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.     

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.     

Meshless local Petrov–Galerkin (MLPG) method in combination with finite element and boundary element approaches

The meshless local Petrov–Galerkin (MLPG) method is an effective truly meshless method for solving partial differential equations using moving least squares (MLS) interpolants. It is, however, computationally expensive for some problems. A coupled MLPG/finite element (FE) method and a coupled MLPG/boundary element (BE) method are proposed in this paper to improve the solution efficiency. A procedure is developed for the coupled MLPG/FE method and the coupled MLPG/BE method so that the continuity and compatibility are preserved on the interface of the two domains where the MLPG and FE or BE methods are applied. The validity and efficiency of the MLPG/FE and MLPG/BE methods are demonstrated through a number of examples. Received 6 June 2000     

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.     

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.     

Baseline rolling resistance for tires’ on-road fuel efficiency using finite element modeling

Calculation of truck tires rolling resistance, using the finite element method and considering variables such as incompressible visco-hyperelastic rubber materials, accurate tire geometry and steady temperature distribution, is presented. The model was validated using experimentally measured contact area and contact stresses. Rolling resistance was calculated for three values of axle load, tire inflation pressure, temperature and speed. In addition, regression analysis was used to propose a mathematical expression for predicting rolling resistance as a function of the considered variables. Finally, the contribution of tire’s rubber components to the internal energy was quantified, and it was found that sidewall and subtread were the most relevant. The results of this study will help differentiate the contribution of pavement parameters, such as mean profile depth and international roughness index, to fuel efficiency.     

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.     

Development of a scalable finite element solution to the Navier–Stokes equations

A scalable numerical model to solve the unsteady incompressible Navier–Stokes equations is developed using the Galerkin finite element method. The coupled equations are decoupled by the fractional-step method and the systems of equations are inverted by the Krylov subspace iterations. The data structure makes use of a domain decomposition of which each processor stores the parameters in its subdomain, while the linear equations solvers and matrices constructions are parallelized by a data parallel approach. The accuracy of the model is tested by modeling laminar flow inside a two-dimensional square lid-driven cavity for Reynolds numbers at 1,000 as well as three-dimensional turbulent plane and wavy Couette flow and heat transfer at high Reynolds numbers. The parallel performance of the code is assessed by measuring the CPU time taken on an IBM SP2 supercomputer. The speed up factor and parallel efficiency show a satisfactory computational performance.The authors wish to acknowledge Mr. W. K. Kwan of The University of Hong Kong for his help in using the IBM SP2 supercomputer.     

Experimental and finite element analysis of ultrasonic vibration−assisted continuous-wave laser surface drilling

In pulsed laser drilling with co-axial assisted gas, material removal mechanism (surface vaporization and melt expulsion) determines the machining/drilling rate and quality of the drilled holes. Incomplete melt expulsion is one of the major causes of laser drilling defects. To improve the drilling efficiency and quality of holes, a novel ultrasonic vibration?assisted continuous-wave laser drilling (UVLD) approach is proposed. The application of ultrasonic vibrations (of frequency of 20?kHz and vibration displacement of 23?µm) during laser surface melting facilitates the melt expulsion in the form of sideways melt flow and droplet ejection from the drilling front. A systematic experimental study on the ultrasonic vibration-assisted laser drilling of AISI 316 stainless steel is performed to investigate the effect of working distance on the geometric features and surface quality of the holes. The experimental results based on high-speed photography indicate that the melt expulsion under the influence of ultrasonic vibrations initiates after the laser melted pool reaches a critical size/volume. Based on this underlying mechanism, a simplified finite element analysis is performed for the UVLD process to predict the hole volumes for the investigated working distances.     

A finite element computational framework for enhanced photostrictive performance in 0–3 composites

Photostriction is a multiphysics phenomenon comprising of both photovoltaic effect and converse piezoelectric effect. The extensively researched photostrictive material is lead lanthanum zirconate titanate, i.e., Pb_0.92La_0.08(Zr_0.65Ti_0.35)_0.98O₃ (PLZT) ceramic. In contrast to the traditional approaches of improving deflection response, the current study proposes a 0–3 composite model to substantially enhance the effective material properties, which in turn significantly improves the deflection response. A computational framework based on finite element analysis is employed to 0–3 photostrictive composite of PLZT as matrix and Pb(Mg_1/3Nb_2/3)O₃-0.35PbTiO₃ (PMN-35PT) as the inclusions. The representative volume element (RVE) or unit cell technique is used to incorporate the local variation of constituent properties and to calculate photostrictive properties such as effective elastic, dielectric, piezoelectric, and pyroelectric properties. An opto-electro-thermo-mechanical finite element formulation was engaged to get the actuation response of photostrictive material bonded to cantilever and simply supported beam. The maximum deflection for cantilever beam attached to photostrictive composite patch having 25% inclusions volume fraction in 0–3 composite is found to be 38% more in comparison to pure PLZT material. It is established that the opto-electro-mechanical 0–3 composite actuators possess high potential in lightweight, compact and wireless actuation applications.

