Computers & Structures

Published by Elsevier
Online ISSN: 0045-7949
Publications
Article
Right ventricular dysfunction is one of the more common causes of heart failure in patients with congenital heart defects. Use of computer-assisted procedures is becoming more popular in clinical decision making process and computer-aided surgeries. A 3D in vivo MRI-based RV/LV combination model with fluid-structure interaction (FSI), RV-LV interaction, and RV-patch interaction was introduced to perform mechanical analysis for human right ventricle with potential clinical applications. Patient-specific RV/LV morphologies were acquired by using planar tagged MRI. The 3D RV/LV FSI model was solved using a commercial finite element package ADINA. Our results indicated that flow and stress/strain distributions in the right ventricle are closely related to RV morphology, material properties and blood pressure conditions. Patches with material properties better matching RV tissue properties and smaller size lead to better RV function recoveries. Computational RV volumes showed very good agreement with MRI data (error < 3%). More patient studies are needed to establish baseline database so that computational simulations can be used to replace empirical and often risky clinical experimentation to examine the efficiency and suitability of various reconstructive procedures in diseased hearts and optimal design can be found.
 
Article
The flow-induced vibration of synthetic vocal fold models has been previously observed to be acoustically-coupled with upstream flow supply tubes. This phenomenon was investigated using a finite element model that included flow-structure-acoustic interactions. The length of the upstream duct was varied to explore the coupling between model vibration and subglottal acoustics. Incompressible and slightly compressible flow models were tested. The slightly compressible model exhibited acoustic coupling between fluid and solid domains in a manner consistent with experimental observations, whereas the incompressible model did not, showing the slightly compressible approach to be suitable for simulating acoustically-coupled vocal fold model flow-induced vibration.
 
Article
Multi-physics right and left ventricle (RV/LV) fluid-structure interaction (FSI) models were introduced to perform mechanical stress analysis and evaluate the effect of patch materials on RV function. The FSI models included three different patch materials (Dacron scaffold, treated pericardium, and contracting myocardium), two-layer construction, fiber orientation, and active anisotropic material properties. The models were constructed based on cardiac magnetic resonance (CMR) images acquired from a patient with severe RV dilatation and solved by ADINA. Our results indicate that the patch model with contracting myocardium leads to decreased stress level in the patch area, improved RV function and patch area contractility.
 
Article
Patients with repaired tetralogy of Fallot account for the majority of cases with late onset right ventricle (RV) failure. A new surgical procedure placing an elastic band in the right ventricle is proposed to improve RV function measured by ejection fraction. A multiphysics modeling approach is developed to combine cardiac magnetic resonance imaging, modeling, tissue engineering and mechanical testing to demonstrate feasibility of the new surgical procedure. Our modeling results indicated that the new surgical procedure has the potential to improve right ventricle ejection fraction by 2-7% which compared favorably with recently published drug trials to treat LV heart failure.
 
Article
In the serosal cavities (e.g. pleural, pericardial) soft tissues slide against each other, lubricated by thin fluid. We used rotational devices to study the tribology of such tissues, which appear to exhibit mixed and hydrodynamic lubrication. To explore mechanism, we modeled the interaction of fluid and soft material in 3D using a simple cylindrical geometry with an uneven solid-fluid interface in rotation. Deformation of the solid, frictional force, and fluid thickness are presented as a function of applied rotational velocity, applied normal load and material properties. The results suggest that the deformation caused by hydrodynamic pressure leads to load-supporting behavior.
 
Article
The flow-induced response of a membrane covering a fluid-filled cavity located in a section of a rigid-walled channel was explored using finite element analysis. The membrane was initially aligned with the channel wall and separated the channel fluid from the cavity fluid. As fluid flowed over the membrane-covered cavity, a streamwise-dependent transmural pressure gradient caused membrane deformation. This model has application to synthetic models of the vocal fold cover layer used in voice production research. In this paper, the model is introduced and responses of the channel flow, the membrane, and the cavity flow are summarized for a range of flow and membrane parameters. It is shown that for high values of cavity fluid viscosity, the intracavity pressure and the beam deflection both reached steady values. For combinations of low cavity viscosity and sufficiently large upstream pressures, large-amplitude membrane vibrations resulted. Asymmetric conditions were introduced by creating cavities on opposing sides of the channel and assigning different stiffness values to the two membranes. The asymmetry resulted in reduction in or cessation of vibration amplitude, depending on the degree of asymmetry, and in significant skewing of the downstream flow field.
 
