NURBS-MF Method And Its Application In The Continuous And Discontinuous Analysis Of Tunnel Structures

In recent years,the design and construction of underground tunnel engineering have gradually developed towards large cross-sections,deeply buried,and heterotypic structures.There are increasing engineering cases crossing complex geotechnical circumstances,which pose new challenges for the structure design and numerical analysis of tunnels.The traditional computational methods for tunnel design rely primarily on the existing experience,and there is no reliable theoretical basis for defining some crucial parameters.Meantime,due to the cumbersome pre-processing process of geometric modeling and high mesh dependency,for the prefabricated tunnel structures that require a continuous-to-discontinuous deformation analysis,the finite element method(FEM)solid model finds its great limitation and difficulty in popularizing and application.It is tough to meet the numerical analysis needs of these deeply buried,heterotypic tunnels with large cross-sections.To address these difficulties,in this thesis,the non-uniform B-spline(NURBS)is used to represent the geometry,and a brand new NURBS-MF(Meshfree)method is developed for the continuous and discontinuous analysis of tunnel structures.The integrated meshfree modeling and analysis of tunnel structures from CAD(Computer Aided Design)to NAM(Numerical Analysis Modeling)is realized in the proposed method.The main research contents and achievements of this thesis mainly include:(1)Meshfree discretization model of tunnel structures based on NURBS.Based on the exact geometry representation ability of NURBS,the concise and accurate parameterized expression of the prefabricated heterotypic tunnel structure with complex geometry and boundary conditions is reached.An automatic nodes generation algorithm based on NURBS parameterization is developed to ensure that when discretizing irregular geometry,the transition between coarse nodes and fine nodes can be easily achieved.This algorithm reduces the computational error and improves the numerical accuracy of the proposed NURBS-MF model.Furthermore,the "directly read-from-CAD" method and the global curves fitting technique make it possible to cross the barrier from a CAD design model to a meshfree discretization model without effort.The proposed techniques further realize the parameterization and automation in the numerical modeling process.After that,the NURBS surface is mapped into a canonical parametric space,in which the discrete meshfree nodes independent of the physical domain are set in a well-organized way.It not only retains the advantages of the NURBS to rapidly model complex curves and surfaces but also avoids the cutting of boundary integral cells and the discarding of invalid integral points.(2)NURBS-MF theory and its implementation.By introducing RKPM and MSPU meshfree interpolating,a NURBS-MF framework is developed for the continuous and discontinuous analysis of tunnel structures.With the help of the fictitious thin layer to enforce the compatible deformation constraints among discontinuous interfaces and to impose homogeneous and inhomogeneous boundary conditions constraints.The stiffness matrix and system solving formula are then derived based on the principle of minimum potential energy.The virtue crack closure technique(VCCT)is used to precisely calculate the stress intensity factors(SIFs),and the maximum hoop stress criterion is utilized to consider the crack propagation direction.On this basis,an algorithm for crack propagation modeling is developed under the NURBS-MF framework.Multiple benchmark validations,such as the Cook beam under point loads,the plate with a central crack,the cantilever beam with a side crack,and the free-curve boundary cantilever beam under distributed loads,give strong proofs of correction and accuracy of the proposed NURBS-MF method.(3)NURBS-MF elastoplastic theory and its implementation.Based on the NURBS-MF discretization modelling and the continuous and discontinuous analysis framework,the NURBS-MF elastoplastic theory is established.The elastoplastic constitutive formula of NURBS-MF is derived according to the associated flow rule.Then,the nonlinear elastoplastic system equations are solved using the tangent stiffness method and iterative algorithm.Compared with the traditional meshfree methods,the proposed theory effectively decreases the integral cost and fundamentally reduces the entire computation time,ensures the nonlinear iteration accuracy and numerical robustness of meshfree methods,and eventually provides a theoretical basis for the analysis and computation of large tunnel structures.The accuracy,efficiency,and other advantages of the elastoplastic models in this thesis are verified and illustrated by benchmark examples such as the thick-walled cylinder and the Cook beam.(4)CAD-NAM integrated automatic analysis system based on NURBS-MF and its application in tunnel structures.The essential techniques of NURBS-MF elastoplastic analysis,including the implementation scheme of the load-structure calculation model in tunnel engineering,the implementation algorithm of stratum springs,and the visualization of the required internal force distribution of the target structure,are studied in detail.Based on the abovementioned theories and algorithms,a CAD-NAM integrated automatic analysis system based on NURBS-MF is successfully developed,taking advantage of the open source MATLAB (?) Toolkit.Under an object-oriented programing architecture,the automatic modeling and analysis of tunnel structures are fulfilled.Only "one-click" is needed from the tunnel CAD design model to the visual output of the numerical analysis results.It is possible to significantly promote the application of meshfree theory in tunnel engineering.The elastoplastic analysis of typical engineering cases(such as the deeply buried water conveyance tunnel and the large cross-section highway tunnel)shows the validity,effectiveness,and practicability of the proposed theory,methodology,and programming.