A hierarchical sequential ALE poromechanics model for tire‐soil‐water interaction on fluid‐infiltrated roads

This paper introduces a hierarchical sequential arbitrary Lagrangian‐Eulerian (ALE) model for predicting the tire‐soil‐water interaction at finite deformations. Using the ALE framework, the interaction between a rolling pneumatic tire and the fluid‐infiltrated soil underneath will be captured numerically. The road is assumed to be a fully saturated two‐phase porous medium. The constitutive response of the tire and the solid skeleton of the porous medium is idealized as hyperelastic. Meanwhile, the interaction between tire, soil, and water will be simulated via a hierarchical operator‐split algorithm. A salient feature of the proposed framework is the steady state rolling framework. While the finite element mesh of the soil is fixed to a reference frame and moves with the tire, the solid and fluid constituents of the soil are flowing through the mesh in the ALE model according to the rolling speed of the tire. This treatment leads to an elegant and computationally efficient formulation to investigate the tire‐soil‐water interaction both close to the contact and in the far field. The presented ALE model for tire‐soil‐water interaction provides the essential basis for future applications, for example, to a path‐dependent frictional‐cohesive response of the consolidating soil and unsaturated soil, respectively. Copyright © 2017 John Wiley & Sons, Ltd.     

Application of piece‐wise linear weight functions for 2D 8‐node quadrilateral element in contact problems

The present study is a continuation of our previous work with the aim to reduce problems caused by standard higher order elements in contact problems. The difficulties can be attributed to the inherent property of the Galerkin method which gives uneven distributions of nodal forces resulting in oscillating contact pressures. The proposed remedy is use of piece‐wise linear weight functions. The methods to establish stiffness and/or mass matrix for 8‐node quadrilateral element in 2D are presented, i.e. the condensing and direct procedures. The energy and nodal displacement error norms are also checked to establish the convergence ratio. Interpretation of calculated contact pressures is discussed. Two new 2D 8‐node quadrilateral elements, QUAD8C and QUAD8D, are derived and tested in many examples, which show their good performance in contact problems. Copyright © 2004 John Wiley & Sons, Ltd.     

Combined interior‐point method and semismooth Newton method for frictionless contact problems

In the present paper, a solution scheme is proposed for frictionless contact problems of linear elastic bodies, which are discretized using the finite element method with lower order elements. An approach combining the interior‐point method and the semismooth Newton method is proposed. In this method, an initial active set for the semismooth Newton method is obtained from the approximate optimal solution by the interior‐point method. The simplest node‐to‐node contact model is considered in the present paper, that is, pairs of matching nodes exist on the contact surfaces. However, the discussions can be easily extended to a node‐to‐segment or segment‐to‐segment contact model. In order to evaluate the proposed method, a number of illustrative examples of the frictionless contact problem are shown. The proposed combined method is compared with the interior‐point method and the semismooth Newton method. Two numerical examples that are difficult to solve using the semismooth Newton method are solved effectively using the proposed combined method. It is shown that the proposed method converges within far fewer iterations than the semismooth Newton methods or the interior‐point method. Copyright © 2009 John Wiley & Sons, Ltd.     

An accurate and robust contact detection algorithm for particle‐solid interaction in combined finite‐discrete element analysis

When applying the combined finite‐discrete element method for analysis of dynamic problems, contact is often encountered between the finite elements and discrete elements, and thus an effective contact treatment is essential. In this paper, an accurate and robust contact detection algorithm is proposed to resolve contact problems between spherical particles, which represent rigid discrete elements, and convex quadrilateral mesh facets, which represent finite element boundaries of structural components. Different contact scenarios between particles and mesh facets, or edges, or vertices have been taken into account. For each potential contact pair, the contact search is performed in an hierarchical way starting from mesh facets, possibly going to edges and even further to vertices. The invalid contact pairs can be removed by means of two reasonable priorities defined in terms of geometric primitives and facet identifications. This hierarchical contact searching scheme is effective, and its implementation is straightforward. Numerical examples demonstrated the accuracy and robustness of the proposed algorithm. Copyright © 2015 John Wiley & Sons, Ltd.     

