本文選題：土 + 結(jié)構(gòu)相互作用　； 參考：《天津大學(xué)》2015年博士論文

【摘要】：近來年,對土—結(jié)構(gòu)相互作用問題的研究廣度和深度逐漸擴(kuò)大,各類復(fù)雜模型越來越龐大且精細(xì)化,導(dǎo)致在有限元分析中單元節(jié)點(diǎn)的自由度數(shù)可謂以十萬百萬計,需高配置的計算設(shè)備和長時間的計算時間才可完成分析,當(dāng)需多個不同工況的比較時則更成倍地增加工作量,亟待一種可行的既滿足計算精度又節(jié)省計算成本的分析計算方法。動力子結(jié)構(gòu)法是將土—結(jié)構(gòu)相互作用體系分成若干子系統(tǒng),先分別求出各子系統(tǒng)的單體反應(yīng),然后再聯(lián)系各單體的反應(yīng),使其滿足相互作用的條件,從而得到整個體系的反應(yīng),大大減少計算量,是一種理想的計算方法,但該方法僅能解決線性問題。本文根據(jù)課題組新近提出的能解決局部非線性問題的線性—非線性混合約束模態(tài)綜合法的思想,在該方法的具體實(shí)施方面進(jìn)行了研究,充分利用現(xiàn)有商業(yè)軟件的優(yōu)勢,將該方法的實(shí)施與ANSYS軟件相結(jié)合,對實(shí)施過程中諸如結(jié)構(gòu)受力全過程中剛度矩陣的提取方法;彈塑性模型中等效彈性模量的計算;一致粘彈性邊界問題;以及非線性的接觸問題等進(jìn)行了深入的分析與研究,使混合約束模態(tài)綜合法能解決復(fù)雜狀況下的土—結(jié)構(gòu)相互作用體系,開辟了動力子結(jié)構(gòu)法的研究領(lǐng)域。本文主要的創(chuàng)新工作與成果有:1.混合約束模態(tài)綜合法在ANSYS的實(shí)施,首先要解決剛度矩陣提取中的對號入座問題,為此在深入分析ANSYS二次開發(fā)四種方法的基礎(chǔ)上,決定采取FORTRAN語言的二次開發(fā)工具UPFs進(jìn)行矩陣提取的開發(fā)工作,自編程序?qū)崿F(xiàn)了按照節(jié)點(diǎn)編號由小到大的順序進(jìn)行矩陣的提取。2.非線性子結(jié)構(gòu)在塑性階段中的剛度矩陣的提取工作是本文的重點(diǎn)難點(diǎn)之一。為了在非線性時程分析中生成某一時刻的彈塑性剛度矩陣,提出了將非線性塑性區(qū)域“等效”為線彈性區(qū)域,即在塑性階段上的小段Δt時間內(nèi)利用分段等效線性化手段,對結(jié)構(gòu)各個進(jìn)入塑性階段的單元進(jìn)行等效處理,并推導(dǎo)了等效彈性模量的公式,完成了對塑性單元的彈性模量和剪切模量等效工作;利用了ANSYS多點(diǎn)重啟動的方法,恢復(fù)結(jié)構(gòu)上一時刻的計算結(jié)果后能繼續(xù)進(jìn)行下一時刻分析;提出了ANSYS與MATLAB程序間的相互調(diào)用和控制的操作方法,從而解決了非線性子結(jié)構(gòu)在塑性階段中的剛度矩陣的有序進(jìn)行。通過算例模型進(jìn)行一般性分析,包括Pushover靜力非線性分析和簡諧波動力時程非線性分析求得響應(yīng)時程曲線,與ANSYS直接計算法所得到的響應(yīng)時程曲線比對吻合良好,驗(yàn)證了在彈塑性階段二次開發(fā)的程序文件所提取的矩陣的正確可行。3.建立了考慮局部非線性的地基土—剪力墻結(jié)構(gòu)相互作用的模型,然后根據(jù)結(jié)構(gòu)存在局部塑性區(qū)域的特點(diǎn),將整體體系中未進(jìn)入非線性階段的區(qū)域劃分為若干個線性子結(jié)構(gòu),而將進(jìn)入塑性階段的局部區(qū)域獨(dú)立劃分為若干個非線性子結(jié)構(gòu)。提出了混合約束模態(tài)綜合法的詳細(xì)分析流程并編寫了開發(fā)程序,著重說明了在ANSYS和MATLAB二者程序之間的實(shí)現(xiàn)過程。4.在土—結(jié)構(gòu)相互作用分析模型中,在地基土邊界引入一致粘彈性邊界條件來模擬半無限域的土體,推導(dǎo)了帶有一致粘彈性邊界的子結(jié)構(gòu)方程,論證了勢能判據(jù)截斷準(zhǔn)則同樣適用于帶有一致粘彈性邊界的線性子結(jié)構(gòu),證明了采用混合約束模態(tài)綜合法同樣能處理復(fù)雜的邊界問題。5.通過選擇合理的目標(biāo)面單元和接觸面單元、迭代計算接觸剛度和設(shè)置摩擦系數(shù),將高度非線性的接觸問題引入混合約束模態(tài)綜合法中。提出了箱型基礎(chǔ)與周圍土體接觸關(guān)系的處理方法,將接觸單元一分為二,目標(biāo)面單元劃入剛度相對較高的箱型基礎(chǔ)的線性子結(jié)構(gòu)內(nèi),接觸面單元劃入剛度相對較低的周圍土體的非線性子結(jié)構(gòu)內(nèi),推導(dǎo)出了箱型基礎(chǔ)與周圍土體具有接觸關(guān)系的線性與非線性模態(tài)綜合方程,拓寬了混合約束模態(tài)綜合法的應(yīng)用領(lǐng)域。6.通過算例計算對線性和非線性土體區(qū)域給出了推薦范圍,當(dāng)設(shè)置一致粘彈性邊界時,非線性子結(jié)構(gòu)的區(qū)域?yàn)?倍的基礎(chǔ)寬度,兩側(cè)線性子結(jié)構(gòu)區(qū)域各為1.5倍的基礎(chǔ)寬度,使得模型總體自由度數(shù)比使用一般自由邊界子結(jié)構(gòu)土體單元自由度數(shù)減少很多,從而提高了計算效率。7.進(jìn)行了混合約束模態(tài)綜合法擴(kuò)展到三維土—結(jié)構(gòu)相互作用分析,重點(diǎn)研究了與二維問題的不同之處,重新推導(dǎo)了適合于三維問題的一致粘彈性邊界條件的子結(jié)構(gòu)方程;重新推導(dǎo)了箱型基礎(chǔ)與周圍土體具有接觸關(guān)系的線性與非線性模態(tài)綜合方程,以及三維模型等效彈性模量的公式,結(jié)果表明混合約束模態(tài)綜合法能解決三維土—結(jié)構(gòu)相互作用復(fù)雜問題。8.在混合約束模態(tài)綜合法的實(shí)施中,通過逐步提取的結(jié)構(gòu)體系全程階段等效彈塑性剛度矩陣,進(jìn)行特征值方程計算得到了結(jié)構(gòu)前n階主要頻率和振型在全時段變化情況,從而了解結(jié)構(gòu)剛度在彈塑性動靜力分析中的變化規(guī)律,可為利用結(jié)構(gòu)動力特性對結(jié)構(gòu)體系進(jìn)行深入分析研究提供支撐。
[Abstract]:In recent years, the breadth and depth of the soil structure interaction have been expanded and the complex models are becoming more and more large and fine. The free degree of unit nodes in the finite element analysis can be described as one hundred thousand million. It needs high configuration of computing equipment and long time calculation time to complete the analysis, when many different workers are needed. In comparison with the situation, the workload is more multiplied, and a feasible analytical method is needed to satisfy both the calculation precision and the cost of calculation. The dynamic substructure method divides the soil structure interaction system into several subsystems, first