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Numerical study on seepage property of karst collapse columns under particle migration
No full textPresently, there is an increasing number of water outburst accidents in China as mining activity continues to develop to deeper ground. In these accidents, water outburst caused by karst collapse columns often results in serious damage, involving both the loss of lives and significant economic loss. Therefore, it is of utmost importance to study the seepage property and water outburst mechanism of karst collapse columns. In this paper, based on the seepage theory and the groundwater dynamic theory of porous media, a fluid-solid coupling model for karst collapse columns was built and then imported into COMSOL Multiphysics to be solved, by considering the heterogeneity of rocks in karst collapse columns, and assuming that the porosity obeyWeibull distribution, thus obtained the parameters, including porosity, seepage, particle concentration, water inflow evolution law. The research results indicate the following: (1) particles in karst collapse columns will be eroded and transported under the effect of fluid as the time, porosity, water inflow and particle migration velocity all increase rapidly, and eventually a main seepage channel will form; (2) the seepage capacity for karst collapse columns initially grows slowly, then water inflow increases gradually with the erosion and migration of the particles
Application of Residual Correction Method on non-Fourier Heat Transfer for Sphere with Time-Dependent Boundary Condition
No full textThe residual correction method is used to predict the temperature distribution of non-Fourier heat transfer with time-dependent boundary condition. The approximate solution of temperature field is obtained by the residual correction method based on the maximum principle in combination with the finite difference method, making it easier and faster to obtain upper and lower approximations of exact solutions, and even can provide clear definitions of the maximum error bounds of the approximate solutions. The proposed method is found to be an effective numerical method with satisfactory accuracy
Characterization and modeling of the multiscale pore structures for porous materials
No full textIn this paper, a stochastic geometrical modeling method for reconstructing three dimensional multiscale pore structures of porous materials is presented. In this method, the pore structure in porous materials is represented by a random but spatially correlated pore-network, in which the results of the Mercury Intrusion Porosimetry (MIP) experiment are used as the basic input information. Beside that, based on the Monte Carlo techniques, an effective computer generation algorithm is developed, and the quantities to evaluate the properties of porous materials are defined and described. Furthermore, numerical implementations are conducted based on experimental data afterwards. This method can be used to generate multiscale pore structure models of a wide class of porous materials
A Fast Regularized Boundary Integral Method for Practical Acoustic Problems
No full textTo predict the sound field in an acoustic problem, the well-known non-uniqueness problem has to be solved. In a departure from the common approaches used in the prior literature, the weak-form of the Helmholtz differential equation, in conjunction with vector test-functions, is utilized as the basis, in order to directly derive non-hyper-singular boundary integral equations for the velocity potential ∅, as well as its gradients q;. Both ∅-BIE and q-BIE are fully regularized to achieve weak singularities at the boundary [i.e., containing singularities of O(r-1)]. Collocation-based boundary-element numerical approaches [denoted as BEM-R-∅-BIE, and BEM-R-q-BIE] are implemented to solve these. To overcome the drawback of fully populated system matrices in BEM, the fast multipole method is applied, and denoted here as FMM-BEM. The computational costs of FMM-BEM are at the scale of O(2nN), which make it much faster than the matrix based operation, and suitable for large practical problems of acoustics
A new implementation of the numerical manifold method (NMM) for the modeling of non-collinear and intersecting cracks
No full textThe numerical manifold method (NMM), based on the finite covers, unifies the continuum analyses and discontinuum analyses without changing a predefined mathematical mesh of the uncracked solid, and has the advantages of being concise in theory as well as being clear in concept. It provides a natural method to analyze complex shaped strong discontinuities as well as weak discontinuities such as multiple cracks, intersecting cracks, and branched cracks. However, the absence of an effective algorithm for cover generation, to date, is still a bottle neck in the research and application in the NMM. To address this issue, a new method for the generation of the finite covers in the NMM is proposed, for the modeling of cracks. In the present algorithm for cover generation, the physical lines such as joints and cracks are described by geometric functions, the mathematical cover is naturally partitioned into different regions by the physical lines, and the regions belonging to a same physical cover, which contains the end points of the physical lines are identified by a simple calculation of the function values of the physical lines. The present method is simple and robust, and is also very fast because it avoids the usage of the complex geometrical algorithms, and the time-consuming judgment of the point-polygon relations, which are commonly used in the previous literature. Several linear elastic fracture problems are analysed here, to demonstrate the validity and the robustness of the proposed algorithms
Modeling Imperfect Interfaces in the Material Point Method using Multimaterial Methods