Article
A three-dimensional simulation of the formation of metachronal waves in rows of pulmonary cilia is presented. The cilia move in a two-layer fluid model. The fluid layer adjacent to the cilia bases is purely viscous while the tips of the cilia move through a viscoelastic fluid. An overlapping fixed-moving grid formulation is employed to capture the effect of the cilia on the surrounding fluid. In contrast with immersed boundary methods, this technique allows a natural enforcement of boundary conditions without the need for smoothing of singular force distributions. The fluid domains are discretized using a finite volume method. The 9 + 2 internal microtubule structure of an individual cilium is modeled using large-deflection, curved, finite-element beams. The microtubule skeleton is cross-linked to itself and to the cilium membrane through spring elements which model nexin links. The cilium membrane itself is considered to be elastic and subject to fluid stresses computed from the moving grid formulation as well as internal forces transmitted from the microtubule skeleton. A cilium is set into motion by the action of dynein molecules exerting forces between adjacent microtubules. Realistic models of the forces exerted by dynein molecules are extracted from measurements of observed cilia shapes.
 
Article
Computational vocal fold models are often used to study the physics of voice production. In this paper the sensitivity of predicted vocal fold flow-induced vibration and resulting airflow patterns to several modeling selections is explored. The location of contact lines used to prevent mesh collapse and assumptions of symmetry were found to influence airflow patterns. However, these variables had relatively little effect on the vibratory response of the vocal fold model itself. Model motion was very sensitive to Poisson's ratio. The importance of these parameter sensitivities in the context of vocal fold modeling is discussed.
 
Article
A new cell-vortex unstructured finite volume method for structural dynamics is assessed for simulations of structural dynamics in response to fluid motions. A robust implicit dual-time stepping method is employed to obtain time accurate solutions. The resulting system of algebraic equations is matrix-free and allows solid elements to include structure thickness, inertia, and structural stresses for accurate predictions of structural responses and stress distributions. The method is coupled with a fluid dynamics solver for fluid-structure interaction, providing a viable alternative to the finite element method for structural dynamics calculations. A mesh sensitivity test indicates that the finite volume method is at least of second-order accuracy. The method is validated by the problem of vortex-induced vibration of an elastic plate with different initial conditions and material properties. The results are in good agreement with existing numerical data and analytical solutions. The method is then applied to simulate a channel flow with an elastic wall. The effects of wall inertia and structural stresses on the fluid flow are investigated.
 
Article
The governing equations for constrained multibody systems are formulated in a manner suitable for their automated, numerical development and solution. The closed loop problem of multibody chain systems is addressed. The governing equations are developed by modifying dynamical equations obtained from Lagrange's form of d'Alembert's principle. The modifications is based upon a solution of the constraint equations obtained through a zero eigenvalues theorem, is a contraction of the dynamical equations. For a system with n-generalized coordinates and m-constraint equations, the coefficients in the constraint equations may be viewed as constraint vectors in n-dimensional space. In this setting the system itself is free to move in the n-m directions which are orthogonal to the constraint vectors.
 
The flow chart for the HBB-BC algorithm.
Performance comparison for the 120-bar dome truss. 
Member stress limitation for the 25-bar spatial truss.
Article
A Hybrid Big Bang–Big Crunch (HBB–BC) optimization algorithm is employed for optimal design of truss structures. HBB–BC is compared to Big Bang–Big Crunch (BB–BC) method and other optimization methods including Genetic Algorithm, Ant Colony Optimization, Particle Swarm Optimization and Harmony Search. Numerical results demonstrate the efficiency and robustness of the HBB–BC method compared to other heuristic algorithms.
 
Article
This paper describes procedures for design sensitivity analysis and optimization of nonlinear structural systems with the computer program ADINA. Formulation of the structural optimization problem, design sensitivity analysis with nonlinear response using incremental finite element procedures, and two strategies to use ADINA for design optimization are described. A database and a modem database management system are used to couple ADINA with design sensitivity analysis and optimization modules. Comparison of optimum designs with linear and nonlinear structural responses for trusses with material and geometric nonlincarities are given. More complex structures can be optimized with the developed procedures to fully exploit the capabilities of ADINA.
 
