【摘要】：隨著科學(xué)的發(fā)展，數(shù)值方法在工程上的應(yīng)用越來越廣泛，其中有限元方法在工程上的應(yīng)用最廣。但有限元在處理大變形的非線性力學(xué)問題中存在網(wǎng)格畸變或纏結(jié)等不足，同時(shí)有限元在求解液體振動(dòng)、裂紋擴(kuò)展、材料相變和成形等不定邊界或可動(dòng)邊界問題時(shí)，需要重新劃分網(wǎng)格，而新舊網(wǎng)格之間物理量轉(zhuǎn)換將產(chǎn)生新的誤差。因此，無網(wǎng)格方法應(yīng)運(yùn)而生。無網(wǎng)格方法不需要借助任何單元，直接利用節(jié)點(diǎn)構(gòu)造插值函數(shù)，避免了有限元方法的以上缺陷。在多種無網(wǎng)格方法中自然單元法以其獨(dú)特的優(yōu)勢(shì)獲得了快速的發(fā)展。 當(dāng)前，超長樁大量應(yīng)用于超高層建筑、大跨橋梁和深水港口工程中。然而，超長樁現(xiàn)階段的研究相對(duì)滯后，工程中仍按普通樁理論進(jìn)行設(shè)計(jì)，現(xiàn)有理論及分析模型不能充分考慮分層土特性或橫縱荷載共同作用的影響，也無法很好地反映超長樁的承載性狀。特別在港口工程中，超長樁通常承受很大的水平荷載，并且在橫縱荷載共同作用下，往往發(fā)生大變形，而傳統(tǒng)有限元方法在模擬計(jì)算大變形的超長樁和土體的相互作用時(shí)存在網(wǎng)格畸變或纏結(jié)等問題。 針對(duì)以上問題本文在自然單元法理論基礎(chǔ)上進(jìn)一步改進(jìn)了插值函數(shù)，，并將其應(yīng)用到成層地基中超長樁水平承載力問題上。主要的研究工作及創(chuàng)新點(diǎn)如下： 1、改進(jìn)了自然單元法的插值函數(shù)，編制三維無網(wǎng)格自然單元法計(jì)算程序。本文采用的是Voronoi圖中二階結(jié)構(gòu)的邊元素作為插值變量，大幅度提高了計(jì)算效率。無網(wǎng)格程序不需要借助任何單元，直接利用節(jié)點(diǎn)構(gòu)造插值函數(shù)，避免了有限元中的網(wǎng)格畸變等問題，彌補(bǔ)了有限元在處理大變形、非線性力學(xué)等問題中存在的明顯缺陷，具有較高的工程實(shí)用價(jià)值和廣闊的應(yīng)用前景。將程序計(jì)算結(jié)果與解析解及有限元計(jì)算結(jié)果相比較，驗(yàn)證了本程序的正確性和合理性。 2、基于變分原理計(jì)入橫縱向荷載共同作用下超長樁的P-Δ效應(yīng)，推導(dǎo)出單元?jiǎng)偠刃拚仃�。針�?duì)橫縱向荷載共同作用下超長樁的大變形問題，建立考慮非線性大變形的無網(wǎng)格自然單元法計(jì)算方法。通過對(duì)實(shí)例的計(jì)算分析，驗(yàn)證了該方法的正確性和合理性，得到P-Δ效應(yīng)特征。結(jié)果表明：由于P-Δ效應(yīng)，樁的位移響應(yīng)與荷載為非線性關(guān)系。當(dāng)?shù)鼗临|(zhì)較差，樁自由長度較大時(shí)，P-Δ效應(yīng)對(duì)樁身位移和內(nèi)力的影響不可忽略。本方法為計(jì)算時(shí)考慮P-Δ效應(yīng)提供了一種簡便易行的方法，在工程設(shè)計(jì)和施工中具有一定的價(jià)值。 3、基于無網(wǎng)格自然單元法計(jì)算并分析了荷載大小、加載順序、長徑比、樁頂約束條件、水平荷載作用位置、樁土相對(duì)剛度比和荷載分布形式等諸多參數(shù)對(duì)超長樁水平承載力的影響，并得出相關(guān)結(jié)論。 4、當(dāng)層狀地基中采用p-y曲線法模擬樁周土非線性特性時(shí)，樁周土水平位移的計(jì)算誤差隨荷載增大而增大。針對(duì)該問題本文采用層狀彈性體系理論考慮土體縱向連續(xù)性，并利用層狀各向同性體的研究方法，建立了適用于樁周層狀地基的水平位移系數(shù)傳遞矩陣解法。根據(jù)有限單元等效載荷的計(jì)算原理，推導(dǎo)出水平位移系數(shù)矩陣，并給出外荷載較大時(shí)，p-y曲線法樁周土體水平位移的修正式。根據(jù)所建立的模型編制程序，對(duì)某三層地基土水平位移系數(shù)矩陣進(jìn)行了計(jì)算和分析，驗(yàn)證了該方法的正確性和合理性。由于計(jì)入了土體的縱向連續(xù)性，本文方法所得的水平位移影響系數(shù)曲線在荷載作用點(diǎn)的及其鄰近區(qū)域較Mindlin解的曲線更平滑，位移小于Mindlin解的結(jié)果。這表明當(dāng)土層間性質(zhì)差異較大時(shí)，本文方法能更好地體現(xiàn)層狀土體實(shí)際分布差異的影響和臨近土層間的相互作用。
[Abstract]:With the development of science, the application of numerical methods to engineering is becoming more and more extensive, and the finite element method is the most widely used in engineering. However, the finite element method has the defects of grid distortion or entanglement in the nonlinear mechanical problems dealing with large deformation. At the same time, the finite element method is used to solve the liquid vibration, crack propagation, material transformation and forming. In the case of boundary or movable boundary, it is necessary to remesh the grid, and the physical quantity conversion between the old and the old grids will produce new errors. Therefore, the meshless method emerges as the times require. The unit method has gained rapid development with its unique advantages.
At present, super long piles are widely used in super high rise buildings, large span bridges and deepwater port engineering. However, the research of super long piles is relatively lagging at the present stage. In the project, the design is still in accordance with the common pile theory. The existing theory and analysis model can not fully consider the effects of the characteristics of layered soil or vertical and longitudinal loads. Bearing behavior of long piles, especially in port engineering, super long piles usually bear large horizontal loads, and large deformation often occurs under the joint action of transverse and longitudinal loads, and the traditional finite element method has the problems of lattice distortion or entanglement in the interaction of large deformation super long piles and soil.