No full textThe “multimaterial” version of the material point method (MPM) extrapolates each material to its own velocity field on a background grid. By reconciling momenta on nodes interacting with two or more materials, MPM is able to automatically handle contact without any need for special contact elements. This paper extends multimaterial MPM to automatically handle imperfect interfaces between materials as well. The approach is to evaluate displacement discontinuity on multimaterial nodes and then add internal forces and interfacial energy determined by an imperfect interface traction law. The concept is simple, but implementation required numerous corrections to make the analysis mesh independent, to work for any stiffness interfaces, and to find the interfacial normal vector. Several examples illustrated the need and demonstrated the validity of the various corrections. A composite mechanics problem found the bulk modulus of a particulate filled composite as a function interface quality. This calculation revealed a scaling effect — interfaces in nanoparticle composites must be better than interfaces in the corresponding microparticle composites for the nanocomposite mechanical properties to be as good as the conventional composite properties
Inverse Nodal Problem for the Differential Operator with a Singularity at Zero
No full textIn this study, some results are given about Sturm-Liouville operator having a singularity at zero. For this problem, asymptotic form of nodal data and a reconstruction formula for the potential function are given. In addition, a numerical example is established and illustrated the results in some tables and graphics
Numerical Analysis on Dual Holes Interactions
No full textBy extending Bückner’s superposition principle and alternating iteration method, this presentation studies the dual holes interactions. A newly developed numerical scheme is embedded in the conventional Gauss-Legendre quadrature routine for evaluating the boundary integral holding stress singularities. This developed scheme can avoid numerical singularity and facilitate the achieved stress field to be exact as that of analytical solution; however the chosen Gaussian integration points must enter a large quantity. This presentation uses an infinite plate with a centered hole strained by remote axial loading as a testing example, and the numerical results are capable of reaching the analytical solution in the evaluation. The accurate stress estimation in the stress field of the dual holes interacting can therefore locate the dual holes in a very close proximity and no divergence will occur during evaluating the interacting stress concentration between holes
A Moving Kriging Interpolation Response Surface Method for Structural Reliability Analysis
Get PDFIn order to obtain reliable structural design, it is of extreme importance to evaluate the failure probability, safety levels of structure (reliability analysis) and the effect of a change in a variable parameter on structural safety (sensitivity analysis) when uncertainties are considered. With a computationally cheaper approximation of the limit state function, various response surface methods (RSMs) have emerged as a convenient tool to solve this especially for complex problems. However, the traditional RSMs may produce large errors in some conditions especially for those highly non-linear limit state functions. Instead of the traditional least squares approximation, in the present paper, a new RSM is proposed which employs moving Kriging interpolation, based on the axial experimental points selected from the region where the most probable failure point (MPFP) is likely to exist to construct the substitute response surface. The proposed method is illustrated by comparing with the results obtained from first order reliability method (FORM) and other conventional RSMs with reference to specific structural reliability analysis problems. The results show that the proposed method improves the accuracy of the reliability analysis with a reasonable computational cost, and could more quickly approach the exact solution
Application of the MLPG Mixed Collocation Method for Solving Inverse Problems of Linear Isotropic/Anisotropic Elasticity with Simply/Multiply-Connected Domains
Get PDFIn this paper, a novel Meshless Local Petrov-Galerkin (MLPG) Mixed Collocation Method is developed for solving the inverse Cauchy problem of linear elasticity, wherein both the tractions as well as displacements are prescribed/measured at a small portion of the boundary of an elastic body. The elastic body may be isotropic/anisotropic and simply connected or multiply-connected. In the MLPG mixed collocation method, the same meshless basis function is used to interpolate both the displacement as well as the stress fields. The nodal stresses are expressed in terms of nodal displacements by enforcing the constitutive relation between stress and the displacement gradient tensor at each nodal point. The equations of linear momentum balance are satisfied at each node using collocation method. The displacement as well as traction boundary conditions are also enforced at each measurement location along the boundary where the conditions are over specified on displacement as well as tractions. The current method is very simple because the inverse problem is directly solved in a fashion similar to a direct problem, without resorting to any iterative optimization. The current method is also very general because it can be applied to arbitrary simply/multiply connected bodies composed of arbitrary isotropic/anisotropic material, and it can also be adapted to solve inverse problems of other physics such as heat transfer, electro-magnetics, etc. Several numerical examples demonstrate the effectiveness and robustness of the current method, even when the prescribed displacement/tractions are corrupted with measurement noises. The extension of the current method to solve nonlinear inverse problems will be straightforward within the framework of incremental loading, which will be explored in future studies