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1.
The aim of this study is to arrive at a better understanding of the phenomenon of locking of low‐order compatible displacement type of finite elements in particular for the hour‐glass mode of the plane four‐node element and dilative materials. To this end the properties of finite elements are investigated in an analytical way, where a finite element is considered as a plane boundary value problem with prescribed boundary displacement (Dirichlet problem). In this paper for the sake of simplicity the simplest possible linear comparison solid, namely isotropic linear elasticity, is applied, although recognizing fully that for a dilative material elasto‐plasticity would be more realistic. From the study described in this paper it is concluded that locking of the four‐node element is not due to any particular numerical formulation of this compatible finite element since, even the analytical solution suffers from this problem. The locking of this element is not related to incompressibility of the material either as the analytical solution shows locking to occur at a parameter set which differs significantly from the one in case of incompressibility. It is shown that locking is a consequence of the combination of the dilative material behaviour and the compatible displacement type of boundary conditions, which leads to infinite isotropic stresses in the element. These infinite isotropic stresses occur at the limit of uniqueness of the solution, which for this element is shown to occur outside the parameter range of the sufficiency of uniqueness. Copyright © 2000 John Wiley & Sons, Ltd.  相似文献   

2.
An efficient finite–discrete element method applicable for the analysis of quasi‐static nonlinear soil–structure interaction problems involving large deformations in three‐dimensional space was presented in this paper. The present method differs from previous approaches in that the use of very fine mesh and small time steps was not needed to stabilize the calculation. The domain involving the large displacement was modeled using discrete elements, whereas the rest of the domain was modeled using finite elements. Forces acting on the discrete and finite elements were related by introducing interface elements at the boundary of the two domains. To improve the stability of the developed method, we used explicit time integration with different damping schemes applied to each domain to relax the system and to reach stability condition. With appropriate damping schemes, a relatively coarse finite element mesh can be used, resulting in significant savings in the computation time. The proposed algorithm was validated using three different benchmark problems, and the numerical results were compared with existing analytical and numerical solutions. The algorithm performance in solving practical soil–structure interaction problems was also investigated by simulating a large‐scale soft ground tunneling problem involving soil loss near an existing lining. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

3.
Analysis of large deformation of geomaterials subjected to time‐varying load poses a very difficult problem for the geotechnical profession. Conventional finite element schemes using the updated Lagrangian formulation may suffer from serious numerical difficulties when the deformation of geomaterials is significantly large such that the discretized elements are severely distorted. In this paper, an operator‐split arbitrary Lagrangian–Eulerian (ALE) finite element model is proposed for large deformation analysis of a soil mass subjected to either static or dynamic loading, where the soil is modelled as a saturated porous material with solid–fluid coupling and strong material non‐linearity. Each time step of the operator‐split ALE algorithm consists of a Lagrangian step and an Eulerian step. In the Lagrangian step, the equilibrium equation and continuity equation of the saturated soil are solved by the updated Lagrangian method. In the Eulerian step, mesh smoothing is performed for the deformed body and the state variables obtained in the updated Lagrangian step are then transferred to the new mesh system. The accuracy and efficiency of the proposed ALE method are verified by comparison of its results with the results produced by an analytical solution for one‐dimensional finite elastic consolidation of a soil column and with the results from the small strain finite element analysis and the updated Lagrangian analysis. Its performance is further illustrated by simulation of a complex problem involving the transient response of an embankment subjected to earthquake loading. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

4.
A procedure for solving quasi‐static large‐strain problems by the material point method is presented. Owing to the Lagrangian–Eulerian features of the method, problems associated with excessive mesh distortions that develop in the Lagrangian formulations of the finite element method are avoided. Three‐dimensional problems are solved utilizing 15‐noded prismatic and 10‐noded tetrahedral elements with quadratic interpolation functions as well as an implicit integration scheme. An algorithm for exploiting the numerical integration procedure on the computational mesh is proposed. Several numerical examples are shown. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