Article
This paper describes a finite element algorithm developed for analysis of nonlinear viscoelastic materials. A single integral constitutive law proposed by Schapery is used to describe viscoelastic material behavior. Work leading to this paper focused on adhesives, but the FE formulation is general and readily extended to structural systems other than plane strain, plane stress and axisymmetric analysis as described. Cartesian strain components are written in terms of current and past stress states. Thus strains are conveniently defined by a stress operator that includes instantaneous compliance and hereditary strain which is updated by recursive computation. Equilibrium at each time step is insured with a modified Newton Raphson technique, incorporating convergence acceleration. Verification analyses show excellent agreement with experimental data for FM-73 adhesive systems. A plane strain analysis of a butt joint is included.
 
Article
We consider Papcovitch–Neuber (PN) solution to the Navier equation, comprising only the vector potential, and develop a new displacement-based 14-node brick element. We assume PN solution in polynomial form. We impose constraints on unknown coefficients of the polynomials such that the element correctly represents linear stress fields. To validate the performance of the new element which we call PN5X1, we conduct several pathological tests available in the literature. PN5X1 predicts, as anticipated, both stresses and displacements accurately at every point inside the elastic continuum for linear stress fields.
 
Article
In this paper, we present a new quadrilateral discrete Kirchhoff flat shell element (called DKQ16) with 16 degrees of freedom (three displacements U, V, W at each corner, a rotation θs at each mid-side) for the linear analysis of plates and shells. This new element is formulated on the basis of the so-called rational element method proposed by Zhong et al. [Zhong WX, Zeng J. J Computat Struct Mech Appl 1996;13:1–8 [in Chinese]]. In this new formulation, the rational quadrilateral plane element (RQ4) is employed for the membrane part and a new discrete Kirchhoff plate element DKQ8 proposed by the present authors [Batoz JL, Hammadi F, Zheng CL, Zhong WX, submitted for publication] is taken for the bending part. The DKQ16 element is one of the most simple quadrilateral flat shell elements. It can be combined with the DKT12 (or Morley) element. Numerical results for some typical problems demonstrate the overall good performance of the new shell element.
 
Article
Recent advances in computational structural and fluid dynamics are discussed in reviews and reports. Topics addressed include fluid-structure interaction and aeroelasticity, CFD techniques for reacting flows, micromechanics, stability and eigenproblems, probabilistic methods and chaotic dynamics, and perturbation and spectral methods. Consideration is given to finite-element, finite-volume, and boundary-element methods; adaptive methods; parallel processing machines and applications; and visualization, mesh generation, and AI interfaces.
 
Article
The paper describes a new four-noded quadrilateral shell element, called QUAD4, which is based on isoparametric principles with modifications which relax excessive constraints. The modifications include reduced order integration for shear terms, enforcement of curvature compatibility, and the augmentation of transverse shear flexibility to account for a deficiency in the bending strain energy. Practical features are discussed, including conversion to a nonplanar shape, coupling between bending and stretching, mass properties, and geometric stiffness. Experimental results are described which illustrate the accuracy and economy claimed for the element.
 
Article
This paper presents an investigation into the hydraulics of regular ogee-profile spillways. The free-surfaces of the fluid for several flow heads as measured in the hydraulics laboratory are used as benchmarks. The finite element computational fluid dynamics software, ADINA, was used to predict the free surface over an ogee spillway and thus model the flow field. Since the actual flow is turbulent the k–ε flow model was used. For the cases considered in this paper, ADINA predicted reasonable free surface results that are consistent with general flow characteristics over spillways. The results are also in close agreement with measured free-surface profiles over the entire length of the spillway.
 
nfluence of the various reinforcements on the global response in compression
nfluence of the various reinforcement in the damage distribution (2D-compression)
Article
Various levels of modelling of reinforced concrete beams are presented and compared. Their complementary character is outlined in some simple cases. Further studies are proposed.
 
