Plane elasticity problem for a multi-wedge system with a thin wedge

The paper presents a method for studying a system of elastic wedges containing a thin wedge with the angle Θ₀, which may be arbitrary small. An analysis shows that the considered problem, involving 2-D vectors of tractions and displacements, cannot be solved by straight-forward extension of the method previously worked out by the authors for analogous scalar problems. The difficulty arises because of the disclosed feature of the dependences between the Mellin transformed displacements and tractions at the boundaries of a thin wedge: they are linearly dependent when their Taylor’s expansions in Θ₀ are represented by the first terms only. The difficulty is removed by using the consequences of the linear dependence and by an appropriate re-arrangement of variables. Then simple physical models, simulating the influence of a thin wedge on a multi-wedge system, become available. The models cover the cases of a very rigid and very compliant thin wedge and also intermediate cases. The ranges of the models applicability are studied analytically and illustrated by numerical results.     

Numerical method and models for anti-plane strain of a system with a thin elastic wedge

The paper presents a general method to find asymptotics for a (multi-)wedge system containing a thin wedge. It employs separation of the symmetric and anti-symmetric parts of the boundary displacements and tractions of the wedge. The method is applicable when the angle of the thin wedge turns to zero. A physical interpretation of the derived equations is obtained by using power expansions of non-polynomial functions, which appear after the Mellin transform. We establish that the first term in the expansion of the symmetric part corresponds to shear, while the first term of the anti-symmetric part describes deflection of the wedge axis. Numerical experiments, performed by using a code developed on the basis of the theory, show that using only the first terms of the expansions insignificantly influence accuracy: the approximate results coincide with the exact values of roots to the third significant digit even for the wedge angle of 30°.     

混凝土楔入劈拉和三点弯曲断裂过程的细观数值模拟Mesoscale simulation on fracture process of wedge splitting and three-point bending of concrete

基于离散元思想和Voronoi单元划分技术,利用混凝土细观刚体弹簧元模型,开展了混凝土楔入劈拉试件和三点弯曲切口梁的断裂过程数值仿真分析。从裂缝开展过程、试件破坏形态、荷载-张口位移曲线(P-CMOD)和断裂能等方面,将数值分析结果与已有的试验结果进行了对比。结果表明,细观刚体弹簧元法较准确地模拟了混凝土楔入劈拉试件和三点弯曲切口梁断裂过程。最后,分析了缝高比和骨料体积含量对混凝土断裂过程的影响规律,发现断裂能随骨料体积含量呈单调递增趋势。     

An evaluation of force terms in the lattice Boltzmann models in simulating shallow water flows over complex topography

Proper approximation of the force terms, especially the bed slope term, is of crucial importance to simulating shallow water flows in lattice Boltzmann (LB) models. However, there is little discussion on the schemes of adding force terms to LB models for shallow water equations (SWEs). In this study, we evaluate the performance of forcing schemes coupled with different LB models (LABSWE and MLBSWE) in simulating shallow water flows over complex topography and try to find out their intrinsic characteristics and applicability. Three cases are adopted for evaluation, including a stationary case, a one-dimensional tidal wave flow over an irregular bed, and a steady flow over a two-dimensional seamount. The simulating results are compared with analytical solutions or the results produced by the finite difference method. For LABSWE, all the forcing schemes, except for the weighting factor method, fail to produce accurate solutions for the test cases; this is probably due to the mismatch between the bed slope term in source terms and the quadratic depth term of the equilibrium distribution functions in these forcing schemes. For MLBSWE, all the forcing schemes are capable of simulating flows over the complex topography accurately; furthermore, those schemes taking into account the collision effect τ to eliminate the momentum induced by forces provide more accurate solutions with quicker convergence as the lattice size decreases. In this view, MLBSWE can bring more flexibility in treating the force terms and thus can be a better tool to simulate shallow water flows over complex topography in practical application.     

混凝土楔入劈拉和三点弯曲断裂过程的细观数值模拟

基于离散元思想和Voronoi单元划分技术,利用混凝土细观刚体弹簧元模型,开展了混凝土楔入劈拉试件和三点弯曲切口梁的断裂过程数值仿真分析。从裂缝开展过程、试件破坏形态、荷载-张口位移曲线(P-CMOD)和断裂能等方面,将数值分析结果与已有的试验结果进行了对比。结果表明,细观刚体弹簧元法较准确地模拟了混凝土楔入劈拉试件和三点弯曲切口梁断裂过程。最后,分析了缝高比和骨料体积含量对混凝土断裂过程的影响规律,发现断裂能随骨料体积含量呈单调递增趋势。     

