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A self-developed finite element limit analysis (FELA) code was employed in this study to investigate the stability of eccentrically loaded strip footings on rock slopes. The research emphasis of this study was on quantifying the inequality phenomenon induced by the slope and eccentric loads of different directions. The generalized Hoek–Brown yield criterion was embedded into the program to simulate the rock nonlinearity. Upper bound theorem, lower bound theorem and adaptive meshing technique were adopted for more reliable calculations. And stability charts were presented to illustrate the influences of various influential factors including the rock property, the slope angle and the footing position on the footing bearing capacity. Furthermore, transformation trends of failure patterns were analyzed for deeper insight into how the failure mechanisms evolving with different influential factors. Detailed design tables were summarized to facilitate the engineering practice and ensure the building safety. [ABSTRACT FROM AUTHOR]

The seismic response is a critical aspect of structural engineering, as it directly influences the design and safety evaluation of such systems. Structural seismic response becomes more complicated when unavoidable uncertainties in the structure are considered. Therefore, solving and analyzing the stochastic dynamic response of structures efficiently and accurately is of great significance. Various uncertainty quantification methods such as the stochastic finite element method, Monte Carlo method, and polynomial chaos expansion method have made significant progress in this field. However, these methods do not provide a comprehensive study of the seismic response of stochastic structures and efficiency problems rapidly emerge as the number of random variables increases. This paper delivers a comprehensive study of the seismic dynamic response of space truss and reticulated shell structure considering uncertainties in material properties, geometry, and loading. To this end, the finite element model of the structure was first modeled and the deterministic solutions were obtained. Then, polynomial surrogates are modeled for the natural frequency, mode participation factor, mode superposition response, and transient response of the structure under stochastic uncertainties. The sparse grid technique is used to select sparse quadrature points, which overcomes the curse of dimensionality caused by full grid integration. The results demonstrate that the sparse grid-based polynomial chaos expansion is more efficient. Uncertainty quantification reveals the uncertainty of modal analysis, response spectrum analysis, and transient response analysis of space truss and reticulated shell under seismic excitation. In summary, this study provides valuable insights and an efficient and accurate uncertainty quantification tool for the seismic dynamic analysis of stochastic structures, ultimately contributing to safer and more robust structural designs. • Analyzing the seismic dynamic response of stochastic structures comprehensively. • Sparse grid-based PCE for quantifying uncertainty in stochastic dynamics. • Addressing the dimensional catastrophe of traditional non-intrusive PCE. • Sparse grid-based PCE metamodel for post-processing is more efficient and accurate. [ABSTRACT FROM AUTHOR]

To address the issue of low accuracy resulting from approximation errors in conventional interval finite element methods, this study presents an ɛ -accelerated bivariate dimension-reduction interval finite element method. The proposed method aims to accurately and efficiently predict the static response of structures with high dimensionality and large uncertainty parameters. We first approximate the structural interval equilibrium equation using a bivariate dimension-reduction method. An explicit expression for the sequence of displacements is derived by approximating the inverse of the structural interval stiffness matrix using the Neumann series. Adjoint-based sensitivity analysis can effectively avoid the response interval expansion caused by parameter coupling. For improving the convergence speed and computational accuracy, the displacement response sequence is accelerated by a vector ɛ acceleration algorithm and an adaptive strategy. Finally, three engineering structures with uncertain-but-bounded parameters are analyzed with the proposed method. Compared with conventional interval analysis methods, the proposed method effectively balances computational accuracy and efficiency, making it more suitable for non-linear and large uncertainty problems with multiple interval parameters. The study shows that ɛ -accelerated bivariate dimension-reduction interval finite element method has a promising application. • An interval finite element method based on bivariate dimension-reduction is proposed. • Explicit sequences and errors for the bounds of displacements were derived. • Dependencies between parameters are addressed by adjoint-based sensitivity analysis. • Convergence speed and accuracy are improved by the adaptive ɛ algorithm. • Structural response intervals are efficiently and accurately predicted. [ABSTRACT FROM AUTHOR]

