排序方式： 共有25条查询结果，搜索用时 15 毫秒
1.
In view of rapid developments in iterative solvers, it is timely to re‐examine the merits of using mixed formulation for incompressible problems. This paper presents extensive numerical studies to compare the accuracy of undrained solutions resulting from the standard displacement formulation with a penalty term and the two‐field mixed formulation. The standard displacement and two‐field mixed formulations are solved using both direct and iterative approaches to assess if it is cost‐effective to achieve more accurate solutions. Numerical studies of a simple footing problem show that the mixed formulation is able to solve the incompressible problem ‘exactly’, does not create pressure and stress instabilities, and obviate the need for an ad hoc penalty number. In addition, for large‐scale problems where it is not possible to perform direct solutions entirely within available random access memory, it turns out that the larger system of equations from mixed formulation also can be solved much more efficiently than the smaller system of equations arising from standard formulation by using the symmetric quasi‐minimal residual (SQMR) method with the generalized Jacobi (GJ) preconditioner. Iterative solution by SQMR with GJ preconditioning also is more elegant, faster, and more accurate than the popular Uzawa method. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
2.
3.
Non‐associated flow rule is essential when the popular Mohr–Coulomb model is used to model nonlinear behavior of soil. The global tangent stiffness matrix in nonlinear finite element analysis becomes non‐symmetric when this non‐associated flow rule is applied. Efficient solution of this large‐scale non‐symmetric linear system is of practical importance. The standard Krylov solver for a non‐symmetric solver is Bi‐CGSTAB. The Induced Dimension Reduction [IDR(s)] solver was proposed in the scientific computing literature relatively recently. Numerical studies of a drained strip footing problem on homogenous soil layer show that IDR(s = 6) is more efficient than Bi‐CGSTAB when the preconditioner is the incomplete factorization with zero fill‐in of global stiffness matrix Kep (ILU(0)‐Kep). Iteration time is reduced by 40% by using IDR(s = 6) with ILU(0)‐Kep. To further reduce computational cost, the global stiffness matrix Kep is divided into two parts. The first part is the linear elastic stiffness matrix Ke, which is formed only once at the beginning of solution step. The second part is a low‐rank matrix Δ, which is re‐formed at each Newton–Raphson iteration. Numerical studies show that IDR(s = 6) with this ILU(0)‐Ke preconditioner is more time effective than IDR(s = 6) with ILU(0)‐Kep when the percentage of yielded Gauss points in the mesh is less than 15%. The total computation time is reduced by 60% when all the recommended optimizing methods are used. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
4.
The steady-state dynamic responses of both flexible and rigid massless foundations with complex geometries on layered media are studied by the finite layer method. The discussion covers both the horizontal and vertical responses including the rocking mode of vibration. The effect of various parameters, namely, the size of the domain, the number of harmonic terms and the material damping of the soil media, on the convergence and accuracy of the results is investigated. Non-homogeneous soil profiles are treated as a matter of course. The results obtained are compared with solutions by other theoretical methods. 相似文献
5.
Hua-You Chai Kok-Kwang Phoon Chang-Fu Wei Ying-Fa Lu 《Journal of Applied Geophysics》2011,73(1):49-58
In the wave field induced by active sources, the observed phase velocity of surface waves is influenced by both mode incompatibility (i.e. non-planar spread of surface waves is idealized as plane waves) and body waves. Effects of sources are usually investigated based on numerical simulations and physical models. Several methods have been proposed to mitigate the effects. In application, however, these methods may also have difficulties since the energy of the body waves depends on soil stratification and parameters. There are multiple modes of surface waves in layered media, among which the higher modes dominate the wave field for soils with the irregular shear velocity profiles. Considering the mode incompatibility and the higher modes, we derive analytical expressions for the effective phase velocity of the surface waves based on the thin layer stiffness method, and investigate the effects of the body waves on the observed phase velocity through the phase analysis of the vibrations of both the surface waves and the body waves. The results indicate that the effective phase velocity of the surface waves in layered media varies with the frequency and the spread distance, and is underestimated compared to that of the plane surface waves in the spread range less than about one wavelength. The oscillations that appeared in the observed phase velocity are due to the involvement of the body waves. The mode incompatibility can be ignored in the range beyond one wavelength, while the influence range of the body waves is far beyond one wavelength. The body waves have a significant influence on the observed phase velocity of the surface waves in soils with a soft layer trapped between the first and the second layers because of strong reflections. 相似文献
6.