Comparative study of an interface crack for different wedge-interface models

Summary  An interface crack problem is investigated under various assumptions on an interface between two elastic materials. The interface is modeled by an additional third structure (thin elastic wedge of differing elastic properties) matching the bonded materials, or by introducing special boundary conditions on the crack line ahead. The main emphasis of the paper is placed on a comparison of the asymptotic expansion of the elastic solutions near the crack tip obtained for the different models. In particular, the behaviour of the stress singularity exponent and the generalized SIF are discussed. Numerical examples are presented. Received 16 August 2000; accepted for publication 26 May 2001     

Influence of non-proportional loading on ratcheting responses and simulations by two recent cyclic plasticity models

Aubin and her coworkers conducted a unique set of experiments demonstrating the influence of loading non-proportionality on ratcheting responses of duplex stainless steel. In order to further explore their new observation, a set of experiments was conducted on stainless steel (SS) 304L under various biaxial stress-controlled non-proportional histories. This new set of data reiterated Aubin and her coworkers’ observation and illustrated many new responses critical to model development and validation. Two recent and different classes of cyclic plasticity models, the modified Chaboche model proposed by Bari and Hassan and the version of the multi-mechanism model proposed by Taleb and Cailletaud, are evaluated in terms of their simulations of the SS304L non-proportional ratcheting responses. A modeling scheme for non-proportional ratcheting responses using the kinematic hardening rule parameters in addition to the conventionally used isotropic hardening rule parameter (yield surface size change) in the modified Chaboche model is evaluated. Strengths and weaknesses of the models in simulating the non-proportional ratcheting responses are identified. Further improvements of these models needed for improving the non-proportional ratcheting simulations are suggested in the paper.     

Numerical simulation of landslide impulsive waves by incompressible smoothed particle hydrodynamics

An incompressible‐smoothed particle hydrodynamics (I‐SPH) formulation is presented to simulate impulsive waves generated by landslides. The governing equations, Navier–Stokes equations, are solved in a Lagrangian form using a two‐step fractional method. Landslides in this paper are simulated by a submerged mass sliding along an inclined plane. During sliding, both rigid and deformable landslides mass are considered. The present numerical method is examined for a rigid wedge sliding into water along an inclined plane. In addition solitary wave generated by a heavy box falling inside water, known as Scott Russell wave generator, which is an example for simulating falling rock avalanche into artificial and natural reservoirs, is simulated and compared with experimental results. The numerical model is also validated for gravel mass sliding along an inclined plane. The sliding mass approximately behaves like a non‐Newtonian fluid. A rheological model, implemented as a combination of the Bingham and the general Cross models, is utilized for simulation of the landslide behaviour. In order to match the experimental data with the computed wave profiles generated by deformable landslides, parameters of the rheological model are adjusted and the numerical model results effectively match the experimental results. The results prove the efficiency and applicability of the I‐SPH method for simulation of these kinds of complex free surface problems. Copyright © 2007 John Wiley & Sons, Ltd.     

Process of selective laser sintering of polymer powders: Modeling,simulation, and validation

Selective laser sintering (SLS) of polymer powders involves multiphysical transient phenomena. A numerical tool for simulating such a process is developed on the basis of the reliable modeling of the corresponding thermo-physical transient phenomena and appropriate numerical methods. The present paper addresses modeling, simulation, and validation aspects that are indispensable for studying and optimizing SLS process. The coupled multiphysical models are detailed, and the numerical tool based on the finite volume method is presented, with validations in terms of numerical and physical accuracy, by considering the shrinkage involved in the process and the successive layers deposition. A parametric analysis is finally proposed in order to test the reliability of the model in terms of representing real physical phenomena and thermal history experienced by the material during the process.     

Developing a unified FVE‐ALE approach to solve unsteady fluid flow with moving boundaries

In this study, an arbitrary Lagrangian–Eulerian (ALE) approach is incorporated with a mixed finite‐volume–element (FVE) method to establish a novel moving boundary method for simulating unsteady incompressible flow on non‐stationary meshes. The method collects the advantages of both finite‐volume and finite‐element (FE) methods as well as the ALE approach in a unified algorithm. In this regard, the convection terms are treated at the cell faces using a physical‐influence upwinding scheme, while the diffusion terms are treated using bilinear FE shape functions. On the other hand, the performance of ALE approach is improved by using the Laplace method to improve the hybrid grids, involving triangular and quadrilateral elements, either partially or entirely. The use of hybrid FE grids facilitates this achievement. To show the robustness of the unified algorithm, we examine both the first‐ and the second‐order temporal stencils. The accuracy and performance of the extended method are evaluated via simulating the unsteady flow fields around a fixed cylinder, a transversely oscillating cylinder, and in a channel with an indented wall. The numerical results presented demonstrate significant accuracy benefits for the new hybrid method on coarse meshes and where large time steps are taken. Of importance, the current method yields the second‐order temporal accuracy when the second‐order stencil is used to discretize the unsteady terms. Copyright © 2009 John Wiley & Sons, Ltd.     