The machining effects of hole drilling is limited by merely changing the amplitude. Adjusting ultrasonic vibration frequency to expand the matching range of machining parameters optimization is necessary to improve hole drilling effects. Therefore, the design, optimization, and experiment evaluation for a novel integrated, fined, low-cost dual-frequency ultrasonic tool shank is proposed, which can work in three vibration modes for micro-nano precision drilling. The principle of the dual-frequency ultrasonic transducer is introduced. The electro-mechanical equivalent circuit model with step horn is applied to study the dual-frequency characteristics. The transducer displacement equation model based on the wave equation theory is deduced to find the shared vibration node of the first and third frequency. Sensitivity analysis by equivalent circuit model and Finite element method (FEM) simulation of the key parameter is both conducted to optimize ultrasonic transducer geometry dimension. The vibration node of mounting flange is specified in an identical position for the dual vibration modes. A prototype of ultrasonic tool shank is fabricated and evaluated in experiments. It demonstrates that the dual working frequency of the ultrasonic transducer is 34.9 kHz and 104.5 kHz in the first and third mode resonant vibration, which is benefit to the low and high frequency drilling. Three working modes of the low, high, and coupling frequency vibration is measured by a self-developed ultrasonic generator. When 40 V voltage is excited, the vibration amplitudes of the low and high frequency are 17.8 µm, and 9.3 µm, respectively, which can meet with the drilling requirement. Moreover, the coupling vibration with the low and high mode are excited simultaneously, and the motion trajectory of the coupling vibration is observed in a "M" shape, which is a novel trajectory for the precision micro-nano drilling. Micro drilling experiments show that the 35 kHz ultrasonic vibration drilling can achieve better machining effect than conventional drilling (CD). The 105 kHz ultrasonic drilling outperforms the CD, 35 kHz and coupling ultrasonic drilling at cutting force reduction. The coupling ultrasonic vibration drilling achieves the lowest chipping diameter. It is to be noted that the 105 kHz-8 µm produce the fined smoothly surface. The 35 kHz, 105 kHz and coupling ultrasonic drilling can produce better surface micro morphology with less quantity and size of craters than that of CD. [Display omitted] • Dual-frequency ultrasonic tool shank in 34.9/104.5 kHz can vibrate in three vibration modes. • The vibration node is optimized in an identical position. • Vibration amplitude can reach at 34.9 kHz/17.8 µm and 104.5 kHz/9.3 µm. • The coupling vibration is tuned in M shape of low/high frequency vibration at 7.4 /3.6 µm. • Tool shank have great potential to parameters optimization in micro drilling. [ABSTRACT FROM AUTHOR]

This study investigates the effect of slope on the lateral bearing capacity of nearshore large-diameter monopiles in cohesive soil by the finite element limit analysis (FELA) method. The reduction coefficient is introduced to quantify the capacity reduction due to the slope effect, and the critical distance making the slope-induced capacity reduction negligible is normalized for generalization. After the validations by cases of different soils, an alternative way to quickly and straightforwardly assess the pile bearing capacity in sloping stratum for the most frequently-encountered cases in engineering practice is provided by multiplying the reduction coefficients in several design tables with the capacity in level stratum. The subsequent parametric studies indicate that the reduction coefficient and critical dimensionless distance are mainly governed by the internal friction angle, slope angle, and pile embedded length-diameter ratio but are almost insensitive to dimensionless cohesion and slope height-pile embedded length ratio. In addition, the failure mode of the pile-slope system would develop from local failure to transitional failure and global failure with a significant drop in pile bearing capacity while the pile-slope parameters cannot guarantee slope stability. [ABSTRACT FROM AUTHOR]

This study is devoted to investigating the effect of nearby strip loading on the lateral bearing capacity of offshore large-diameter monopiles at the crest of marine clay slope by the finite element limit analysis (FELA) method. After the successive validations by cases of rigid piles and strip footings at the clay slope crest, the safe domains for the laterally loaded large-diameter monopiles are defined by the failure envelopes relating the dimensionless lateral bearing capacity Hu/(cuD2) to dimensionless strip loading q/cu. Particularly, all failure envelopes are depicted by closed-form expressions and design charts can then be given for a quick and straightforward assessment of dimensionless lateral bearing capacity for a wide range of frequently-encountered cases. In addition, the interaction between the pile bearing capacity and nearby strip loading is characterized by introducing the relationship of normalized parameters Hu/(cuD2) and q/cu, then graphically explained by plastic multiplier contour plots. Several kinds of representative curves are given successively to further clarify the effects of dimensionless factors on the interaction. [ABSTRACT FROM AUTHOR]