5.
A method is presented for coupling cubic‐order quadrilateral finite elements with the finite side of a new coordinate ascent hierarchical infinite element. At a common side shared by a hierarchical infinite element and an arbitrary number of finite elements, the displacements are minimized in the least square sense with respect to the degrees‐of‐freedom of the finite elements. This leads to a set of equations that relate the degrees‐of‐freedom of the finite and hierarchical infinite elements on the shared side. The method is applied to a non‐homogeneous cross‐anisotropic half‐space subjected to a non‐uniform circular loading with Young's and shear moduli varying with depth according to the power law. A constant mesh constructed from coupled finite and hierarchical infinite elements is used and convergence is sought simply by increasing the degree of the interpolating polynomial. The displacements and stresses produced by conical and parabolic circular loads applied on the surface are obtained. The efficiency of the proposed method is demonstrated through convergence and comparison studies. New results produced by a frusto‐conical circular load applied on the surface of a half‐space made up of heavily consolidated London clay are provided. The non‐homogeneity parameter and degree of anisotropy are shown to influence the soil response. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

6.
Fused glass prepared without the addition of a flux is generally more homogeneous than a pressed powder pellet and thus ideal for analysis of bulk samples by LA‐ICP‐MS. In this work, a new glass‐making method using a boron nitride crucible was developed to prepare homogenous glass samples from silicate rock powder. The apparatus consisted of a small boron nitride vessel with net volume of about 34 mm3 and two molybdenum strips. Applying the summed metal oxide normalisation technique, both major and trace element contents in the fused glass were measured by LA‐ICP‐MS. Analyses of five geochemical reference materials (spanning the compositional range basalt–andesite–rhyolite) indicated that the measured SiO2, Al2O3 and P2O5 contents matched the preferred values to within 5%, and the other major elements generally matched the preferred values to within 8%. Except for the transition metals, the measured trace element contents generally matched the preferred values to within 10%. Compared with the iridium heater method developed by Stoll et al. (2008), element volatilisation during high‐temperature melting was effectively suppressed in our method, but metal segregation caused by reduction of BN may cause loss of Cr, Ni and Cu. Although analysis with a large spot size has the advantage of improving counting statistics, matrix effects induced by mass loading of the ICP may hamper the accurate determination of some elements.  相似文献   

7.
Laser ablation inductively coupled plasma mass spectrometry (LA‐ICP‐MS) is a high spatial resolution analytical method which has been applied to the analysis of silicic tephras. With current instrumentation, around 30 trace elements can be determined from single glass shards as small as ～ 40 µm, separated from tephra deposits. As a result of element fractionation during the ablation process using a 266 nm laser, a relatively complex calibration strategy is required. Nonetheless, such a strategy gives analyses which are accurate (typically within ±5%) and have an analytical precision which varies from ～ ±2% at 100 ppm, to ～ ±15% at 1 ppm. Detection limits for elements used in correlation and discrimination studies are well below 1 ppm. Examples of the application of trace element analysis by LA‐ICP‐MS in tephra studies are presented from the USA, New Zealand and the Mediterranean. Improvements in instrumental sensitivity in recent years have the potential to lower detection limits and improve analytical precision, thus allowing the analysis of smaller glass shards from more distal tephras. Laser systems operating at shorter wavelengths (e.g. 193 nm) are now more widely available, and produce a much more controllable ablation in glasses than 266 nm lasers. Crater sizes of <10 µm are easily achieved, and at 193 nm many of the elemental fractionation issues which mar longer wavelengths are overcome. By coupling a short wavelength laser to a modern ICP‐MS it should be possible to determine the trace element composition of glass shards as small as 20 µm and, providing sample preparation issues can be overcome, the determination of the more abundant trace elements in glass shards as small as 10 µm is within instrumental capabilities. This will make it possible to chemically fingerprint tephra deposits which are far from their sources, and will greatly extend the range over which geochemical correlation of tephras can be undertaken. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

