本文選題：復(fù)雜層狀地基 + 基礎(chǔ)-地基動(dòng)力相互作用�。� 參考：《大連理工大學(xué)》2014年博士論文

【摘要】：地基動(dòng)力剛度的求解是結(jié)構(gòu)-地基動(dòng)力相互作用分析的關(guān)鍵環(huán)節(jié),求得地基動(dòng)力剛度后可以與有限元等數(shù)值分析程序相結(jié)合進(jìn)行上部結(jié)構(gòu)和地基系統(tǒng)在地震、爆炸等荷載作用下動(dòng)力響應(yīng)的求解。大量的理論研究和分析表明,復(fù)雜層狀地基對(duì)基礎(chǔ)以及上部結(jié)構(gòu)的動(dòng)力特性有十分重要的影響,尤其是當(dāng)?shù)鼗哂懈飨虍愋蕴匦詴r(shí),廣大的研究者和工程技術(shù)人員已經(jīng)意識(shí)到這一點(diǎn),并開(kāi)展了很多相關(guān)的研究工作,提出了多種針對(duì)層狀地基動(dòng)力剛度求解的數(shù)值算法。從結(jié)構(gòu)-地基動(dòng)力相互作用問(wèn)題的發(fā)展現(xiàn)狀看,目前的研究算法往往具有局限性,或者對(duì)層狀地基的層數(shù)和厚度有限制,或者對(duì)地基的各向同異性特性有限制,或者對(duì)基礎(chǔ)近場(chǎng)的開(kāi)挖有限制等。 本文基于層狀地基動(dòng)力方程的積分變換,結(jié)合精細(xì)積分算法和對(duì)偶波動(dòng)方程的應(yīng)用,提出了一種求解復(fù)雜層狀地基上明置或埋置基礎(chǔ)動(dòng)力剛度矩陣的混合算法。該算法克服了已有算法的局限性,并具有以下特性：(1)對(duì)任意水平層狀地基具有廣泛適用性,對(duì)地基的厚度、彈性地基材料屬性沒(méi)有任何限制；(2)計(jì)算中采用精細(xì)積分算法,保證了計(jì)算結(jié)果可以根據(jù)要求達(dá)到很高的精度,某種意義上可以認(rèn)為其求解精度由計(jì)算所用的計(jì)算機(jī)精度決定的；(3)該算法中的矩陣維數(shù)均較小,因此有較高的求解效率；(4)此算法基于矩陣數(shù)值計(jì)算,數(shù)值求解穩(wěn)定。 本文主要研究?jī)?nèi)容和取得成果有： 1、針對(duì)各向同性層狀地基,利用Hankel變換將頻率-空間域內(nèi)的波動(dòng)方程轉(zhuǎn)換到頻率-波數(shù)域內(nèi),并解耦為平面內(nèi)運(yùn)動(dòng)和出平面運(yùn)動(dòng)。引入對(duì)偶向量將二階常微分方程降階為一階常微分方程,應(yīng)用精細(xì)積分算法進(jìn)行求解,最后分別利用Fourier逆變換和Hankel逆變換得到各向同性層狀地基表面廣義平面波動(dòng)問(wèn)題和三維波動(dòng)問(wèn)題的格林函數(shù)。利用此算法求解得到的格林函數(shù)可以求解各向同性層狀地基表面條帶基礎(chǔ)和任意形狀基礎(chǔ)的動(dòng)力剛度矩陣。數(shù)值算例驗(yàn)證了本文算法的準(zhǔn)確性。 2、針對(duì)各向異性層狀地基,利用Fourier變換將頻率-空間域內(nèi)的波動(dòng)方程轉(zhuǎn)化到頻率-波數(shù)域內(nèi)的二階常微分方程,引入對(duì)偶向量將其轉(zhuǎn)化為一階常微分方程,應(yīng)用精細(xì)積分算法求解得到頻率-波數(shù)域內(nèi)層狀地基表面的動(dòng)力柔度矩陣。最后利用Fourier逆變換得到各向異性層狀地基表面廣義平面波動(dòng)問(wèn)題和三維波動(dòng)問(wèn)題的格林函數(shù)。利用求解得到的格林函數(shù)求解層狀地基表面條帶基礎(chǔ)和任意形狀基礎(chǔ)的動(dòng)力剛度／柔度矩陣,進(jìn)而分析層狀地基的各向異性特性對(duì)層狀地基表面基礎(chǔ)動(dòng)力剛度的影響。結(jié)果表明,層狀地基的各向異性特性對(duì)基礎(chǔ)-地基動(dòng)力相互作用有顯著的影響。 3、埋置基礎(chǔ)的研究對(duì)實(shí)際工程有重大的應(yīng)用價(jià)值,對(duì)前述求解層狀地基表面格林函數(shù)的方法進(jìn)行擴(kuò)展,求解各向同性和各向異性層狀地基內(nèi)部任意點(diǎn)的格林函數(shù),進(jìn)而結(jié)合容積算法求解開(kāi)挖條帶基礎(chǔ)和任意形狀埋置基礎(chǔ)動(dòng)力剛度矩陣,數(shù)值算例驗(yàn)證了本文算法的精確性。 4、利用本文提出的求解層狀地基動(dòng)力響應(yīng)的混合算法,分析層狀地基相鄰基礎(chǔ)動(dòng)力相互作用問(wèn)題,并對(duì)層狀地基厚度、地基材料阻尼比、基礎(chǔ)間距、層狀地基剪切波速比值以及地基的各項(xiàng)異性特性對(duì)基礎(chǔ)-地基-基礎(chǔ)動(dòng)力相互作用進(jìn)行廣泛的參數(shù)分析。結(jié)果表明,層狀地基的不均勻特性以及各向異性特性對(duì)相鄰基礎(chǔ)動(dòng)力相互作用均有顯著的影響。 5、在求解得到剛性基礎(chǔ)的動(dòng)力阻抗函數(shù)基礎(chǔ)上,進(jìn)一步求解層狀地基表面剛性基礎(chǔ)在集中荷載作用下基礎(chǔ)底部地基應(yīng)力分布,研究應(yīng)力分布在各種荷載作用下隨頻率的變化規(guī)律以及層狀地基的各向異性特性對(duì)應(yīng)力分布的影響,為基礎(chǔ)和地基承載力設(shè)計(jì)提供可靠的數(shù)值依據(jù)。 6、在得到頻域解的前提下,利用Pade級(jí)數(shù)將頻率-空間域離散的基礎(chǔ)動(dòng)剛度擬合成連分式的表達(dá)形式,通過(guò)混合變量技術(shù)構(gòu)造成層狀地基時(shí)域內(nèi)的運(yùn)動(dòng)方程,然后利用精細(xì)積分時(shí)程算法進(jìn)行求解,最終得到層狀地基上任意形狀基礎(chǔ)時(shí)域內(nèi)動(dòng)荷載作用下的動(dòng)力響應(yīng)。
[Abstract]:The solution of the dynamic stiffness of the foundation is the key link of the structure - foundation dynamic interaction analysis , and the dynamic response of the superstructure and the foundation system under the action of earthquake , explosion and the like can be solved by combining the numerical analysis program such as finite element and the like after the dynamic stiffness of the foundation is obtained .

