Parameter identification for coupled finite element–boundary element models

To solve problems involving semi-infinite domains, one efficient approach is to use finite elements (FE) to model the regions where detailed information about materials with complicated properties is needed and to use boundary elements (BE) to simulate the semi-infinite parts. In this paper, a parameter identification algorithm is developed for coupled FE–BE models in detail. The algorithm is designed to identify all the material parameters in the FE domain and the BE domain simultaneously. Its validity is illustrated using two examples. The distribution of the observational points is also briefly tested and discussed. The numerical results reveal that this is a stable and fast-converging algorithm.     

3-D boundary element–finite element method for the dynamic analysis of piled buildings

A boundary element–finite element model is presented for the three-dimensional dynamic analysis of piled buildings in the frequency domain. Piles are modelled as compressible Euler–Bernoulli beams founded on a linear, isotropic, viscoelastic, zoned-homogeneous, unbounded layered soil, while multi-storey buildings are assumed to be comprised of vertical compressible piers and rigid slabs. Soil–foundation–structure interaction is rigorously taken into account with an affordable number of degrees of freedom. The code allows the direct analysis of multiple piled buildings, so that the influence of other constructions can be taken into account in the analysis of a certain element. The formulation is outlined before presenting validation results and an application example.     

A Petrov–Galerkin finite element scheme for the regularized long wave equation

A Petrov-Galerkin finite element method (FEM) for the regularized long wave (RLW) equation is proposed. Finite elements are used in both the space and the time domains. Dispersion correction and a highly selective dissipation mechanism are introduced through additional streamline upwind terms in the weight functions. An implicit, conditionally stable, one-step predictor–corrector time integration scheme results. The accuracy and stability are investigated by means of local expansion by Taylor series and the resulting equivalent differential equation. An analysis based on a linear Fourier series solution and the Von Neumanns stability criterion is also performed. Based on the order of the analytical approximations and of the domain discretization it is concluded that the scheme is of third order in the nonlinear version and of fourth order in the linear version. Three numerical experiments of wave propagation are presented and their results compared with similar ones in the literature: solitary wave propagation, undular bore propagation, and cnoidal wave propagation. It is concluded that the present scheme possesses superior conservation and accuracy properties.This work has been partially supported by the Fundação para a Ciência e Tecnologia, under project POCTI/ECM/41800/2001.     

A Pian–Sumihara type element for modeling shear bands at finite deformation

A monolithic numerical solution of a partial differential equation (PDE) model for shear bands, which includes a thermal softening rate dependent plastic flow rule and finite thermal conductivity, is presented. The formulation accounts for large deformation kinematics and includes incrementally objective treatment of the hypoplastic constitutive relations. Regularization is achieved by including finite thermal conductivity, which informs the PDE system of a length scale, governed by competition between shear heating and thermal diffusion. The monolithic solution scheme is then used to eliminate splitting errors during the solution of the discretized system. The scheme is presented in a general, mixed formulation, which allows for many choices of shape functions. We study and compare two elements, which have been implemented with the monolithic nonlinear solver: the Irreducible Shear Band Quad (ISBQ) and the Pian Sumihara Shear Band Quad (PSSBQ). ISBQ employs the same interpolation as an irreducible four node quad while PSSBQ is a mixed, assumed stress element. The algorithmic approximations to the Lie derivative and Jaumann rate of Kirchhoff stress are available in the literature for ISBQ type elements, and are derived in this paper for the PSSBQ. These expressions are used to achieve an incrementally objective formulation. It is found that the PSSBQ converges faster than the ISBQ with mesh refinement, and that the convergence of the ISBQ can be improved with a remeshing procedure.     

3D mass-redistributed finite element method in structural–acoustic interaction problems

A 2D mass-redistributed finite element method (MR-FEM) for pure acoustic problems was recently proposed to reduce the dispersion error. In this paper, the 3D MR-FEM is further developed to solve more complicated structural–acoustic interaction problems. The smoothed Galerkin weak form is adopted to formulate the discretized equations for the structure, and MR-FEM is applied in acoustic domain. The global equations of structural–acoustic interaction problems are then established by coupling the MR-FEM for the acoustic domain and the edge-based smoothed finite element method for the structure. The perfect balance between the mass matrix and stiffness matrix is able to improve the accuracy of the acoustic domain significantly. The gradient smoothing technique used in the structural domain can provide a proper softening effect to the “overly-stiff” FEM model. A number of numerical examples have demonstrated the effectiveness of the mass-redistributed method with smoothed strain.     

