VI
表目錄…………………………………………………………………VIII
圖目錄…………………………………………………………………X
第一章 緒論…………………………………………………………1
1.1 研究動機……………………………………………………1
1.2 研究目的與方法……………………………………………2
第二章 文獻回顧……………………………………………………3
2.1 褶皺的分類…………………………………………………3
2.2 褶皺的發育過程……………………………………………4
2.3 彈性材料褶皺理論…………………………………………5
2.4 非等向性材料簡介…………………………………………8
2.5 受切縱應變與岩層平行剪切的褶皺應變狀態……………13
第三章 研究方法……………………………………………………22
3.1 分析方法簡介………………………………………………22
3.2 預壓縮–擾動法……………………………………………24
3.3 預壓縮量對褶皺的影響……………………………………26
3.4 擾動量對褶皺的影響………………………………………26
3.5 數值分析模型規劃…………………………………………27
3.6 非等向性材料性質驗證……………………………………28
第四章 二維彈性岩層數值模擬……………………………………36
4.1 等向性理論公式驗證………………………………………36
4.2 非等向性材料受拱彎褶皺模型規劃………………………39
4.3 非等向性材料受拱彎褶皺數值模擬結果…………………40
4.3.1 對稱軸平行座標軸2方向，且n = 3………………………40
4.3.2 對稱軸平行座標軸1方向，且n = 3………………………44
4.3.3 對稱軸平行座標軸3方向，且n = 3………………………47
4.3.4 對稱軸平行座標軸2方向，介質非等向性之模擬………48
4.3.5 介質與硬層材料方向性不同之模擬………………………50
4.4 二維非等向性材料拱彎褶皺劈理模擬……………………51
4.5 結果與討論…………………………………………………56
第五章 結論與討論………………………………………………101
5.1 結論………………………………………………………101
5.2 討論………………………………………………………102
參考文獻………………………………………………………………104
附錄A…………………………………………………………………107

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