Based on the integral transformation of the dynamic equation of the layered foundation , combined with the application of the fine integral algorithm and the dual wave equation , a hybrid algorithm is proposed to solve the basic dynamic stiffness matrix on a complex layered foundation . The algorithm overcomes the limitations of the existing algorithm and has the following characteristics : ( 1 ) It has wide applicability to any horizontal layered foundation , and has no restrictions on the thickness of the foundation and the properties of the elastic foundation material ;
( 2 ) A fine integration algorithm is adopted in the calculation to ensure that the calculation results can reach very high accuracy according to the requirements , and the accuracy of the calculation can be considered to be determined by the computer accuracy used in the calculation .
( 3 ) the number of the matrix dimension in the algorithm is smaller , so that the algorithm has higher solving efficiency ;
( 4 ) The algorithm is based on matrix numerical calculation , and the numerical solution is stable .

The main research contents and achievements are as follows :

1 . According to the isotropic layered foundation , the wave equation in the frequency - space domain is transformed into the frequency - wave number domain by Hankel transformation , and the solution is decoupled into plane motion and plane motion . The second order ordinary differential equation is introduced into the first order ordinary differential equation by introducing the dual vector , and the Green function of the generalized planar wave problem and the three - dimensional wave problem of the isotropic layered foundation surface is obtained by using the inverse transformation and Hankel inverse transformation respectively .

2 . According to the anisotropic layered foundation , the wave equation in the frequency - space domain is transformed into the second order ordinary differential equation in the frequency - wave number domain by using the Fourier transform , the dual vector is introduced into the first order ordinary differential equation , and the dynamic flexibility matrix of the surface of the layered foundation in the frequency - wave number domain is obtained by using a fine integration algorithm . Finally , the effect of the anisotropic property of the layered foundation on the dynamic stiffness of the surface foundation of the layered foundation is obtained by using the Green function obtained by the solution . The results show that the anisotropic property of the layered foundation has a significant influence on the foundation - foundation dynamic interaction .

3 . The research on the buried foundation has great application value to the practical engineering , and the method for solving the Green function of the surface of the layered foundation is extended to solve the Green function of any point inside the isotropic and anisotropic layered foundation , and then the excavation strip foundation and the embedded basic dynamic stiffness matrix are solved by the volume algorithm , and the accuracy of the algorithm is verified by numerical examples .

4 . Based on the hybrid algorithm for the dynamic response of the layered foundation , this paper analyzes the interaction of the adjacent basic dynamic of the layered foundation , and analyzes the parameters of the foundation - foundation - foundation dynamic interaction with the thickness of the layered foundation , the damping ratio of the foundation material , the basal spacing , the shear wave velocity ratio of the layered foundation and the anisotropy of the foundation . The results show that the non - uniform characteristics and the anisotropy of the layered foundation have significant influence on the interaction of adjacent basic dynamic forces .

5 . On the basis of solving the dynamic impedance function of the rigid foundation , the stress distribution of the foundation under concentrated load of the rigid foundation of the surface of the layered foundation is further solved . The influence of the stress distribution with the frequency and the anisotropy of the layered foundation on the stress distribution are studied under various loads , which provides a reliable numerical basis for the design of foundation and foundation bearing capacity .

6 . Under the precondition of obtaining the frequency domain solution , the fundamental dynamic stiffness of the frequency - space domain is synthesized by the Pade series . The motion equation in the time domain of the layered foundation is constructed by the mixed variable technique , then the fine integral time history algorithm is used to solve the motion equation , and finally , the dynamic response under the action of any shape base time domain dynamic load on the layered foundation is obtained .
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類號(hào)】：TU435

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本文編號(hào)：2030541