On the derivation of structural models with general thermomechanical prestress

The vibrating behaviour of thin structures is affected by prestress states. Hence, the effects of thermal prestress are important research subjects in view of ambient vibration monitoring of civil structures. The interaction between prestress, geometrically non-linear behaviour, as well as damping and its coupling with the aforementioned phenomena has to be taken into account for a comprehensive understanding of the structural behaviour. Since the literature on this subject lacks a clear procedure to derive models of thin prestressed and damped structures from 3D continuum mechanics, this paper presents a new derivation of models for thin structures accounting for generic prestress, moderate rotations and viscous damping. Although inspired by classical approaches, the proposed procedure is quite different, because of (i) the definition of a modified Hu–Washizu (H-W) functional, accounting for stress constraints associated with Lagrange multipliers, in order to derive lower-dimensional models in a convenient way; (ii) an original definition of a (mechanical and thermal) strain measure and a rotation measure enabling one to identify the main terms in the strain energy and to derive a cascade of lower-dimensional models (iii) a new definition of “strain–rotation domains” providing a clear interpretation of the classical assumptions of “small perturbations” and “small strains and moderate rotations”; (iv) the introduction of a pseudo-potential with stress constraints to account for viscous damping. The proposed procedure is applied to thin beams.     

Simulation of liquid–vapour phase transitions and multiphase flows by an improved lattice Boltzmann model

An improved lattice Boltzmann (LB) model with a new scheme for the interparticle interaction force term is proposed in this paper. Based on the improved LB model, the equation-free method is implemented for simulating liquid–vapour phase change and multiphase flows. The details of phase separation are presented by numerical simulation results in terms of coexistence curves and spurious currents. Compared with existing models, the proposed model can give more accurate results in a wider temperature range with the spurious currents reduced and less time consumed. Characteristics of phase separation can be quickly and accurately reflected by the proposed method. Then, the contact angle of the solid surface is numerically investigated based on the proposed model. The proposed model is valid for steady flow with near zero velocity; unsteady cases will be investigated in further studies. This work will be helpful for our long-term aim of multi-scale modelling of convective boiling.     

The Solution Asymptotics of Classical and Nonclassical, Static and Dynamic Boundary-Value Problems for Thin Bodies

An asymptotic method for solution of classical and nonclassical boundary-value problems of the theory of elasticity for thin bodies (beams, rods, plates, and shells) is expounded. Studies on the asymptotic theory of thin bodies are reviewed. Asymptotic results are compared with those obtained by other applied theories. The asymptotic approach has been found out to be related to Saint Venant's principle. The correctness of this principle is mathematically proved for one class of problems. A fundamentally new asymptotics in the components of the stress tensor and the displacement vector is revealed in considering new classes of problems. On their basis, the applicability domains are outlined for various models of understructures. Solutions are obtained to certain classes of dynamic problems for thin bodies, particularly, those simulating seismic effects. The resonance conditions are established and ways of preventing them are pointed out.     

Extension of the volume-of-fluid method for analysis of free surface viscous flow in an ideal gas

The volume-of-fluid (VOF) method is a simple and robust technique for simulating free surface flows with large deformations and intersecting free surfaces. Earlier implementations used Laplace's formula for the normal stress boundary condition at the interface between the liquid and vapour phases. We have expanded the interfacial boundary conditions to include the viscous component of the normal stress in the liquid phase and, in a limited manner, to allow the pressure in the vapour phase to vary. Included are sample computations that show the accuracy of added third-order-accurate differencing schemes for the convective terms in the Navier-Stokes equation (NSE), the viscous terms in the normal stress at the interface and the solution of potential flow in the vapour phase coupled with the solution of the NSE in the liquid phase. With these modifications we show that the VOF method can accurately predict the instability of a thin viscous sheet flowing through a stagnant vapour phase.     

The method of partial discretization in free vibration problems of circular plates with variable distribution of parameters

This paper presents the results of applying the partial discretization method to study thin circular plates of varying thickness carrying concentrated inclusions. In this method, the plate with distributed or discrete-distributed mass is reduced to a discrete K-step degree system with the same rigidity function as that of the original plate. The most important task in this method is to form the influence matrix using Cauchy’s influence function. This matrix is further used to obtain a few first terms of the characteristic series in the frequency parameter. The use of this method together with Bernstein’s double estimators and the first three terms retained in the characteristic series reveals its rapid convergence to the exact solutions obtained by Conway and other authors. This demonstrates the rationality and efficiency of the method Published in Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 135–144, March 2006.     