A direct constraint‐Trefftz FEM for analysing elastic contact problems

A direct constraint technique, based on the hybrid‐Trefftz finite element method, is first presented to solve elastic contact problems without friction. For efficiency, static condensation is employed to condense a large model down to a smaller one which involves nodes within the potential contact surfaces only. This model can remarkably reduce computational time and effort. Subsequently, the contact interface equation is constructed by introducing the contact conditions of compatibility and equilibrium. Based on the formulation developed, a general solution strategy, which is applicable to the well‐known three classical situations (receding, conforming and advancing) is developed. Finally, three typical examples related to the three situations mentioned are provided to verify the reliability and applicability of the approach. Copyright © 2005 John Wiley & Sons, Ltd.     

Stress analysis of gear teeth using displacement potential function and finite differences

A new numerical approach has been developed for the analysis of displacements and stresses in arbitrary‐shaped elastic bodies subjected to mixed boundary conditions. An ideal mathematical model, based on the displacement‐potential function, has been used in the finite‐difference solution to investigate the state of stresses at the critical sections of spur gear teeth. Two different types of gear tooth and two different regions of loading are included in the present analysis. The solutions found by the present approach are compared and discussed in the light of available finite‐element results in the literature. Copyright © 2001 John Wiley & Sons, Ltd.     

Self‐contact and fictitious domain using a difference convex approach

A numerical approach of contact or self‐contact of thin structures is performed using a relaxed orientation‐preserving condition inserted in the difference of convex function framework. This method is analyzed on academic examples and cellular media. Copyright © 2007 John Wiley & Sons, Ltd.     

A 3D beam‐to‐beam contact finite element for coupled electric–mechanical fields

In this paper the formulation of an electric–mechanical beam‐to‐beam contact element is presented. Beams with circular cross‐sections are assumed to get in contact in a point‐wise manner and with clean metallic surfaces. The voltage distribution is influenced by the contact mechanics, since the current flow is constricted to small contacting spots. Therefore, the solution is governed by the contacting areas and hence by the contact forces. As a consequence the problem is semi‐coupled with the mechanical field influencing the electric one. The electric–mechanical contact constraints are enforced with the penalty method within the finite element technique. The virtual work equations for the mechanical and electric fields are written and consistently linearized to achieve a good level of computational efficiency with the finite element method. The set of equations is solved with a monolithic approach. Copyright © 2005 John Wiley & Sons, Ltd.     

A particle method for two‐phase flows with large density difference

A new numerical approach for solving incompressible two‐phase flows is presented in the framework of the recently developed Consistent Particle Method (CPM). In the context of the Lagrangian particle formulation, the CPM computes spatial derivatives based on the generalized finite difference scheme and produces good results for single‐phase flow problems. Nevertheless, for two‐phase flows, the method cannot be directly applied near the fluid interface because of the abrupt discontinuity of fluid density resulting in large change in pressure gradient. This problem is resolved by dealing with the pressure gradient normalized by density, leading to a two‐phase CPM of which the original singlephase CPM is a special case. In addition, a new adaptive particle selection scheme is proposed to overcome the problem of ill‐conditioned coefficient matrix of pressure Poisson equation when particles are sparse and non‐uniformly spaced. Numerical examples of Rayleigh–Taylor instability, gravity current flow, water‐air sloshing and dam break are presented to demonstrate the accuracy of the proposed method in wave profile and pressure solution. Copyright © 2015 John Wiley & Sons, Ltd.     

A new finite‐element formulation for electromechanical boundary value problems

In this paper, a new finite‐element formulation for the solution of electromechanical boundary value problems is presented. As opposed to the standard formulation that uses scalar electric potential as nodal variables, this new formulation implements a vector potential from which components of electric displacement are derived. For linear piezoelectric materials with positive definite material moduli, the resulting finite‐element stiffness matrix from the vector potential formulation is also positive definite. If the material is non‐linear in a fashion characteristic of ferroelectric materials, it is demonstrated that a straightforward iterative solution procedure is unstable for the standard scalar potential formulation, but stable for the new vector potential formulation. Finally, the method is used to compute fields around a crack tip in an idealized non‐linear ferroelectric material, and results are compared to an analytical solution. Copyright © 2002 John Wiley & Sons, Ltd.     