The finite element (FE) simulation of large‐scale soil–structure interaction problems (e.g. piled‐raft, tunnelling, and excavation) typically involves structural and geomaterials with significant differences in stiffness and permeability. The symmetric quasi‐minimal residual solver coupled with recently developed generalized Jacobi, modified symmetric successive over‐relaxation (MSSOR), or standard incomplete LU factorization (ILU) preconditioners can be ineffective for this class of problems. Inexact block diagonal preconditioners that are inexpensive approximations of the theoretical form are systematically evaluated for mitigating the coupled adverse effects because of such heterogeneous material properties (stiffness and permeability) and because of the percentage of the structural component in the system in piled‐raft foundations. Such mitigation led the proposed preconditioners to offer a significant saving in runtime (up to more than 10 times faster) in comparison with generalized Jacobi, modified symmetric successive over‐relaxation, and ILU preconditioners in simulating piled‐raft foundations. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
7.
Zhang Jin-Zhang Zhang Dong-Ming Huang Hong-Wei Phoon Kok Kwang Tang Chong Li Gang 《Acta Geotechnica》2022,17(4):1129-1145
Acta Geotechnica - The scale of fluctuation (SOF) is the critical parameter to describe the soil spatial variability, which significantly influences the embedded geostructures. Due to the limited... 相似文献
8.
K.K. Phoon J.V. Retief 《Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards》2015,9(3):125-127
ISO2394:2015 contains a new informative Annex D on “Reliability of Geotechnical Structures”. The emphasis in Annex D is to identify and characterize critical elements of the geotechnical reliability-based design process, while respecting the diversity of geotechnical engineering practice. This paper highlights the main features of Annex D and gaps for future work. 相似文献
9.
This paper examines the performance of the Jacobi preconditioner when used with two Krylov subspace iterative methods. The number of iterations needed for convergence was shown to be different for drained, undrained and consolidation problems, even for similar condition number. The differences were due to differences in the eigenvalue distribution, which cannot be completely described by the condition number alone. For drained problems involving large stiffness ratios between different material zones, ill‐conditioning is caused by these large stiffness ratios. Since Jacobi preconditioning operates on degrees‐of‐freedom, it effectively homogenizes the different spatial sub‐domains. The undrained problem, modelled as a nearly incompressible problem, is much more resistant to Jacobi preconditioning, because its ill‐conditioning arises from the large stiffness ratios between volumetric and distortional deformational modes, many of which involve the similar spatial domains or sub‐domains. The consolidation problem has two sets of degrees‐of‐freedom, namely displacement and pore pressure. Some of the eigenvalues are displacement dominated whereas others are excess pore pressure dominated. Jacobi preconditioning compresses the displacement‐dominated eigenvalues in a similar manner as the drained problem, but pore‐pressure‐dominated eigenvalues are often over‐scaled. Convergence can be accelerated if this over‐scaling is recognized and corrected for. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
10.
Kok-Kwang Phoon 《Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards》2019,13(2):101-130
The calculated response from a numerical model will deviate from the measured one given the presence of modelling idealizations and real world construction effects. This deviation can be directly captured by a ratio between the measured and the calculated quantity. The ratio is also called a model factor in many design guides. The probabilistic distribution of the model factor is arguably the most common and simplest complete representation of model uncertainty. The characterisation of model uncertainty is identified as one of the critical elements in a geotechnical reliability-based design process in Annex D of ISO 2394:2015 “General Principles on Reliability of Structures”. This Spotlight paper reviews the databases for various geo-structures and determines their associated model statistics. Foundation load test databases are the most prevalent. A recent effort to compile a large generic database (PILE/2739) that contains 2739 field load tests conducted on various piles and installed in different soils and countries, is highlighted. This systematic compilation of load test data is part of a broader research agenda to digitalise foundation design for “precision construction”, which is targeted at characterising “site-specific” model factors and soil parameters based on both site-specific and generic data for further customisation of design to a particular site. The mean and COV of the model factor for a range of geo-structures, geomaterials, and limit states (both ultimate and serviceability) are summarized in a form suitable for adoption in design and codes of practice. Based on this summary, it is proposed that a model factor for a design model can be classified as: (1) moderately conservative (1?≤?mean?相似文献