to find the single reaction of each subsystem, and then to contact the reaction of the various monomers, so that it satisfies the phase. The condition of interaction, thus obtaining the reaction of the whole system, greatly reducing the amount of calculation, is an ideal calculation method, but this method can only solve the linear problem. In this paper, the idea of the linear nonlinear mixed constraint mode synthesis method which can solve local nonlinear problems recently proposed by the project group is the concrete implementation of this method. In order to make full use of the advantages of the existing commercial software, the implementation of the method is combined with the ANSYS software, and the method of extracting the stiffness matrix in the whole process of structural stress, the calculation of the equivalent elastic modulus in the elastoplastic model, the uniform viscoelastic boundary boundary problem and the nonlinear contact problem are carried out in the implementation process. In the analysis and research, the mixed constrained modal synthesis method can solve the soil structure interaction system under complex conditions and open up the research field of the dynamic substructure method. The main innovation work and achievements of this paper are as follows: 1. the implementation of the hybrid constrained modal synthesis method in the ANSYS, first of all, we should solve the problem of the number of seats in the stiffness matrix extraction. On the basis of the in-depth analysis of the four methods of the two development of ANSYS, the two development tool UPFs of the FORTRAN language is adopted to develop the matrix extraction. The self compiled program realizes the extraction of the stiffness matrix of the.2. nonlinear substructure in the plastic phase according to the node number from small to large. In order to generate the elastoplastic stiffness matrix of a certain moment in the nonlinear time history analysis, it is proposed that the nonlinear plastic region is "equivalent" to the linear elastic region, that is, the piecewise equivalent linearization method is used in the small segment delta T time of the plastic stage, and the units that enter the plastic stage are carried out. The formula of the equivalent elastic modulus is derived, and the equivalent work of the elastic modulus and the shear modulus of the plastic unit is completed. Using the method of ANSYS multi point restart, the next time analysis can be carried out after the recovery of the calculation results at the time of the structure, and the operation of mutual call and control between the ANSYS and the MATLAB program is put forward. This method solves the order of the stiffness matrix of the nonlinear substructure in the plastic stage. Through the example model, the general analysis is carried out, including the Pushover static nonlinear analysis and the harmonic dynamic time history nonlinear analysis to obtain the response time history curve, which is in good agreement with the response time curve comparison obtained by the ANSYS direct calculation method. To verify the correctness and feasibility of the matrix extracted from the program documents developed at the two time of the elastoplastic stage, the model of the soil shear wall structure interaction with local nonlinearity is established by.3.. Then, according to the characteristics of the local plastic region in the structure, the region which has not entered the nonlinear stage in the whole system is divided into several lines. The partial region that enters the plastic stage