Article
This paper assesses the global performance and the underlying assumptions of a recently developed one-dimensional model characterising the elastic lateral-torsional buckling behaviour of singly symmetric tapered thin-walled open beams, which is able to account for the influence of the pre-buckling deflections. A comparative study involving the critical load factors and buckling modes yielded by (i) the one-dimensional model and (ii) two-dimensional shell finite element analyses (reference results) is presented and discussed. The results concern I-section cantilevers and simply supported beams (i) with uniform or linearly tapered webs, (ii) equal or unequal uniform flanges and (iii) acted by point loads applied at the free end or mid-span sections, respectively. In general, the one-dimensional predictions are found to agree well with the shell finite element results. Some significant discrepancies are also recorded (for the shorter beams), which are due to the occurrence of relevant cross-section distortion or localised buckling phenomena.
 
Article
The geometrically nonlinear free vibration of symmetrically laminated rectangular plates (1st and higher modes) and the higher mode of an isotropic plate with fully clamped boundary conditions is studied, using the hierarchical finite element method (HFEM). The relationships between the vibration amplitude ratio and nonlinear frequencies, and between the vibration amplitude ratio and nonlinear mode shapes are discussed. The mode bending stresses and membrane forces at large amplitude for laminated plates are presented. The comparison between the nonlinear frequency ratio calculated from this study and the one from a published paper is in good agreement. The large variation of in-plane membrane forces over the plate span for some of the laminated plates has been observed. This will definitely affect the application of Berger's hypothesis to the geometrically nonlinear analysis of these laminated plates. It has been found that the geometrically nonlinear dynamic properties of laminated plates varies from plate to plate depending not only on the aspect ratio and boundary conditions, but also on the lamination and material properties of the lamina considered.
 
Article
The interactive multidisciplinary aircraft design code was used for numerical simulation of Tupolev-204 airplane in-flight flutter tests. Dynamic structure loading is generated by symmetric and antisymmetric harmonic excitation of spoilers with smooth frequency sweep from 1 to 5 Hz. Major features of theoretical approach are described. Calculated and experimental results are compared. The influence of unsteady aerodynamic forces and onboard control system on dynamic loading of elastic structure is shown.
 
Article
Development of a nonconforming eight to 26-node hexahedron for three-dimensional (3-D) thermal-elasto-plastic finite element analysis (FEA) is presented. The nonconforming element satisfies the MacNeal and Harder patch test and does not lock in plastic deformation, eliminating the need for selective reduced integration. The enhanced displacement and strain fields are fully consistent with a linear thermal strain field. In some cases this eliminates the need for isothermal elements in thermal-elasto-plastic FEA. Several cases are presented for validation purposes. In addition, a 3-D thermal-elasto-plastic analysis of a weld is presented, using selective reduced integration and nonconforming elements with both constant and linear thermal strain fields. The nonconforming elements show improved behaviour over selective reduced integration, but are found to be about 20% more expensive on a per iteration basis when all the elements are replaced. However, for the problem considered, the nonconforming elements provide about 2.5 times more degrees of freedom (DOF). Adaptive processes could reduce this by utilizing nonconforming elements only where they are required.
 
Article
A comprehensive elasto-plastic constitutive model developed by the first two authors has been inserted into the user-supplied material model of ADINA for two- and three-dimensional solid elements. Material property data are initial and saturated uniaxial stress-strain curves and a few constants which are easily determined by simple tests. The performance of this model is demonstrated through various examples involving different loading paths and histories. These include cyclic hardening and softening, various nonproportional loading paths, ratcheting (cyclic creep), analysis of crack propagation and closure behaviour. These results are compared with data from experiments or those obtained using the classical elasto-plastic material models provided with ADINA. It is clearly shown that this new model is far superior to those currently available and is relatively simple to implement
 
Article
A close relationship exists between neural and fuzzy systems since they both work with degrees of imprecision in a space that is not defined by sharp deterministic boundaries. Fuzzy neural technologies can be fused into a unified methodology known as fuzzy neural networks. A neural network with the proposed architecture maps a fuzzy input vector to fuzzy output. A learning algorithm is derived from the fuzzy actual output and the fuzzy target output. The fuzzy neural networks have been applied to PCP diagnosis, Concrete mix design and for the design of industrial roofs.
 