8.
Strain‐softening in geomaterials often leads to ill‐posed boundary‐valued problems (BVP), which cannot be solved with finite element methods without introducing some kind of regularization such as nonlocal plasticity. Hereafter we propose to apply spectral analysis for testing the performance of nonlocal plasticity in regularizing ill‐posed BVP and producing mesh‐independent solutions when local plasticity usually fails. The spectral analysis consists of examining the eigenvalues and eigenvectors of the global tangential stiffness matrix of the incremental equilibrium equations. Based on spectral analysis, we propose a criterion for passing or failing the test of constitutive regularization in the context of BVP. If the eigenvalues of the tangential operator are all positive then the regularization succeeds, otherwise it fails and may not prevent artificial mesh‐dependent solutions from appearing. The approach is illustrated in the particular case of a biaxial compression with strain‐softening plasticity. In this particular case, local softening plasticity is found to produce negative eigenvalues in the tangential stiffness matrix, which indicates ill‐posed BVP. In contrast, nonlocal softening plasticity always produces positive eigenvalues, which regularizes ill‐posed BVP. The dominant eigenvectors, which generate localized deformation patterns, have a bandwidth independent of mesh size, provided that the mesh is fine enough to capture localization. These mesh‐independent eigenmodes explain why nonlocal plasticity produces numerical solutions that are mesh‐independent. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

9.
A simple flux‐free fusion technique was developed to analyse major and trace element compositions of silicate rocks. The sample powders were melted in a molybdenum capsule sealed in a graphite tube to make a homogenous glass in a temperature‐controlled one‐atmosphere furnace. The glass was then measured for both major and trace element concentrations by LA‐ICP‐MS using a calibration strategy of total metal‐oxide normalisation. The optimum conditions (i.e., temperature and duration) to make homogeneous glasses were obtained by performing melting experiments using a series of USGS reference materials including BCR‐2, BIR‐1, BHVO‐2, AGV‐1, AGV‐2, RGM‐1, W‐2 and GSP‐2 with SiO2 contents from 47 to 73% m/m. Analytical results of the USGS reference materials using our method were generally consistent with the recommended values within a discrepancy of 5–10% for most elements. The routine precision of our method was generally better than 5–10% RSD. Compared with previous methods of LA‐ICP‐MS whole‐rock analyses, our flux‐free fusion method is convenient and efficient in making silicate powder into homogeneous glass. Furthermore, it limits contamination and loss of volatile elements during heating. Therefore, our new method has great potential to provide reliable and rapid determinations of major and trace element compositions for silicate rocks.  相似文献   

10.
Previous laser ablation‐ICP‐MS bulk analyses have been confined to volcanic glasses and glass disks or powder pellets similar to those used for XRF analysis. This study proposes a method to determine twenty trace elements (fourteen rare earth elements, Sc, Y, Zr, Nb, Hf and Ta) by LA‐ICP‐MS directly from polished thick sections and rock slabs of six fine‐grained crystalline and aphanitic rocks (five volcanic rocks and one pelitic tillite). Laser scanning of eight to ten 20 mm long linear tracks using a spot size of 160 μm, with a total ablated area of 26–32 mm2, was performed. Quantification was carried out by (a) internal standardisation using Si and (b) without applying internal standardisation. In the latter method, external determination of one element in conventional LA‐ICP‐MS quantification is no longer needed. Although the fine‐grained rocks studied contained variable amounts of volatiles (up to 4%), this method gave results that agree within 10% relative with those obtained by internal standardisation using Si. Two USGS basalt glass reference materials (BCR‐2G and BHVO‐2G) were used for external calibration. The results and the associated trace element patterns and ratios of elemental pairs obtained from both methods of quantification showed good agreement with the results from solution nebulisation ICP‐MS within 20% (mostly within 10%) relative. Fine‐grained rocks are common and include volcanic, sedimentary and low‐grade metamorphic rocks (e.g., basalt, andesite, rhyolite, shale, mudstone, tillite, loess, pelite and slate) and their trace element contents and associated ratios are important geochemical tracers in studies focusing on the composition and evolution of the crust and mantle. Our method provides a simple and quantitative way to determine trace elements in fine‐grained rocks even with those displaying complex textures.  相似文献   

11.
A challenging computational problem arises when a discrete structure (e.g. foundation) interacts with an unbounded medium (e.g. deep soil deposit), particularly if general loading conditions and non‐linear material behaviour is assumed. In this paper, a novel method for dealing with such a problem is formulated by combining conventional three‐dimensional finite‐elements with the recently developed scaled boundary finite‐element method. The scaled boundary finite‐element method is a semi‐analytical technique based on finite‐elements that obtains a symmetric stiffness matrix with respect to degrees of freedom on a discretized boundary. The method is particularly well suited to modelling unbounded domains as analytical solutions are found in a radial co‐ordinate direction, but, unlike the boundary‐element method, no complex fundamental solution is required. A technique for coupling the stiffness matrix of bounded three‐dimensional finite‐element domain with the stiffness matrix of the unbounded scaled boundary finite‐element domain, which uses a Fourier series to model the variation of displacement in the circumferential direction of the cylindrical co‐ordinate system, is described. The accuracy and computational efficiency of the new formulation is demonstrated through the linear elastic analysis of rigid circular and square footings. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

