有限單元法在巖土工程問題中應用非常廣泛,很多商業軟件如Plaxis/Abaqus/Comsol等都采用有限單元解法.盡管各類商業軟件使用方便,但其使用對用戶來說往往是一個“黑箱子”.相比而言,開源的有限元程序計算方法透明、計算過程可控,用戶可根據自己的需求進行必要的修改,這一點對於科研人員特別重要.然而,長期以來由於有限元開源程序的欠缺、教學方法以介紹理論為主,開源有限元的使用在國內相對較少.然而,科研領域的很多新的東西很難實現在商業軟件中（除非通過復雜的二次開發,The second development often need to have the ability to write some programs,如Abaqus的Umat子程序、Plaxis的UDSM等）,If master the basic process of some open-source finite element and the corresponding subroutine writing method,Based on their development program or commercial software development interface research work will be highly beneficial to.
This is aimed at the material nonlinear problems in geotechnical engineering（The deformation and stress analysis of all kinds of elasto-plastic constitutive model、Seepage analysis of nonlinear coefficient of permeability, etc）,包括前處理輸入文件的准備、計算可執行文件的編譯生成、後處理輸出文件的可視化等,其中的編程模塊盡可能做到讓學員零基礎開始,通過提供標准程序庫使用搭積木、擺樂高的形式模塊化進行,To strengthen our easy-to-use、可操作性.You just need to know the structure of simple programming statements can be,甚至都不需要懂某種編程語言的具體語法.Through the study to achieve the following goals： You will find that you have learned to a programming language（盡管沒有進行單獨的語言學習）,發揮通過實例學習的益處.At the same time introduceParaview等後處理軟件的使用及其Fortran/Python等接口程序.Examples include nonlinear finite element method (fem) in the retaining wall、地基穩定、The application of the stability of the slope stability and so on three big problems, etc.同時現場講解源程序的修改與重新編譯,方便各個領域可以更好地交叉融合、擴展應用.We selected model application cases,全程干貨,Allows you to fully familiar with seepage model,提高模型應用能力、數據分析和圖表制作技能
The finite element programming basics
Finite element method based introduction（離散化、Storage strategy and equations、邊界條件的處理）
編程語言Fortran及編譯工具Intel Visual Fortran(IVF)簡介、Python開發環境Spyder簡介
Fortran/Matlab/Julia/PythonAnd other open source code and libraries（geomlib/femlib）簡介
Nonlinear finite element model of related modules and calculation process
Geotechnical engineering material nonlinear problem is introduced
Nonlinear finite element often stiffness method to realize the module
Finite element analysis of numerical basis and often stiffness method
Skyline method such as integral coefficient matrix storage and equation solving method directly
Overall coefficient matrix assembly（預條件）Conjugate gradient method equation
牛頓（-拉夫森）Iteration to solve the basic principle and the numerical implementation
Stress invariant、屈服函數、The plastic potential function、Several kinds of typical failure criterion and undefined singularity processing
Initial strain method to realize the stiffness method often（Virtual viscoplastic algorithm）、The realization of the initial stress stiffness method often method
圖2 Several failure criteria（米塞斯、Flexor les card、Moore cullen）
圖3 Often stiffness method（左）、Variable stiffness method（右）示意圖
Nonlinear finite element tangent stiffness method to realize the module
Elastic-plastic stress-strain relationship of constitutive integral（前向歐拉法、後向歐拉法）
Plastic flow rule、Tangent stiffness method of non uniform and consistent tangent modulus
The stress integration algorithm of recently point projection methodCPPM (Closest Point Projection Method) 實現
The stress integration algorithm of cutting plane methodCPA (Cutting Plane Algorithm) 實現
The stress integration algorithm of radial return methodRR (Radial Return)With the algorithm convergence criteria
圖5 CPPM和CPA算法示意
The foundation stability、Retaining wall stability、Slope stability application module
應用實例
The foundation bearing capacity problem（位移控制、力控制）
Retaining wall stability problem（Initial stress method to improve）
Slope stability problem（Strength subtraction and safety coefficient of automatic search）
輸入文件准備、輸出文件IrfanView、Paraview可視化（A handy operation and explain）
Pyhton/Fortran90The source code according to the need to modify and recompile(Applied in the spatial variability of rock mass with parameters)
圖 Slope stability analysis of strength subtraction（The direct method and iterative method）流程圖
圖 Square foundation bearing capacity（3 d part and its profile）
Figure in the foundation soil strain invariant（Failure surface）
圖 Retaining wall stability analysis（主動土壓力）
圖 Slope stability （Failure surface）
Nonlinear finite element：And based on the basic theory and algorithmPython、FortranProgram implementation and case analysis