In this paper, the interpolation function is further improved on the basis of the theory of natural element method, and applied to the horizontal bearing capacity of the super long pile in the layered foundation. The main research work and innovation points are as follows:
1, the interpolation function of the natural element method is improved and the three-dimensional meshless natural element method is developed. This paper uses the edge elements of the two order structure in the Voronoi diagram as the interpolation variable, which greatly improves the computational efficiency. The problems of grid distortion make up the obvious defects of the finite element method in dealing with large deformation, nonlinear mechanics and other problems. It has high practical value and wide application prospect. The results of the program calculation are compared with the analytical solution and the finite element calculation results, which verify the correctness and rationality of the program.
2, based on the variational principle, the P- delta effect of a super long pile under the joint action of transverse and longitudinal loads is calculated and the element stiffness correction matrix is derived. In view of the large deformation of a super long pile under the joint action of transverse and longitudinal loads, a meshless natural element method for calculating the nonlinear large deformation is established. The P- delta effect shows that the displacement response of the pile is nonlinear due to the P- delta effect. The effect of the P- delta effect on the displacement and internal force of the pile can not be ignored when the soil quality is poor and the free length of the pile is large. This method provides a simple and easy method to consider the P- delta effect in the calculation. It has a certain value in engineering design and construction.
3, based on the meshless natural element method, the effects of load size, loading order, length diameter ratio, pile top constraint conditions, horizontal load position, relative stiffness ratio of pile and soil and load distribution form on the horizontal bearing capacity of super long pile are analyzed and the related conclusions are obtained.
4, when the p-y curve method is used to simulate the nonlinear characteristics of pile soil, the calculation error of the horizontal displacement of pile soil increases with the increase of load. In this paper, the longitudinal continuity of soil is considered by the theory of layered elastic system, and the layered soil is used to establish the layered soil foundation. The horizontal displacement coefficient transfer matrix method is used. According to the calculation principle of the equivalent load of the finite element, the horizontal displacement coefficient matrix is derived, and the modified formula of the horizontal displacement of the soil around the pile under the p-y curve is given when the external load is large. According to the established program, the horizontal displacement coefficient matrix of a three layer ground soil is calculated and divided. The correctness and rationality of the method is verified. As the longitudinal continuity of the soil is taken into account, the curve of the influence coefficient of horizontal displacement obtained by this method is more smooth than the Mindlin solution in the loading point and its adjacent area, and the displacement is less than the result of Mindlin solution. It can better reflect the difference between the actual distribution of layered soil and the interaction between adjacent soil layers.
【學(xué)位授予單位】：上海大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2013
【分類號(hào)】：TU473.1

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