     

Hybrid molecular dynamics–finite element simulations of the elastic behavior of polycrystalline graphene

In this paper, we develop an efficient multiscale molecular dynamics (MD)–finite element (FE) modeling scheme capable of determining the elastic and fracture properties of polycrystalline graphene. The local elastic properties of a grain boundary (GB) connecting two adjacent graphene grains, with different lattice orientations, were first determined using MD simulations. In a two-dimensional medium, randomly distributed grains connected with GBs were then created using the Voronoi tessellation method. The constructed Voronoi diagrams were used to create FE models of the polycrystalline graphene, where the GBs were represented by interphase regions with their local properties determined using MD. The grains were modeled as pristine graphene and the accuracy of the polycrystalline FE model was validated with MD simulations of a geometrically identical polycrystalline graphene. The results reveal good agreement between MD and FE simulations. They further show that the elastic and fracture properties of polycrystalline graphene are greatly influenced by the grain size and the misorientation angle. They also indicate that the predicted elastic properties are in agreement with earlier reported experimental and MD results. We believe that this newly proposed multiscale scheme could be easily integrated into current design software to model graphene based nano- and micro-devices.     

Fracture analysis of epoxy/SWCNT nanocomposite based on global–local finite element model

A global–local multiscale finite element method (FEM) is proposed to study the interaction of nanotubes and matrix at the nanoscale near a crack tip. A 3D FE model of a representative volume element (RVE) in crack tip is built. The effects of the length and chirality of single walled carbon nanotube (SWCNT) in a polymer matrix on the fracture behavior were studied in the presence of van der Waals (vdW) interaction as inter-phase region. Detailed results show that with increasing the weight percentage of SWCNT, fracture toughness improves. Three situations of nanotube directions with respect to crack are considered. Results show that bridging condition has minimum stress intensity factor. In addition, it can be seen that the crack resistance improves by increasing the length and chirality for all kinds of nanotubes. Finally, epoxy/SWCNT 10 wt.% has lower stress intensity factor compared to epoxy/halloysite 10 wt.% in similar loading state.     

Free vibration analyses of multiple delaminated angle-ply composite conical shells – A finite element approach

In this paper, the finite element method is employed to investigate the effects of delamination on free vibration characteristics of graphite–epoxy pretwisted shallow angle-ply composite conical shells. The generalized dynamic equilibrium equation is derived from Lagrange’s equation of motion neglecting Coriolis effect for moderate rotational speeds. The theoretical formulation is based on the Mindlin’s theory and the multi-point constraint algorithm is considered for an eight noded isoparametric plate bending element. The standard eigenvalue problem is solved by applying the QR iteration algorithm. The mode shapes are also depicted for a typical laminate configuration. Non-dimensional natural frequencies obtained are the first known results for the type of analyses carried out here.     

Dynamic analysis of bridge–vehicle system with uncertainties based on the finite element model

A new method of dynamic analysis on the bridge–vehicle interaction problem considering uncertainties is proposed in this paper. The bridge is modeled as a simply supported Euler–Bernoulli beam with Gaussian random elastic modulus and mass density of material with moving forces on top. These forces are time varying with a coefficient of variation at each time instance and they are considered as Gaussian random processes. The mathematical model of the bridge–vehicle system is established based on the finite element model in which the Gaussian random processes are represented by the Karhunen–Loéve expansion and the equations will be solved by the Newmark  -β$\beta$ method. The proposed method is compared with the Monte Carlo method in numerical simulations with good agreements for cases with different vehicle speed and level of uncertainties in the excitation and system parameters. The mean value and variance of the structural responses are found to be very accurate even with large uncertainties in the excitation forces. The proposed method is also found to have superior performance in the computational efficiency compared with the Monte Carlo method.     

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.