本文選題：非飽和多孔介質(zhì) + 一維問題　； 參考：《浙江大學(xué)》2013年碩士論文

【摘要】：多孔介質(zhì)的波動問題是巖土工程、地震工程、海洋工程、環(huán)境工程等領(lǐng)域的重要基礎(chǔ)課題,而瞬態(tài)響應(yīng)是波動理論中的重要一環(huán)。本文即單層多孔介質(zhì)的一維瞬態(tài)響應(yīng)問題開展了半解析研究,并得到了一些成果。 針對單層非飽和多孔介質(zhì)一維瞬態(tài)響應(yīng)問題,采用Zienkiewicz基于Biot理論提出的非飽和多孔介質(zhì)波動方程,考慮兩相流體和固體顆粒的壓縮性以及慣性、粘滯和機(jī)械耦合作用,采用半解析的方法獲得了十類典型非齊次邊界條件下單層非飽和多孔介質(zhì)的一維瞬態(tài)響應(yīng)解。首先推導(dǎo)出無量綱化后以位移表示的控制方程,并將其寫成矩陣形式。然后將邊界條件齊次化,求解控制方程所對應(yīng)的特征值問題,得到了滿足齊次邊界條件的特征值和相對應(yīng)的特征函數(shù)。根據(jù)變異系數(shù)法并利用特征函數(shù)的正交性,得到了一系列僅粘滯耦合的關(guān)于時間的二階常微分方程及相應(yīng)的初始條件。在此基礎(chǔ)上,運用改進(jìn)后的精細(xì)時程積分法給出了常微分方程組的數(shù)值解。最后,通過若干算例驗證了本文結(jié)果的正確性并探討了不同滲透系數(shù)、荷載頻率、流體飽和度以及邊界條件下單層非飽和多孔介質(zhì)一維瞬態(tài)動力響應(yīng)的特點。該方法不受材料參數(shù)和邊界條件的限制,具有良好的計算精度、穩(wěn)定性和適用性。 針對單層非飽和多孔介質(zhì)瞬態(tài)響應(yīng)求解過程中遇到的動力矩陣不可逆問題,對原有的精細(xì)時程積分法進(jìn)行了一定改進(jìn)。這一改進(jìn)拓寬了精細(xì)積分法的適用范圍,使其能應(yīng)用于剛度矩陣奇異或接近奇異的情形,從而滿足本文各類邊界條件下的瞬態(tài)響應(yīng)問題求解。
[Abstract]:The wave problem of porous media is an important basic subject in geotechnical engineering, seismic engineering, ocean engineering, environmental engineering and so on, and the transient response is an important part of wave theory. In this paper, the one-dimensional transient response of single-layer porous media is studied by semi-analytical method, and some results are obtained. In view of the one-dimensional transient response of single layer unsaturated porous media, Zienkiewicz's wave equation based on Biot's theory is used to consider the compressibility of two-phase fluid and solid particles, as well as the inertial, viscous and mechanical coupling effects. The one-dimensional transient response solutions of monolayer unsaturated porous media under ten kinds of typical inhomogeneous boundary conditions are obtained by semi-analytical method. First, the governing equations expressed by displacement after dimensionless are derived and written in matrix form. Then the boundary conditions are homogeneous and the eigenvalue problem corresponding to the governing equation is solved. The eigenvalues and the corresponding eigenfunctions satisfying the homogeneous boundary conditions are obtained. According to the variation coefficient method and the orthogonality of the eigenfunction, a series of second order ordinary differential equations about time and corresponding initial conditions are obtained. On this basis, the numerical solutions of ordinary differential equations are obtained by using the improved precise time integration method. Finally, several examples are given to verify the correctness of the present results and the characteristics of one-dimensional transient dynamic response of single-layer unsaturated porous media under boundary conditions are discussed, such as different permeability coefficient, load frequency, fluid saturation and boundary conditions. The method is not limited by material parameters and boundary conditions, and has good accuracy, stability and applicability. In order to solve the irreversible problem of dynamic matrix in the process of solving the transient response of single layer unsaturated porous media, the original fine time integration method is improved. This improvement broadens the scope of application of the precise integration method and enables it to be applied to the singular or near singular cases of stiffness matrix, thus satisfying the solution of transient response problems under various boundary conditions in this paper.
【學(xué)位授予單位】：浙江大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：TU435;O357.3

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