The ultimate bearing capacity of an eccentrically loaded strip footing above twin square tunnels buried in rock masses was examined using the generalized Hoek-Brown (GHB) yield criteria. To get reliable findings, the stability assessments were carried out using finite element limit analysis (FELA) code in combination with a sophisticated adaptive remeshing approach. Case studies with two different tunnel layouts, parallel and symmetrical, were examined. Comprehensive parametric analyses were given to demonstrate the effect of load eccentricity, rock mass strength parameters, and tunnel position on the stability of the strip footing. The visualized results of the FELA programme were presented to show how the failure mechanism would change with different influential factors. Moreover, the results were validated by comparing them to earlier investigations. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, an efficient l 1-regularized reconstruction method named the primal-dual interior-point (PDIP) method is presented for three-dimensional bioluminescence tomography (BLT) based on the adaptive finite element framework. Taking into account the sparse characteristic of the bioluminescent source, the BLT inverse problem is considered to be a linear programming problem and is represented by its primal and dual form. The source localization and quantification are obtained by solving the primal-dual Newton equation system. The comparisons between PDIP and the classical conjugate gradient least square (CGLS) algorithm are implemented to validate our method. Results from numerical simulation and an in vivo mouse experiment demonstrate the credibility and the potential of the proposed method in practical BLT reconstruction. [Copyright &y& Elsevier]

Random adaptive finite element limit analysis (RAFELA) is introduced to investigate the stability of the footing-voids system with random soils. The emphasis of this study is, for the footing-void system, on quantifying the influence of spatial variability on its bearing capacity and the failure probability. Of particular interest is that random field theory is utilized to characterize the spatial variability of soil, and at the same time, failure probability is calculated by imposing Monte-Carlo simulations on independent cases. Strict close bearing capacity could be obtained within the scope embraced by upper bound (UB) results and lower bound (LB) results. By imposing the proposed modelling, comprehensive parametric studies were carried out, especially for the soil spatial correlation parameters and geometry parameters. The results indicated that the failure probability would increase with the farther distance between the void and the footing, the greater coefficient of variation (COV) and the smaller vertical correlation length. Detailed design tables were presented to assess potential failure probability under different conditions. Typical failure patterns are also summarized, revealing a positive correlation between the failure probability and the diffusion degree of failure curves. [ABSTRACT FROM AUTHOR]

The undrained stability of dual circular tunnels buried in spatially random soils is investigated by imposing the random adaptive finite element limit analysis (RAFELA). The emphasis is on quantifying the effect of influential factors including the geometry parameters and spatially variability parameters on the bearing capacity and failure probability of tunnels by assuming a lognormal distribution on undrained shear strength within a spatial correlation structure. Predictions were obtained by the scope enclosed by upper bound (UB) and lower bound results (LB) results within 5% relative errors. To account for a combined effect simultaneously caused by depths of tunnels, spaces between tunnels, soil weights, and spatially variability parameters on the stability of tunnels, all independent variables are involved in parametric studies in pairs. Results revealed several failure patterns and announced how the stability evolves with changes in tunnel geometry and soil spatial variability. [ABSTRACT FROM AUTHOR]

In this study, finite element limit analysis (FELA) is employed to investigate the undrained seismic bearing capacity of strip footings placed on two-layered slopes. Upper bound theorem (UB), lower bound theorem (LB) and adaptive meshing technique were used in parametric studies to investigate the effects of various factors on seismic bearing capacity N cs and failure mechanism, especially the seismic coefficient k h and the shear strength ratio of top layer and bottom layer c u1 / c u2. The angle of the slope β , the absolute strength of top layer c u /γ B , horizontal offset distance b and the thickness of top layer D are also taken into consideration. Furthermore, the comparisons between present study and previous studies are provided. Detailed design tables are presented to distinguish the failure patterns and estimate the seismic bearing capacity of slopes under different conditions. [ABSTRACT FROM AUTHOR]