Article
Geometrically nonlinear elastic-plastic analysis of 2D-problems of structural mechanics, based on the application of degenerated isoparametric finite elements, is carried out. The investigations concentrate on the derivation of nonlinear equilibrium equations using the total Lagrangian formulation. Large rotation increments and a displacement dependent pressure loading are taken into account, developing, in consequence, additional components of the corresponding stiffness matrix. For the elastic-plastic behaviour the Prandtl-Reuss associated flow rule and the von Mises plastic yield criterion are adopted. The Riks-Wempner constant arc length method, together with Newton-Raphson iterations, are employed to solve the incremental nonlinear equations in question. Several numerical sample problems are presented and compared with analytical reference solutions. A proof of the good accuracy of the presented method is given.
 
Article
The concept of isogeometric analysis, whereby the parametric func- tions that are used to describe CAD geometry are also used to approx- imate the unknown fields in a numerical discretisation, has progressed rapidly in recent years. This paper advances the field further by outlin- ing an isogeometric Boundary Element Method (IGABEM) that only re- quires a representation of the geometry of the domain for analysis, fitting neatly with the boundary representation provided completely by CAD. The method circumvents the requirement to generate a boundary mesh representing a significant step in reducing the gap between engineering design and analysis. The current paper focuses on implementation details of 2D IGABEM for elastostatic analysis with particular attention paid towards the differences over conventional boundary element implementa- tions. Examples of Matlab R{\deg} code are given whenever possible to aid understanding of the techniques used.
 
Article
In this paper we review some finite element methods to approximate the eigenvalues of Maxwell equations. The numerical schemes we are going to consider are based on two different variational formulations. Our aim is to compare the performances of the methods depending on the shape of the domain. We shall see that the nodal elements can give good results only using the penalized formulation and only if the domain is a convex or smooth polygon. In the case of domains with reentrant corners it turns out that the edge elements are efficient. Moreover we propose a new non-standard finite element method in order to deal with the penalized formulation in presence of reentrant corners: a biquadratic element with a suitable projection.
 
Article
The purpose of this paper is to examine the current state of development of the finite element method with regard to engineering applications. First is presented a personal view of the origins of the method, describing the sequence of events at Berkeley. Next is a discussion of the state-of-the-art of structural dynamic analysis, with mention of important recent advances. Finally, two examples drawn from earthquake engineering experience are discussed which demonstrate some limitations of present capabilities. Specific areas requiring new program development are mentioned; the need for a combined analytical-experimental approach is emphasized.
 
Article
Many finite element models have been proposed for the analysis of sandwich plates. In general, these elements can be classified into two broad streams. The first is based on the assumed displacement approach, and the second on the assumed-stress hybrid approach. Within each stream, the characteristics of the elements vary greatly in terms of the formulation complexity, accuracy and applicability. An overview is given of the state-of-the-art finite element analysis applied to sandwich plate structures.
 
Article
Linearization plays a key role both in formulation as well as numerical analysis of problems in the mechanics of solids and structures. This paper provides a unifying definition of linearization and illustrates some of the operational consequences. Finite motion of elastic plates is chosen to demonstrate how the linearization process may be utilized in the context of motion of initially-stressed, materially nonlinear elastic plates.
 
Article
A hybrid method for quantification of the loading of shotcrete tunnel shells, combining thermochemomechanical material modeling of shotcrete with 3D in situ displacement measurements in the framework of the non-linear finite element method, is presented. Histories of displacement fields, determined from in situ measurements by suitable interpolation functions, are prescribed on the outer boundary of a part of the tunnel, discretized in 2D or 3D. The main goal is the determination of fields of safety degrees, amounting to 0% for the unloaded shell and to 100% for the material loaded up (locally) to the compressive strength. A comprehensive investigation of the significance of the individual material characteristics of shotcrete as well as that of the third dimension in space on the structural behavior is performed. The Sieberg tunnel in Lower Austria, constituting a part of the high capacity railway line between Vienna and Salzburg, is used as the vehicle for this investigation. This tunnel was very recently completed.
 