12.
As a hybrid method, the nodal‐based discontinuous deformation analysis (NDDA) greatly improves the stress accuracy within each DDA block by coupling a well‐defined finite element mesh inside the DDA block; at the same time, the NDDA inherits the unique block kinematics of the standard DDA method. Each finite element mesh line inside the DDA block is treated as a potential crack, which enables the transformation of the block material from continuum to discontinuum through the tensile and shear fracturing mechanism. This paper introduces a double minimization procedure into the NDDA method to further improve the accuracy of the stresses evaluated at the finite element mesh lines and thus to obtain a more realistic fracture model. Three numerical examples are employed to demonstrate the improved stress accuracy by the implemented double minimization procedure and the accuracy and capability of the enhanced NDDA method in capturing brittle fracturing process. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

13.
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14.
An efficient, clean procedure for the measurement of element mass fractions in bulk rock nanoparticulate pressed powder pellets (PPPs) by 193 nm laser ablation ICP‐MS is presented. Samples were pulverised by wet milling and pelletised with microcrystalline cellulose as a binder, allowing non‐cohesive materials such as quartz or ceramics to be processed. The LA‐ICP‐MS PPP analytical procedure was optimised and evaluated using six different geological reference materials (JP‐1, UB‐N, BCR‐2, GSP‐2, OKUM and MUH‐1), with rigorous procedural blank quantification employing synthetic quartz. Measurement trueness of the procedure was equivalent to that achieved by solution ICP‐MS and LA‐ICP‐MS analysis of glass. The measurement repeatability was as low as 0.5–2% (1s, n = 6) and, accordingly, PPP homogeneity could be demonstrated. Calibration based on the reference glasses NIST SRM 610, NIST SRM 612, BCR‐2G and GSD‐1G revealed matrix effects for glass and PPP measurement with NIST SRM 61×; using basalt glasses eliminated this problem. Most significantly, trace elements not commonly measured (flux elements Li, B; chalcophile elements As, Sb, Tl, In, Bi) could be quantified. The PPP‐LA‐ICP‐MS method overcomes common problems and limitations in analytical geochemistry and thus represents an efficient and accurate alternative for bulk rock analysis.  相似文献   

15.
This paper presents a simplified finite element analysis technique, the ‘Press‐Replace’ technique, to model pile penetration problems in geotechnical engineering, particularly, pile jacking. The method is employed in standard finite element analysis software. The method involves a straining and a consequent geometry update phase. First, a cone penetration test in (undrained) clay is modelled and compared with the results of analytical, semi‐analytical and more advanced finite element techniques. The model sensitivity for the step size and mesh is investigated using a hypoplastic constitutive model. An optimum way of modelling based on the numerical performance is shown. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

16.
LA‐ICP‐MS is one of the most promising techniques for in situ analysis of geological and environmental samples. However, there are some limitations with respect to measurement accuracy, in particular for volatile and siderophile/chalcophile elements, when using non‐matrix‐matched calibration. We therefore investigated matrix‐related effects with a new 200 nm femtosecond (fs) laser ablation system (NWRFemto200) using reference materials with different matrices and spot sizes from 10 to 55 μm. We also performed similar experiments with two nanosecond (ns) lasers, a 193 nm excimer (ESI NWR 193) and a 213 nm Nd:YAG (NWR UP‐213) laser. The ion intensity of the 200 nm fs laser ablation was much lower than that of the 213 nm Nd:YAG laser, because the ablation rate was a factor of about 30 lower. Our experiments did not show significant matrix dependency with the 200 nm fs laser. Therefore, a non‐matrix‐matched calibration for the multi‐element analysis of quite different matrices could be performed. This is demonstrated with analytical results from twenty‐two international synthetic silicate glass, geological glass, mineral, phosphate and carbonate reference materials. Calibration was performed with the certified NIST SRM 610 glass, exclusively. Within overall analytical uncertainties, the 200 nm fs LA‐ICP‐MS data agreed with available reference values.  相似文献   