A formulation for electrostatic‐mechanical contact and its numerical solution

The progress in advanced technology fields requires more and more sophisticated formulations to consider contact problems properly. This paper is devoted to the development of a new constitutive model for electrostatic‐mechanical contacts, based on a micro–macro approach to describe the contact behaviour. The electric‐mechanical contact constitutive law is obtained considering the real microscopic shape of the contacting surfaces, the microscopic behaviour of force transmission and current flow. Some thermo‐mechanical macroscopic models based on microscopic characterizations have already been developed to compute the normal and tangential contact stiffness and the thermal contact resistance. On the basis of such macroscopic models, a similar model, suitable for the electric‐mechanical field, is developed. With reference to the thermal constriction resistance the electric contact resistance is studied, assuming a flux tube around each contacting asperity, and choosing a suitable geometry for its narrowing at the contact zone. The contact element geometry is based on well known theoretical and experimental micro‐mechanical laws, suitably adapted for the FEM formulation. The macroscopic stiffness matrix is calculated on the basis of the microscopic laws and it is continuously updated as a function of the changes in the mechanical and electric significant parameters. A consistent linearization of the set of equations is developed to improve the computational speed, within the framework of implicit methods. Copyright © 2005 John Wiley & Sons, Ltd.     

Vademecum‐based GFEM (V‐GFEM): optimal enrichment for transient problems

This paper proposes a generalized finite element method based on the use of parametric solutions as enrichment functions. These parametric solutions are precomputed off‐line and stored in memory in the form of a computational vademecum so that they can be used on‐line with negligible cost. This renders a more efficient computational method than traditional finite element methods at performing simulations of processes. One key issue of the proposed method is the efficient computation of the parametric enrichments. These are computed and efficiently stored in memory by employing proper generalized decompositions. Although the presented method can be broadly applied, it is particularly well suited in manufacturing processes involving localized physics that depend on many parameters, such as welding. After introducing the vademecum‐generalized finite element method formulation, we present some numerical examples related to the simulation of thermal models encountered in welding processes. Copyright © 2016 John Wiley & Sons, Ltd.     

hp‐Generalized FEM and crack surface representation for non‐planar 3‐D cracks

A high‐order generalized finite element method (GFEM) for non‐planar three‐dimensional crack surfaces is presented. Discontinuous p‐hierarchical enrichment functions are applied to strongly graded tetrahedral meshes automatically created around crack fronts. The GFEM is able to model a crack arbitrarily located within a finite element (FE) mesh and thus the proposed method allows fully automated fracture analysis using an existing FE discretization without cracks. We also propose a crack surface representation that is independent of the underlying GFEM discretization and controlled only by the physics of the problem. The representation preserves continuity of the crack surface while being able to represent non‐planar, non‐smooth, crack surfaces inside of elements of any size. The proposed representation also provides support for the implementation of accurate, robust, and computationally efficient numerical integration of the weak form over elements cut by the crack surface. Numerical simulations using the proposed GFEM show high convergence rates of extracted stress intensity factors along non‐planar curved crack fronts and the robustness of the method. Copyright © 2008 John Wiley & Sons, Ltd.     

Uniformly convergent non‐standard finite difference methods for singularly perturbed differential‐difference equations with delay and advance

A new class of fitted operator finite difference methods are constructed via non‐standard finite difference methods ((NSFDM)s) for the numerical solution of singularly perturbed differential difference equations having both delay and advance arguments. The main idea behind the construction of our method(s) is to replace the denominator function of the classical second‐order derivative with a positive function derived systematically in such a way that it captures significant properties of the governing differential equation and thus provides the reliable numerical results. Unlike other FOFDMs constructed in standard ways, the methods that we present in this paper are fairly simple to construct (and thus enrich the class of fitted operator methods by adding these new methods). These methods are shown to be ε‐uniformly convergent with order two which is the highest possible order of convergence obtained via any fitted operator method for the problems under consideration. This paper further clarifies several doubts, e.g. why a particular scheme is not suitable for the whole range of values of the associated parameters and what could be the possible remedies. Finally, we provide some numerical examples which illustrate the theoretical findings. Copyright © 2005 John Wiley & Sons, Ltd.     

