This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solve...This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.展开更多
In deep underground mining,achieving stable support for roadways along with long service life is critical and the complex geological environment at such depths frequently presents a major challenge.Owing to the coupli...In deep underground mining,achieving stable support for roadways along with long service life is critical and the complex geological environment at such depths frequently presents a major challenge.Owing to the coupling action of multiple factors such as deep high stress,adjacent faults,cross-layer design,weak lithology,broken surrounding rock,variable cross-sections,wide sections up to 9.9 m,and clusters of nearby chambers,there was severe deformation and breakdown in the No.10 intersection of the roadway of large-scale variable cross-section at the−760 m level in a coal mine.As there are insufcient examples in engineering methods pertaining to the geological environment described above,the numerical calculation model was oversimplifed and support theory underdeveloped;therefore,it is imperative to develop an efective support system for the stability and sustenance of deep roadways.In this study,a quantitative analysis of the geological environment of the roadway through feld observations,borehole-scoping,and ground stress testing is carried out to establish the FLAC 3D variable cross-section crossing roadway model.This model is combined with the strain softening constitutive(surrounding rock)and Mohr–Coulomb constitutive(other deep rock formations)models to construct a compression arch mechanical model for deep soft rock,based on the quadratic parabolic Mohr criterion.An integrated control technology of bolting and grouting that is mainly composed of a high-strength hollow grouting cable bolt equipped with modifed cement grouting materials and a high-elongation cable bolt is developed by analyzing the strengthening properties of the surrounding rock before and after bolting,based on the Heok-Brown criterion.As a result of on-site practice,the following conclusions are drawn:(1)The plastic zone of the roof of the cross roadway is approximately 6 m deep in this environment,the tectonic stress is nearly 30 MPa,and the surrounding rock is severely fractured.(2)The deformation of the roadway progressively increa展开更多
A new numerical strategy to model nonlinear damage behavior of RC beam-column member based on level of material and superconvergent computation is presented in this paper. A fiber damage analysis model (FDAM) for RC b...A new numerical strategy to model nonlinear damage behavior of RC beam-column member based on level of material and superconvergent computation is presented in this paper. A fiber damage analysis model (FDAM) for RC beam-column member is established by analyzing section of fiber beam column element with the uniaxial damage constitutive relations of con-crete. The damage index of RC member through statistical analysis of concrete fibers damage is defined in the extreme section of beam elements, which can describe the nonlinear damage behavior of RC beam-column member under any loadings. The newly proposed element energy projection (EEP) method is applied to the inelastic analysis of FDAM. EEP superconvergent formulas for section forces and deformations of beam-column are established, and general algorithm and numerical strategy adopting EEP super-convergent computation for section deformation increment are proposed in the classical Newton-Raphson process. Both analysis and numerical test show that the EEP method can effectively find out the nonlinear feature of the distribution, and accurately obtain the damage distribution of RC beamcolumn. The proposed numerical scheme in this paper proves to be effective and convenient in its use and can be easily integrated into the present inelastic FEM programs of structure analysis.展开更多
基金the National Science and Tech-nology Council,Taiwan for their financial support(Grant Number NSTC 111-2221-E-019-048).
文摘This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.
基金supported by the National Natural Science Foundation of China(Grant Nos.52074296,52004286)the China Postdoctoral Science Foundation(Grant Nos.2020T130701,2019M650895).
文摘In deep underground mining,achieving stable support for roadways along with long service life is critical and the complex geological environment at such depths frequently presents a major challenge.Owing to the coupling action of multiple factors such as deep high stress,adjacent faults,cross-layer design,weak lithology,broken surrounding rock,variable cross-sections,wide sections up to 9.9 m,and clusters of nearby chambers,there was severe deformation and breakdown in the No.10 intersection of the roadway of large-scale variable cross-section at the−760 m level in a coal mine.As there are insufcient examples in engineering methods pertaining to the geological environment described above,the numerical calculation model was oversimplifed and support theory underdeveloped;therefore,it is imperative to develop an efective support system for the stability and sustenance of deep roadways.In this study,a quantitative analysis of the geological environment of the roadway through feld observations,borehole-scoping,and ground stress testing is carried out to establish the FLAC 3D variable cross-section crossing roadway model.This model is combined with the strain softening constitutive(surrounding rock)and Mohr–Coulomb constitutive(other deep rock formations)models to construct a compression arch mechanical model for deep soft rock,based on the quadratic parabolic Mohr criterion.An integrated control technology of bolting and grouting that is mainly composed of a high-strength hollow grouting cable bolt equipped with modifed cement grouting materials and a high-elongation cable bolt is developed by analyzing the strengthening properties of the surrounding rock before and after bolting,based on the Heok-Brown criterion.As a result of on-site practice,the following conclusions are drawn:(1)The plastic zone of the roof of the cross roadway is approximately 6 m deep in this environment,the tectonic stress is nearly 30 MPa,and the surrounding rock is severely fractured.(2)The deformation of the roadway progressively increa
基金supported by the National Natural Science Foundation of China (Grant Nos. 50938001, 51008048)
文摘A new numerical strategy to model nonlinear damage behavior of RC beam-column member based on level of material and superconvergent computation is presented in this paper. A fiber damage analysis model (FDAM) for RC beam-column member is established by analyzing section of fiber beam column element with the uniaxial damage constitutive relations of con-crete. The damage index of RC member through statistical analysis of concrete fibers damage is defined in the extreme section of beam elements, which can describe the nonlinear damage behavior of RC beam-column member under any loadings. The newly proposed element energy projection (EEP) method is applied to the inelastic analysis of FDAM. EEP superconvergent formulas for section forces and deformations of beam-column are established, and general algorithm and numerical strategy adopting EEP super-convergent computation for section deformation increment are proposed in the classical Newton-Raphson process. Both analysis and numerical test show that the EEP method can effectively find out the nonlinear feature of the distribution, and accurately obtain the damage distribution of RC beamcolumn. The proposed numerical scheme in this paper proves to be effective and convenient in its use and can be easily integrated into the present inelastic FEM programs of structure analysis.