17.
This paper presents a ‘Eulerian‐like’ finite element technique to simulate the large accumulated displacements of piles subjected to multiple hammer blows. For each hammer blow, results are obtained using a standard small strain finite element model and, at the end of each hammer blow, material flow is taken into account with reference to a fixed finite element mesh. Residual stresses calculated at the Gauss integration points of the deformed finite element mesh are mapped on to the fixed finite element mesh, and these stresses are used as initial stresses for the next hammer blow. At the end of each hammer blow, stiffness and mass matrices are recalculated for the volume of material remaining inside the fixed finite element mesh. Results obtained with and without allowing material to flow through the fixed mesh are compared for several hammer blows. Build up of residual stresses, soil flow and yielded points around the pile are presented for plugged, partially‐plugged and unplugged piles. Using the new finite element technique, the driving of a pile from the soil surface is studied. The ability to analyse this and other large deformation problems is the main advantage of the new finite element technique. Copyright © 2000 John Wiley & Sons, Ltd.  相似文献   

18.
In geomechanics, limit analysis provides a useful method for assessing the capacity of structures such as footings and retaining walls, and the stability of slopes and excavations. This paper presents a finite element implementation of the kinematic (or upper bound) theorem that is novel in two main respects. First, it is shown that conventional linear strain elements (6‐node triangle, 10‐node tetrahedron) are suitable for obtaining strict upper bounds even in the case of cohesive‐frictional materials, provided that the element sides are straight (or the faces planar) such that the strain field varies as a simplex. This is important because until now, the only way to obtain rigorous upper bounds has been to use constant strain elements combined with a discontinuous displacement field. It is well known (and confirmed here) that the accuracy of the latter approach is highly dependent on the alignment of the discontinuities, such that it can perform poorly if an unstructured mesh is employed. Second, the optimization of the displacement field is formulated as a standard second‐order cone programming (SOCP) problem. Using a state‐of‐the‐art SOCP code developed by researchers in mathematical programming, very large example problems are solved with outstanding speed. The examples concern plane strain and the Mohr–Coulomb criterion, but the same approach can be used in 3D with the Drucker–Prager criterion, and can readily be extended to other yield criteria having a similar conic quadratic form. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

19.
The discontinuous deformation analysis (DDA) with second‐order displacement functions was derived based on six‐node triangular mesh in order to satisfy the requirement for the accurate calculations in practical applications. The matrices of equilibrium equations for the second‐order DDA were given in detail for program coding. By close comparison with widely used finite element method and closed form solutions, the advantages of the modified DDA were illustrated. The program coding was carried out in C++ environment and the new code applied to three examples with known analytical solutions. A very good agreement was achieved between the analytical and numerical results produced by the modified DDA code. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

20.
We present a new method for the decomposition of silicate rocks by flux‐free fusion in preparation for whole‐rock trace element determination (Sc, Rb, Sr, Y, Zr, Nb, Cs, Ba, rare earth elements and Hf) that is especially applicable to zircon‐bearing felsic rocks. The method was verified by analyses of RMs of mafic (JB‐1a, JB‐2, JGb‐1) and felsic rocks (JG‐3, JR‐3, JSd‐1, GSP‐2, G‐2). Pellets of powdered sample (up to 500 mg) without flux were weighed and placed in a clean platinum crucible. The samples were then fused in a Siliconit® tube furnace and quenched to room temperature. The optimum condition for the fusion of granitic rock was determined to be heating for 2–3 min at 1600 °C. The fused glass in the platinum crucible after heating was decomposed using HF and HClO4 in a Teflon® beaker. Decomposed and diluted sample solutions were analysed using a quadrupole inductively coupled plasma‐mass spectrometer. Replicate analyses (n = 4 or 5) of the RMs revealed that analytical uncertainties were generally < 3% for all elements except Zr and Hf (～ 6%) in JG‐3. These higher uncertainties may be attributed to sample heterogeneity. Our analytical results for the RMs agreed well with recommended concentrations and recently published concentrations, indicating complete decomposition of our rock samples during fusion.  相似文献   

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