Efficient parallel algorithms for elastic–plastic finite element analysis

This paper presents our new development of parallel finite element algorithms for elastic–plastic problems. The proposed method is based on dividing the original structure under consideration into a number of substructures which are treated as isolated finite element models via the interface conditions. Throughout the analysis, each processor stores only the information relevant to its substructure and generates the local stiffness matrix. A parallel substructure oriented preconditioned conjugate gradient method, which is combined with MR smoothing and diagonal storage scheme are employed to solve linear systems of equations. After having obtained the displacements of the problem under consideration, a substepping scheme is used to integrate elastic–plastic stress–strain relations. The procedure outlined controls the error of the computed stress by choosing each substep size automatically according to a prescribed tolerance. The combination of these algorithms shows a good speedup when increasing the number of processors and the effective solution of 3D elastic–plastic problems whose size is much too large for a single workstation becomes possible.     

A 3-D six-noded finite element containing a λ singularity

A three-dimensional six-noded prism (wedge) finite element containing a singularity of order is developed. The interpolation functions of the displacement allow for variations proportional to the power of the distance from the crack front along the crack surface and to the distance in the perpendicular direction. The element is compatible with standard wedge (6-noded) and brick (8-noded) isoparametric elements. Three problems are studied to examine the proposed element, namely, a penny-shaped crack in a cylinder, an edge crack in an homogeneous material, and a crack perpendicular to a bimaterial interface.     

A gradient recovery–based adaptive finite element method for convection-diffusion-reaction equations on surfaces

In this paper, we present an adaptive mesh refinement method for solving convection-diffusion-reaction equations on surfaces, which is a fundamental subproblem in many models for simulating the transport of substances on biological films and solid surfaces. The method considered is a combination of well-known techniques: the surface finite element method, streamline diffusion stabilization, and the gradient recovery–based Zienkiewicz-Zhu error estimator. The streamline diffusion method overcomes the instability issue of the finite element method for the dominance of the convection. The gradient recovery–based adaptive mesh refinement strategy enables the method to provide high-resolution numerical solutions by relatively fewer degrees of freedom. Moreover, the implementation detail of a surface mesh refinement technique is presented. Various numerical examples, including the convection-dominated diffusion problems with large variations of solutions, nearly singular solutions, discontinuous sources, and internal layers on surfaces, are presented to demonstrate the efficacy and accuracy of the proposed method.     

A three dimensional immersed smoothed finite element method (3D IS-FEM) for fluid–structure interaction problems

A three-dimensional immersed smoothed finite element method (3D IS-FEM) using four-node tetrahedral element is proposed to solve 3D fluid–structure interaction (FSI) problems. The 3D IS-FEM is able to determine accurately the physical deformation of the nonlinear solids placed within the incompressible viscous fluid governed by Navier-Stokes equations. The method employs the semi-implicit characteristic-based split scheme to solve the fluid flows and smoothed finite element methods to calculate the transient dynamics responses of the nonlinear solids based on explicit time integration. To impose the FSI conditions, a novel, effective and sufficiently general technique via simple linear interpolation is presented based on Lagrangian fictitious fluid meshes coinciding with the moving and deforming solid meshes. In the comparisons to the referenced works including experiments, it is clear that the proposed 3D IS-FEM ensures stability of the scheme with the second order spatial convergence property; and the IS-FEM is fairly independent of a wide range of mesh size ratio.     

Mechanical property analysis of kenaf–glass fibre reinforced polymer composites using finite element analysis

Nowadays, natural fibres are used as a reinforcing material in polymer composites, owing to severe environmental concerns. Among many different types of natural resources, kenaf plants have been extensively exploited over the past few years. In this experimental study, partially eco-friendly hybrid composites were fabricated by using kenaf and glass fibres with two different fibre orientations of 0° and 90°. The mechanical properties such as tensile, flexural and impact strengths of these composites have been evaluated. From the experiment, it was observed that the composites with the 0° fibre orientation can withstand the maximum tensile strength of 49.27 MPa, flexural strength of 164.35 MPa, and impact strength of 6 J. Whereas, the composites with the 90° fibre orientation hold the maximum tensile strength of 69.86 MPa, flexural strength of 162.566 MPa and impact strength of 6.66 J. The finite element analysis was carried out to analyse the elastic behaviour of the composites and to predict the mechanical properties by using NX Nastran 9.0 software. The experimental results were compared with the predicted values and a high correlation between the results was observed. The morphology of the fractured surfaces of the composites was analysed using a scanning electron microscopy analysis. The results indicated that the properties were in the increasing trend and comparable with pure synthetic fibre reinforced composites, which shows the potential for hybridization of kenaf fibre with glass fibre.     

The combined finite–discrete element method for structural failure and collapse

A combined finite–discrete element model for failure and collapse of structural systems comprising of reinforced concrete beam or column type structural members has been developed and implemented into a combined finite–discrete element code. The results obtained using the proposed model compare well with analytical and experimental results. In addition the rotational capacities obtained are in good agreement with published experimental results.     