Article
The geometrically nonlinear formulation of three-dimensional (3D) curved beam elements with large rotations has recently aroused much interest. The element geometry is usually constructed using coordinates of the nodes of the centroidal or reference axis and the orthogonal nodal vectors representing the principal bending directions. The element displacement field is described using three translations at the element nodes and three rotations about the local axes. These types of 3D beam element formulations are, however, restricted to small nodal rotations between two successive load increments. The beam element formulation presented in this paper removes such restrictions; this is accomplished by defining beam geometry using nodal displacements and tangent vectors instead of rotation angles at the two ends of the curved beam element. The fact that, unlike rotation angles, vectors can be added without difficulty, allows large rotations be made within a load increment. Removing all the transcendental trigonometrical cosine and sine functions, the formulation has the advantage of being simple and purely algebraic.
 
Article
A numerical model for the coupled analysis of cross-sections made of anisotropic materials under general combined loading was formulated in an accompanying paper (1). In this paper, additional aspects concerning its implementation and the scheme for nonlinear analysis are discussed. The model is validated by analyzing several isotropic and anisotropic elastic problems; excellent accuracy was obtained compared to closed-form solutions. Further, the case of a RC section presenting crack-induced anisotropy is investigated. The capability of the model to capture interactions between tangent and normal forces is proved. The conclusion drawn is that the developed model is a suitable sectional constitutive equation for 3D beam elements for realistic structural analysis.
 
Article
Existing methods of automatic mesh generation for 3D solid objects are reviewed. Although the 3D Delaunay triangulation recently aroused much attention, its suitability as a finite element mesh generator is questioned. Although in 2D Delaunay triangulation, the ‘max-min’ angle criterion can be verified over the entire domain, no equivalent or similar criterion can be defined for its extension to 3D situations to ensure that tetrahedron elements so generated are well proportioned for numerical calculations.In this paper, a simple but versatile 3D triangulation scheme based on the advancing front technique for the discretization of arbitrary volumes is presented. To ensure that the tetrahedron elements generated are as equilateral as possible, the ratio of volume of the element to the sum of squares of edges put into a dimensionless form is adopted to judge the quality of a tetrahedron element. The quality of the finite element mesh can thus be ensured if the shape of each tetrahedron element is carefully controlled in the mesh construction process. Through the study of numerous examples of various characteristics, it is found that high-quality tetrahedron element meshes are obtained by the proposed algorithm.
 
Article
This paper presents the exact stiffness matrix of 3D-beam element with a class of continuously varying cross-sectional properties, which is derived using direct stiffness method and transfer functions of the beam. A nodal load vector for continuously distributed beam loading is also described using transfer functions. All the transfer functions, which occur in the stiffness matrix and nodal load vector, are evaluated numerically. Results of numerical experiments show that this new element satisfies all the relevant equations.
 
Article
The paper deals with the use of Saint Venànt’s general rod theory for deriving the stiffness matrix for 3D beam elements with general cross-section. The elastic factors of the section are obtained through the numerical solution of the Saint Venànt differential equations. Different discretization strategies have been investigated including FEM and BEM alternatives the one based on 6-node triangular elements appears to be the best choice.
 
Article
This paper addresses the bending and free vibrations of multilayered cylindrical shells with piezoelectric properties using a semi-analytical axisymmetric shell finite element model with piezoelectric layers using the 3D linear elasticity theory. In the present 3D axisymmetric model, the equations of motion are expressed by expanding the displacement field using Fourier series in the circumferential direction. Thus, the 3D elasticity equations of motion are reduced to 2D equations involving circumferential harmonics. In the finite element formulation the dependent variables, electric potential and loading are expanded in truncated Fourier series. Special emphasis is given to the coupling between symmetric and anti-symmetric terms for laminated materials with piezoelectric rings. Numerical results obtained with the present model are found to be in good agreement with other finite element solutions.
 
Article
High pulsating blood pressure and severe stenosis make fluid–structure interaction (FSI) an important role in simulating blood flow in stenotic arteries. A three-dimensional nonlinear model with FSI and a numerical method using GFD are introduced to study unsteady viscous flow in stenotic tubes with cyclic wall collapse simulating blood flow in stenotic carotid arteries. The Navier–Stokes equations are used as the governing equations for the fluid. A thin-shell model is used for the tube wall. Interaction between fluid and tube wall is treated by an incremental boundary iteration method. Elastic properties of the tube wall are determined experimentally using a polyvinyl alcohol hydrogel artery stenosis model. Cyclic tube compression and collapse, negative pressure and high shear stress at the throat of the stenosis, flow recirculation and low shear stress just distal to the stenoses were observed under physiological conditions. These critical flow and mechanical conditions may be related to platelet aggregation, thrombus formation, excessive artery fatigue and possible plaque cap rupture. Computational and experimental results are compared and reasonable agreement is found.
 
