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The purpose of this paper is to investigate a model for convection induced by the selective absorption of radiation in a fluid layer. The concentration based internal heat source is modelled quadratically. Both linear instability and global nonlinear energy stability analyses are tested using three dimensional simulations. The results show that the linear threshold accurately predicts on the onset of instability in the basic steady state. However, the required time to arrive at the steady state increases significantly as the Rayleigh number tends to the linear threshold.

The author introduce the stability analysis of the problem of convection induced by absorption of radiation in fluid layer, then the author select a situations which have very big subcritical region. Then, the author develop a three dimensions simulation for the problem. To do this, first, the author transform the problem to velocity – vorticity formulation, then the author use a second order finite difference schemes. The author use implicit and explicit schemes to enforce the free divergence equation. The size of the Box is evaluated according to the normal modes representation. Moreover, the author adopt the periodic boundary conditions for velocity and temperature in the $x, y$ dimensions.

This paper explores a model for convection induced by the selective absorption of radiation in a fluid layer. The results demonstrate that the linear instability thresholds accurately predict the onset of instability. A three-dimensional numerical approach is adopted.

As the author believe, this paper is one of the first studies which deal with study of stability of convection using a three dimensional simulation. When the difference between the linear and nonlinear thresholds is very large, the comparison between these thresholds is very interesting and useful.

To solve the instability problem of Zhangjiayao landslide caused by rainfall, the internal mechanism of slope instability and the supporting effect of anti-slide piles are studied. The research results can provide theoretical basis for the prevention and control of loess landslides.

A three-dimensional finite element model of Zhangjiayao landslide is established by field geological survey, laboratory test and numerical simulation.

The results show that Zhangjiayao landslide is a loess-mudstone contact surface landslide, and rainfall leads to slope instability and traction landslide. The greater the rainfall intensity, the faster the pore water pressure of the slope increases and the faster the matrix suction decreases. The longer the rainfall duration, the greater the pore water pressure of the slope and the smaller the matrix suction. Anti-slide pile treatment can significantly improve slope stability. The slope safety factor increases with the increase of embedded depth of anti-slide pile and decreases with the increase of pile spacing.

Based on the unsaturated soil seepage theory and finite element strength reduction method, the failure mechanism of Zhangjiayao landslide was revealed, and the anti-slide pile structure was optimized and designed based on the pile-soil interaction principle. The research results can provide theoretical basis for the treatment of loess landslides.

1. A three-dimensional finite element model of Zhangjiayao landslide is established.

2. Zhangjiayao landslide is a loess-mudstone contact surface landslide.

3. The toe of Zhangjiayao slope is first damaged by heavy rainfall, resulting in traction landslide.

4. The deformation of Zhangjiayao slope is highly dependent on rainfall intensity and duration.

5. The anti-slide pile can effectively control the continuous sliding of Zhangjiayao slope.

A three-dimensional finite element model of Zhangjiayao landslide is established.

Zhangjiayao landslide is a loess-mudstone contact surface landslide.

The toe of Zhangjiayao slope is first damaged by heavy rainfall, resulting in traction landslide.

The deformation of Zhangjiayao slope is highly dependent on rainfall intensity and duration.

The anti-slide pile can effectively control the continuous sliding of Zhangjiayao slope.

This study is an attempt to estimate the influence of the presence of cavities on the stability of slopes in earth dams under rapid drawdown conditions. The purpose of this paper is to study the influence of different factors, such as the diameter and location of cavities, in addition to their existence effects.

A series of finite element simulation models were developed using PLAXIS 2D finite element software to analyse the stability of slopes in earth dams while considering various effects from cavities in the subsoil under rapid drawdown conditions.

The results indicated that the presence of cavities and an increase in the diameter of cavities decreased the stability of the upstream face dramatically for all examined locations in a horizontal direction; however, this effect was less on the downstream side. The results also showed that variations in the location of cavities in the horizontal direction have a greater effect on the stability than those in the vertical direction. The results revealed that increasing shear strength parameters of embankment does not reduce the influence of cavities on stability when those cavities are in critical locations.

A numerical model has been developed to simulate the effects of cavities on the stability of slopes in water-retaining structures/earth dams. The stability of earth dam slopes on upstream and downstream sides under rapid drawdown conditions considering various cavity effects, including their existence, diameter and location, were numerically analysed.

Since robot’s structural stiffness is usually less than 1 N/µm, mode coupling chatter occurs frequently during robotic milling process, and chatter frequency is close to the natural frequency of the robot itself. Chatter not only affects the surface quality but also damages the robot and reduces the positioning accuracy. Therefore, it is necessary to predict chatter in robotic machining process.

A three-dimensional dynamic model for robot’s spatial milling plane is established, and a corresponding stability criterion is obtained. First, the cutting force in milling plane is transformed into the coordinate system of the robot principal stiffness direction based on homogeneous transformation matrix. Then the three-dimensional stability criterion under milling process can be obtained by using system stability analysis. Furthermore, the circle diagram of mode coupling chatter stability is drawn. Each feeding direction’s stability under the two processing forms, referred as spindle vertical milling and spindle horizontal milling, is analyzed.

The experimental results verify that the three-dimensional stability criterion can avoid chatter by selecting machining feed direction in stable area.

This paper established a three-dimensional dynamic model in robot’s spatial milling plane and proposed a three-dimensional stability criterion according to the Routh criterion. The work is also expected to be an efficient tool in the development of robotic milling technology.