is divided into several nonlinear substructures independently. The detailed analysis process of the mixed constrained modal synthesis method is proposed and the development program is written. The implementation process between the ANSYS and the MATLAB two programs is emphasized, and the.4. is in the soil structure interaction analysis model, and the foundation is in the foundation. The soil boundary is introduced into the uniform viscoelastic boundary condition to simulate the soil in the semi infinite domain. The substructure equation with the uniform viscoelastic boundary is derived. It is proved that the potential energy criterion truncation criterion is also applicable to the linear substructure with the uniform viscoelastic boundary. It is proved that the mixed constrained modal synthesis method can also deal with complex boundary questions. By selecting the reasonable target surface element and the contact surface element,.5., the contact stiffness and the friction coefficient are iteratively calculated, and the highly nonlinear contact problem is introduced into the mixed constrained modal synthesis method. The contact relationship between the box type foundation and the surrounding soil is proposed. The contact element is divided into two parts and the target surface unit is divided into the stiffness phase. In the linear substructure of the higher box foundation, the contact surface element is inserted into the nonlinear substructure of the surrounding soil with relatively low stiffness. The linear and nonlinear modal synthesis equations of the contact relationship between the box type foundation and the surrounding soil are derived, and the application field of the mixed constrained modal synthesis method,.6., is widened by the calculation example. The range of linear and nonlinear soil is recommended. When the uniform viscoelastic boundary is set, the region of the nonlinear substructure is 2 times the base width and the basic width of the linear substructure of the two sides is 1.5 times, making the total degree of freedom of the model less than the free degree of the soil unit using the general free boundary substructure. The hybrid constrained modal synthesis method is extended to the three-dimensional soil structure interaction analysis, and the difference between the.7. and the two dimensional problem is studied. The substructure equation of the uniform viscoelastic boundary condition suitable for three dimensional problems is rederived, and the contact relation between the box foundation and the surrounding soil is re derived. The linear and nonlinear modal synthesis equations of the system and the formula of the equivalent elastic modulus of the three-dimensional model show that the mixed constrained modal synthesis method can solve the complex problem of the three-dimensional soil structure interaction..8., in the implementation of the mixed constrained modal synthesis method, can be obtained by gradually extracting the equivalent elastoplastic stiffness matrix in the whole process stage of the structure. The eigenvalue equation is used to calculate the changes of the main frequencies and modes of the n order before the structure, so as to understand the change law of the structural stiffness in the elastoplastic dynamic static analysis, which can provide support for the in-depth analysis of the structural system by using the dynamic characteristics of the structure.
【學(xué)位授予單位】：天津大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2015
【分類號】：TU470

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