In this study, the seismic stability of a slope containing a laterally loaded pile under seismic conditions is evaluated by the finite-element limit analysis (FELA) approach. The seismic action is idealized as a horizontal seismic coefficient, ranging from 0 to 0.3, within the framework of the pseudo-static approach, and applied as an accelerogram of earthquakes to the numerical model in the seismic analysis. By means of the adaptive meshing technique, the finite-element method, and limit theorem of plasticity, the slope failure mechanism need not be presumed in advance. The feasibility of the FELA is validated by comparing the obtained factors of safety and critical sliding surfaces with those provided by published literature. Based on this, the effects of various factors (e.g., horizontal seismic coefficient, internal friction angle, cohesion, slope angle, slope height, and lateral load atop the pile) on the factor of safety and failure mechanism, with a normalized parameter (seismic-multiplier) is proposed. Furthermore, some detailed design tables and four representative slope failure patterns are presented to estimate the seismic stability of the slope containing a laterally loaded pile. [ABSTRACT FROM AUTHOR]

This study employed finite element limit analysis (FELA) to investigate the influence of eccentric loads on the bearing capacity of footings above single and double continuous voids. Upper bound theorem (UB), lower bound theorem (LB), and adaptive meshing techniques were used in a parametric study to investigate the influence of some factors, including the relative distance between double voids, the depth of voids, the geometry of voids, the variation of soil shear strength, and the eccentricity of loadings on the bearing capacity of footings. The results indicated that, for the footings inclined above a single void, the bearing capacity with a void located on the same side of the eccentric load was less than that in an opposite position. In addition, the failure mechanisms were summarized and analyzed in this study. [ABSTRACT FROM AUTHOR]

Finite element limit analysis (FELA) is used to study the undrained bearing capacity of strip footing above voids in two-layered clays. Based on the FELA results, design charts and equations are provided to calculate the undrained bearing capacity factor N s . The impact of parameters on N s also has been investigated, including undrained shear stress ratio of the soil, thickness of the top layer, location, size, width, height and spacing of the voids. The failure mechanisms for a single void maybe classified into three categories: roof failure, combined roof and wall failure, bearing failure without void failure. [ABSTRACT FROM AUTHOR]

This paper presents a finite beam element method (FBEM) for analyzing the behavior of a two-pile foundation under eccentric and inclined loads located at sloping ground. A simplified physical model for the two-pile foundation is presented by dint of the strain wedge technique and FBEM. The emphasis is on establishing an element stiffness matrix, taking the P -Δ effect, the strengthening effect on the pile stiffness and the Pasternak's soil resistance into consideration. The global stiffness matrix can thus be assembled by these element stiffness matrixes, and the node force and deflection were identified by FBEM. The results are compared with field observations and exhibit satisfactory accuracy. [ABSTRACT FROM AUTHOR]

Adaptive finite element limit analysis (AFELA) is employed to investigate the stability of two circular tunnels at different depths in cohesive-frictional soils subjected to surcharge loading. The upper and lower bounds of the tunnel stability numbers are obtained, with the relative errors being found within ±5%. Five parametric studies are conducted to evaluate the effects of the horizontal and vertical spacing ratio, overburden stress factor, cover depth ratio and soil internal friction angle on the tunnel stability numbers. Design tables and charts are provided to facilitate engineers' use. In addition, typical failure mechanisms are discussed and examined. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the stability of dual circular tunnels in a rock mass subjected to surcharge loading using adaptive finite element limit analysis (AFELA). The tunnels are modelled under plain-strain conditions, and the rock mass is assumed to be a homogeneous and isotropic material obeying the Hoek-Brown failure criterion. For the studied problem, numerical kinematic and static approaches are employed to calculate the rigorous upper and lower bounds of the stability number N , which has been bracketed within ±5% from above and below. The calculated results are presented in the form of dimensionless stability charts, and the typical failure mechanisms are discussed through parametric studies of the problem variables using the visualized results of AFELA. [ABSTRACT FROM AUTHOR]

The stability of dual unlined square tunnels subjected to surcharge loading in rock masses, obeying Generalized Hoek-Brown (GHB) failure criterion, is investigated by adaptive finite element limit analysis (AFELA) under plane strain conditions. Both upper bound (UB) and lower bound (LB) of the dimensionless stability number N are obtained, with the relative errors being found within 7%. Extensive parametric studies are conducted to investigate the effects of the center-to-center distance ratio, cover depth ratio, geological strength index (GSI) and material constant for intact rock (m i). The results are presented in the form of dimensionless stability tables and charts for engineers to use, and typical failure mechanisms are discussed. The results obtained in this study compare reasonably well with the solutions reported in the literature. [ABSTRACT FROM AUTHOR]