Article
An accurate stress/strain recovery procedure for laminated, composite plates that can be implemented in standard finite element programs is developed. The formulation is based on an asymptotic analysis and starts from a three-dimensional, anisotropic elasticity problem that takes all possible deformation into account. After a change of variable, which introduces intrinsic two-dimensional description for the deformation of the reference plane, the variational asymptotic method is then used to rigorously split this three-dimensional problem into two reduced-dimensional problems: a nonlinear, two-dimensional analysis of the reference surface of the deformed plate (an equivalent single-layer plate model), and a linear, one-dimensional analysis of the normal-line element through the thickness. The latter is solved by a one-dimensional finite element method and provides a constitutive law between the generalized, two-dimensional strains and stress resultants for the plate analysis, and a set of recovering relations to approximately express the three-dimensional displacement, strain and stress fields in terms of two-dimensional variables determined from solving the equations of the plate analysis. The strain energy functional that is asymptotically correct through the second-order in the small parameters is then cast into the form of Reissner’s theory. Although it is not in general possible to construct an asymptotically correct Reissner-like composite plate theory, an optimization procedure is used to drive the present theory as close as possible to being asymptotically correct, while maintaining the simplicity and beauty of the Reissner-like formulation. A computer program based on the present procedure, called variational asymptotic plate and shell analysis, has been developed. Its utility is demonstrated by inserting the recovery procedure into the plate element of a general-purpose finite element code. Numerical results obtained for a variety of laminated, composite plates show that three-dimensional field variables recovered from the present theory agree very well with those from exact solutions.
 
Article
A numerical model for the coupled analysis of arbitrary shaped cross sections made of heterogeneous-anisotropic materials under 3D combined loading is formulated. The theory is derived entirely from equilibrium considerations and based on the superposition of the 3D section’s distortion and the traditional plane section hypothesis. 3D stresses and strains fields are obtained as well as a section stiffness matrix reflecting coupling effects between normal and tangential forces due to material anisotropy. Traditional generalized strains and stresses are maintained as input and output variables. The proposed model is suitable as a constitutive law for frame elements in the analysis of complete structures.
 
Article
Several vibration isolation methods are investigated using the 3D direct boundary element method. The results of the present numerical simulation are initially compared to an analytical and other numerical solutions. After this validation of the programme, a source isolation example from literature is investigated. A comparison between numerical results and measured data is finally presented for the case of vibration isolation by an open trench, that was constructed for full-scale testing. The influence of different parameters on the amplitude reduction, due to the presence of a trench, is studied.
 
Article
This paper presents a new beam–column formulation which can be used for the accurate, yet efficient, modelling of 3D reinforced concrete (R/C) frames. The formulation is intended for modelling the nonlinear elastic behaviour of a whole R/C beam–column with only one element, which is an essential ingredient of adaptive elasto-plastic analysis. On the longitudinal axis level, quartic shape functions are used to represent the two transverse displacements. A constant axial force criterion is employed instead of shape functions for the axial displacement, which is largely responsible for the accuracy of the proposed formulation. For concrete, the formulation assumes a nonlinear compressive stress–strain relationship and no tensile resistance; whereas for steel, a linear stress–strain relationship is utilised. On the cross-sectional level, the formulation is capable of modelling the interaction between the axial force and the biaxial moments for a general R/C cross-section, with explicit expressions obtained using a novel approach based on integration over triangular subdomains. The paper provides the details of the proposed formulation, and presents several verification examples to demonstrate the accuracy of this formulation and its ability to model the nonlinear elastic response of reinforced concrete beam–columns with only one element per member.
 