Adaptive meshless local maximum-entropy finite element method for convection–diffusion problems

In this paper, a meshless local maximum-entropy finite element method (LME-FEM) is proposed to solve 1D Poisson equation and steady state convection–diffusion problems at various Peclet numbers in both 1D and 2D. By using local maximum-entropy (LME) approximation scheme to construct the element shape functions in the formulation of finite element method (FEM), additional nodes can be introduced within element without any mesh refinement to increase the accuracy of numerical approximation of unknown function, which procedure is similar to conventional p-refinement but without increasing the element connectivity to avoid the high conditioning matrix. The resulted LME-FEM preserves several significant characteristics of conventional FEM such as Kronecker-delta property on element vertices, partition of unity of shape function and exact reproduction of constant and linear functions. Furthermore, according to the essential properties of LME approximation scheme, nodes can be introduced in an arbitrary way and the $C^0$ continuity of the shape function along element edge is kept at the same time. No transition element is needed to connect elements of different orders. The property of arbitrary local refinement makes LME-FEM be a numerical method that can adaptively solve the numerical solutions of various problems where troublesome local mesh refinement is in general necessary to obtain reasonable solutions. Several numerical examples with dramatically varying solutions are presented to test the capability of the current method. The numerical results show that LME-FEM can obtain much better and stable solutions than conventional FEM with linear element.     

A continuum eight‐parameter shell finite element for large deformation analysis

Abstract

In this paper, a finite element formulation, using eight independent parameters and high‐order spectral/hp functions, for nonlinear analysis is presented. This formulation allows the use of a third‐order thickness stretch kinematics, which also avoids Poisson's locking. Full nonlinear terms up to quadratic in the Green–Lagrange strain tensorare retained. Several nontrivial problems are solved using the presented formulation. A comparison between this formulation and others found in the literature,and with shell and solid elements in commercial codes ABAQUS and ANSYS are presented and the differences are brought out.     

Modelling multiple cohesive crack propagation using a finite element–scaled boundary finite element coupled method

This paper presents an extension of the recently-developed finite element–scaled boundary finite element (FEM–SBFEM) coupled method to model multiple crack propagation in concrete. The concrete bulk and fracture process zones are modelled using SBFEM and nonlinear cohesive interface finite elements (CIEs), respectively. The CIEs are automatically inserted into the SBFEM mesh as the cracks propagate. The algorithm previously devised for single crack propagation is augmented to model problems with multiple cracks and to allow cracks to initiate in an un-cracked SBFEM mesh. It also addresses crack propagation from one subdomain into another, as a result of partitioning a coarse SBFEM mesh, required for some mixed–mode problems. Each crack in the SBFEM mesh propagates when the sign of the Mode-I stress intensity factor at the crack tip turns positive from negative. Its propagation angle is determined using linear elastic fracture mechanics criteria. Three concrete beams involving multiple crack propagation are modelled. The predicted crack propagation patterns and load–displacement curves are in good agreement with data reported in literature.     

3D-assembled graphene–LiFePO4 frameworks with enhanced electrochemical performance

In the on-going development of power sources and energy-storage devices, achieving both high power and large energy capacity with a high discharge rate is still a great challenge. In this paper, three dimension assembled graphene–LiFePO₄ (G–LFP) composites were prepared by one-step hydrothermal method. LiFePO₄ (LFP) particles became smaller and were dispersed uniformly on the graphene sheets after compositing with graphene. Compared to the pristine LFP, the electrochemical properties of the G–LFP are greatly improved, especially the rate capability and the cyclic performance. At 10 C, the G–LFP holds nearly 80 % of the initial capacity and has a flat voltage platform, while for the LFP, its capacity drops down to 65 % and its voltage platform is not noticeable. After 600 cycles at 10 C, the specific capacity of the G–LFP decreases from 135 to 125 mA hg^?1 with a capacity loss of 5.1 %, while it drops from 105  to 86  mA hg^?1 with a capacity loss of 30 % for the LFP. The reason for the improvement of the electrochemical performances could be ascribed to the introduction of graphene which enhances the conductivity and diminishes the LFP size which improves the diffusion of lithium ions.     

Evaluation of a simple finite element method for the calculation of effective electrical conductivity of compression moulded polymer–graphite composites

Finite element (FE) techniques can be used for the calculation of the effective properties of random heterogeneous materials, the required input simply consisting of phase properties and representative three-dimensional models of material microstructure. This approach has been widely exploited in recent years, although limited by the considerable amount of computational power required to obtain statistically accurate results. By using simple microstructural models of compression moulded polymer–graphite composites and a FE code modified for execution on graphical processing units, we show that reliable predictions of electrical properties for these materials can now be obtained in a reasonable computational time and with acceptable accuracy and precision. By using an approach based on design of experiments, we also perform a set of simulations aimed at determining the microstructural details which are most significant for the effective properties of these materials.