Analysis of photonic crystals using the hybrid finite‐element/finite‐difference time domain technique based on the discontinuous Galerkin method

Two‐dimensional photonic crystal structures are analyzed by a recently developed hybrid technique combining the finite‐element time‐domain (FETD) method and the finite‐difference time‐domain (FDTD) method. This hybrid FETD/FDTD method uses the discontinuous Galerkin method as framework for domain decomposition. To the best of our knowledge, this is the first hybrid FETD/FDTD method that allows non‐conformal meshes between different FETD and FDTD subdomains. It is also highly parallelizable. These properties are very suitable for the computation of periodic structures with curved surfaces. Numerical examples for the computation of the scattering parameters of two‐dimensional photonic bandgap structures are presented as applications of the hybrid FETD/FDTD method. Numerical results demonstrate the efficiency and accuracy of the proposed hybrid method. Copyright © 2012 John Wiley & Sons, Ltd.     

Hybrid displacement function element method: a simple hybrid‐Trefftz stress element method for analysis of Mindlin–Reissner plate

In order to develop robust finite element models for analysis of thin and moderately thick plates, a simple hybrid displacement function element method is presented. First, the variational functional of complementary energy for Mindlin–Reissner plates is modified to be expressed by a displacement function F, which can be used to derive displacement components satisfying all governing equations. Second, the assumed element resultant force fields, which can satisfy all related governing equations, are derived from the fundamental analytical solutions of F. Third, the displacements and shear strains along each element boundary are determined by the locking‐free formulae based on the Timoshenko's beam theory. Finally, by applying the principle of minimum complementary energy, the element stiffness matrix related to the conventional nodal displacement DOFs is obtained. Because the trial functions of the domain stress approximations a priori satisfy governing equations, this method is consistent with the hybrid‐Trefftz stress element method. As an example, a 4‐node, 12‐DOF quadrilateral plate bending element, HDF‐P4‐11 β, is formulated. Numerical benchmark examples have proved that the new model possesses excellent precision. It is also a shape‐free element that performs very well even when a severely distorted mesh containing concave quadrilateral and degenerated triangular elements is employed. Copyright © 2014 John Wiley & Sons, Ltd.     

Time‐domain Galerkin method for dynamic load identification

This paper proposes a new method called time‐domain Galerkin method (TDGM) for investigating the structural dynamic load identification problems. Firstly, the shape functions are adopted to approximate three parameters, such as the dynamic load, kernel function response, and measured structural response Secondly, defining a residual function could be expressed as the difference of the measured response and the computational response. Thirdly, select an appropriate weighting function to multiply the defined residual function and make integral operation with respect to time to be zero. Finally, when the shape functions are chosen as the weighting function, it establishes the forward model called TDGM. Furthermore, the regularization method could have effectiveness in solving the ill‐posed matrix of load reconstruction and obtaining the accurate identified results of the dynamic load. Compared with the traditional Green kernel function method (GKFM), TDGM can effectively overcome the influences of noise and improve the accuracy of the dynamic load identification. Three numerical examples are provided to demonstrate the correctness and advantages of TDGM. Copyright © 2015 John Wiley & Sons, Ltd.     

Development of a finite element contact analysis algorithm for charged‐hydrated soft tissues with large sliding

This paper focuses on a finite element analysis of contact phenomena with large sliding between charged‐hydrated biological soft tissues, such as articular cartilages, based on the triphasic theory. The impenetrability constraint between the contacting bodies and the continuity of the interstitial fluid and ion phases at the contact surfaces are imposed by applying a Lagrange multiplier approach with the contact pressure, chemical potential of the fluid and electrochemical potentials of ions as Lagrange multipliers. A node‐to‐segment one‐pass approach is adopted to cope with large deformations and sliding between the contact surfaces. To pass the contact patch test, contact boundary integrations are performed on both the master and slave contact surfaces. On the other hand, the degrees of freedom of the multipliers at the master nodes are eliminated by projecting the master nodes onto the slave surface to avoid overconstraint. The effectiveness of the proposed algorithm is verified by a couple of numerical examples, in which continuous distributions of displacement, fluid flow, ionic molar flow and Lagrange multipliers on or across the contact surface are confirmed. Copyright © 2008 John Wiley & Sons, Ltd.