Article
The present paper deals with the problem of determining the optimal joint positions and cross-sectional parameters of linearly elastic space frames with imposed stress and free frequency constraints. The frame is assumed to be acted on by different load systems, including temperature and self-weight loads. The stress state analysis includes tension, bending, shear, and torsion of beam elements. By a sequence of quadratic programming problems, the optimal design is attained. The sensitivity analysis of distinct as well as multiple frequencies is performed through analytic differentiation with respect to design parameters. Illustrative examples of optimal design of simple and medium complexity frames are presented, and the particular case of bimodal optimal solution is considered in detail.
 
Article
The newly developed immersed object method (IOM) [Tai CH, Zhao Y, Liew KM. Parallel computation of unsteady incompressible viscous flows around moving rigid bodies using an immersed object method with overlapping grids. J Comput Phys 2005; 207(1): 151–72] is extended for 3D unsteady flow simulation with fluid–structure interaction (FSI), which is made possible by combining it with a parallel unstructured multigrid Navier–Stokes solver using a matrix-free implicit dual time stepping and finite volume method [Tai CH, Zhao Y, Liew KM. Parallel computation of unsteady three-dimensional incompressible viscous flow using an unstructured multigrid method. In: The second M.I.T. conference on computational fluid and solid mechanics, June 17–20, MIT, Cambridge, MA 02139, USA, 2003; Tai CH, Zhao Y, Liew KM. Parallel computation of unsteady three-dimensional incompressible viscous flow using an unstructured multigrid method, Special issue on “Preconditioning methods: algorithms, applications and software environments. Comput Struct 2004; 82(28): 2425–36]. This uniquely combined method is then employed to perform detailed study of 3D unsteady flows with complex FSI. In the IOM, a body force term F is introduced into the momentum equations during the artificial compressibility (AC) sub-iterations so that a desired velocity distribution V0 can be obtained on and within the object boundary, which needs not coincide with the grid, by adopting the direct forcing method. An object mesh is immersed into the flow domain to define the boundary of the object. The advantage of this is that bodies of almost arbitrary shapes can be added without grid restructuring, a procedure which is often time-consuming and computationally expensive. It has enabled us to perform complex and detailed 3D unsteady blood flow and blood–leaflets interaction in a mechanical heart valve (MHV) under physiological conditions.
 
Different elements used for modelling the infilled frame.
The sequence of formation of the plastic hinges/cracks in the infilled space frame.
Discretization, loads and masses for the infilled space frame. 
The sequence of formation of the cracks and the hinges in the infilled space frame at different times.
Article
An inelastic finite element model to simulate the behaviour of reinforced concrete frames infilled with masonry panels subjected to static load and earthquake excitation has been presented. Under the loads, the mortar may crack causing sliding and separation at the interface between the frame and the infill. Further, the infill may get cracked and/or crushed which changes its structural behaviour and may render the infill ineffective, leaving the bare frame to take all the load which may lead to the failure of the framing system itself. In this study, a mathematical model to incorporate this behaviour has been presented.
 
Article
An algorithm for the discretization of parametric 3D surfaces has been extended to the family of discrete surfaces represented by a triangular mesh of arbitrary topology. The limit surface is reconstructed from the mesh using the modified Butterfly scheme which is an interpolating subdivision technique yielding a C1 surface. The recovered surface is discretized directly in the physical space by the advancing front technique, thereby parameterization of the surface is not required. The mesh gradation is controlled by the octree data structure that simultaneously serves as a localization tool for the intersection investigation. Considering the discrete nature of the surface, special attention is paid to the proper implementation of the point-to-surface projection algorithm in order to achieve robustness and reasonable efficiency of the algorithm. The performance of the proposed strategy is presented on a few examples.
 
Article
Algorithms for geometrically nonlinear finite element analysis are presented which exploit the vector processing capability of the VPS-32, which is closely related to the CYBER 205. By manipulating vectors (which are long lists of numbers) rather than individual numbers, very high processing speeds are obtained. Long vector lengths are obtained without extensive replication or reordering by storage of intermediate results in strategic patterns at all stages of the computations. Comparisons of execution times with those from programs using either scalar or other vector programming techniques indicate that the algorithms presented are quite efficient.
 
Top-cited authors
Klaus-Jürgen Bathe
  • Massachusetts Institute of Technology
A. Kaveh
  • Iran University of Science and Technology
Yi Min Xie
  • RMIT University
Grant P. Steven
Gabriele Milani
  • Politecnico di Milano