Our recent results on stability and multiplicity of flow states for confined flows of an incompressible Newtonian fluid are surveyed. The considered laminar flows are caused by either thermal, mechanical, or electromagnetic effects and beyond the stability limit exhibit multiplicity of stable, steady or oscillatory, asymptotic states. Stability diagrams as well as examples of multiple flow states are given. It is concluded that beyond the critical value of the characteristic non‐dimensional parameter, and below the threshold to stochastic or turbulent state, multiple stable asymptotic flow states can be expected. This means that at such flow regimes, any computational (experimental) result may be strongly dependent on its initial condition and/or computational (experimental) path. Uncertainties of experimental and numerical modeling, which follow from this conclusion, are discussed. The global spectral Galerkin method using divergence free basis functions has been employed for the spatial approximation of the velocity and temperature fields. Several numerical experiments were performed comparing the present and other formulations, each of which confirmed the computational efficiency of the present approach over other classical numerical methods.

The purpose of this study is to implement a new class of similarity transformation in analyzing the three-dimensional boundary layer flow of hybrid nanofluid. The Cu-Al₂O₃/water hybrid nanofluid is formulated using the single-phase nanofluid model with modified thermophysical properties.

The governing partial differential equations are reduced to the ordinary (similarity) differential equations using the proposed similarity transformation. The resulting equations are programmed in Matlab software through the bvp4c solver to obtain their solutions. The features of the reduced skin frictions and the velocity profiles for different values of the physical parameters are analyzed and discussed.

The non-uniqueness of the solutions is observed for certain physical parameters. The dual solutions are perceived for both permeable and impermeable cases and being the main agenda of the work. The execution of stability analysis proves that the first solution is undoubtedly stable than the second solution. An increase in the mass transpiration parameter leads to the uniqueness of the solution. Oppositely, as the injection parameter increase, the two solutions remain. However, no separation point is detected in this problem within the considered parameter values. The present results are decisive to the pair of alumina and copper only.

The present findings are original and can benefit other researchers particularly in the field of fluid dynamics. This study can provide a different insight of the transformation that is applicable to reduce the complexity of the boundary layer equations.

A numerical method is developed which can simulate the interaction between a finite compliant panel and an unsteady potential flow. A boundary‐element technique yields the flow solution whilst finite‐differences are used to solve the wall dynamics; these are then coupled to generate a fully interactive wall/flow system. Thus, the evolution of any wall disturbance can be followed. Parallel computing is appropriately employed and a stability investigation of a realistic compliant panel is carried out. Three‐dimensional flexural waves are found below a critical flow speed whilst beyond this threshold, essentially two‐dimensional unstable divergence waves are found. The form of divergence shows good agreement with that seen in experimental studies. The versatility of this new method will permit the investigation of a wide variety of single‐ and multi‐panel configurations subject to different forms of excitation.

This paper considers an application of optimisation techniques in landfill design. In order to reduce the environmental impact, the maximisation of the landfill storage capacity is obtained as a constrained optimisation problem by the simplex method of linear programming. The proposed approach allows the designer to model the external surface of the waste in respect of some geometrical constraints and three‐dimensional stability, evaluated for one or more prefixed slip surfaces. Analytical expressions needed to assemble a computer program are given and an illustrative example is also presented.

When explicit integral analysis is performed on a numerical model with viscoelastic artificial boundary elements, an instability phenomenon is likely to occur in the boundary area, reducing the computational efficiency of the numerical calculation and limiting the use of viscoelastic artificial boundary elements in the explicit dynamic analysis of large-scale engineering sites. The main purpose of this study is to improve the stability condition of viscoelastic artificial boundary elements.

A stability analysis method based on local subsystems was adopted to analyze and improve the stability conditions of three-dimensional (3D) viscoelastic artificial boundary elements. Typical boundary subsystems that can represent the localized characteristics of the overall model were established, and their analytical stability conditions were derived with an analysis based on the spectral radius of the transfer matrix. Then, after analyzing the influence of each physical parameter on the analytical-stability conditions, a method for improving the stability condition of the explicit algorithm by increasing the mass density of the artificial boundary elements was proposed.

Numerical wave propagation simulations in uniform and layered half-space models show that, on the premise of ensuring the accuracy of the viscoelastic artificial boundary, the proposed method can effectively improve the numerical stability and the efficiency of the explicit dynamic calculations for the overall system.

The stability improvement method proposed in this study are significant for improving the applicability of viscoelastic artificial boundary elements in explicit dynamic calculations and the calculation efficiency of wave analysis at large-scale engineering sites.

The influence of buoyancy forces on oscillatory Marangoni flow in liquid bridges of different aspect ratio is investigated by three‐dimensional, time‐dependent numerical solutions and by laboratory experiments using a microscale apparatus and a thermographic visualisation system. Liquid bridges heated from above and from below are investigated. The numerical and experimental results show that for each aspect ratio and for both the heating conditions the onset of the Marangoni oscillatory flow is characterized by the appearance of a standing wave regime; after a certain time, a second transition to a travelling wave regime occurs. The three‐dimensional flow organization at the onset of instability is different according to whether the bridge is heated from above or from below. When the liquid bridge is heated from below, the critical Marangoni number is larger, the critical wave number (m) is smaller and the standing wave regime is more stable, compared with the case of the bridge heated from above. For the critical azimuthal wave number, two correlation laws are found as a function of the geometrical aspect ratio A.