Motion of a hot wedge in a melting medium

In [1–3] a series of problems of the motion of heat sources at a temperature higher than the melting point of the surrounding medium was considered. The heat source could be a laser beam or a hot body. Here, the case of a thin wedge heated to a temperature higher than the melting point of the surrounding medium and moving at a constant velocity is investigated. The velocity is high enough for the molten layer formed to be thin. The problem is solved by the method of integral relations. The shape of the molten zone, the drag on the wedge and other flow characteristics of the melt are determined. Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 52–57, September–October, 1988.     

A new analytical model for pressure estimation of symmetrical water impact of a rigid wedge at variable velocities

In this paper we present an analytical solution to symmetrical water impact problems of a two-dimensional wedge. Unlike previous studies, we have taken into account the effect of velocity reduction of the solid body upon impact in order to determine impact pressure as well as the overall force acting on the body. This feature of our study provides a better estimate of the transitory nature of the phenomenon and leads to a more precise evaluation of the true dynamic load borne by the body. We obtained the solution to this problem through a generalization of the Wagner formulation and the use of an existing analytical prediction model of the entry velocity of the wedge. This approach allows us to obtain an original analytical equation for pressure in terms of the kinetics and geometrical parameters of the impact. The validity of the proposed model is demonstrated by a favourable comparison between the analytical results and the physical experiments carried out on several wedge models.     

Anatomy of coupled constitutive models for ratcheting simulation

This paper critically evaluates the performance of five constitutive models in predicting ratcheting responses of carbon steel for a broad set of uniaxial and biaxial loading histories. The models proposed by Prager, Armstrong and Frederick, Chaboche, Ohno-Wang and Guionnet are examined. Reasons for success and failure in simulating ratcheting by these models are elaborated. The bilinear Prager and the nonlinear Armstrong-Frederick models are found to be inadequate in simulating ratcheting responses. The Chaboche and Ohno-Wang models perform quite well in predicting uniaxial ratcheting responses; however, they consistently overpredict the biaxial ratcheting responses. The Guionnet model simulates one set of biaxial ratcheting responses very well, but fails to simulate uniaxial and other biaxial ratcheting responses. Similar to many earlier studies, this study also indicates a strong influence of the kinematic hardening rule or backstress direction on multiaxial ratcheting simulation. Incorporation of parameters dependent on multiaxial ratcheting responses, while dormant for uniaxial responses, into Chaboche-type kinematic hardening rules may be conducive to improve their multiaxial ratcheting simulations. The uncoupling of the kinematic hardening rule from the plastic modulus calculation is another potentially viable alternative. The best option to achieve a robust model for ratcheting simulations seems to be the incorporation of yield surface shape change (formative hardening) in the cyclic plasticity model.     

On a modified Monte-Carlo method and variable soft sphere model for rarefied binary gas mixture flow simulation

The effect of new terms in the improved algorithm, the modified direct simulation Monte-Carlo (MDSMC) method, is investigated by simulating a rarefied binary gas mixture flow inside a rotating cylinder. Dalton law for the partial pressures contributed by each species of the binary gas mixture is incorporated into our simulation using the MDSMC method and the direct simulation Monte-Carlo (DSMC) method. Moreover, the effect of the exponent of the cosine of deflection angle (α) in the inter-molecular collision models, the variable soft sphere (VSS) and the variable hard sphere (VHS), is investigated in our simulation. The improvement of the results of simulation is pronounced using the MDSMC method when compared with the results of the DSMC method. The results of simulation using the VSS model show some improvements on the result of simulation for the mixture temperature at radial distances close to the cylinder wall where the temperature reaches the maximum value when compared with the results using the VHS model.     

The hybrid control of vibration of thin plate with active constrained damping layer

This paper concerns in the active and passive hybrid control of vibration of the thin plate with Local Active Constrained damping Layer (LACL). The governing equations of system are formulated based on the constitutive equations of elastic, viscoelastic, piezoelectric materials. Galerkin method and GHM method are employed to transform partial differential equations into ordinary ones with a lower dimension. LQR method of classical control theory is used in simulating calculation. Numeral results show that the active and passive hybrid control manner obtained in this paper is a better one for vibration control of the plate. Project supported by the National Science Foundation of China (19632001) and the Research Foundation of Xian Jiaotong University