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In this paper, a finite element procedure is used to study the dynamic behaviour of a paper web in a free span between two rollers, including effects of transport velocity and surrounding air. The paper web is modelled as a three-dimensional orthotropic structure. The influence of air is accounted for by utilizing fluid-solid interaction analyses based on acoustic theory. The contribution of transport velocity is included through gyroscopic matrices and forces. The structural response on harmonic excitations has been studied using linear and non-linear models. Results show that air significantly reduces eigenfrequencies of the web. So called ''edge-flutter'' is nothing but the result of skew tension profile. Excessive web vibration can be eliminated by adjusting the web tension.

A model that predicts the paper behavior during the printing process at various time intervals is proposed. The tendency of wrinkling can therefore be observed. This model will accommodate any paper topology induced by moisture effects or otherwise, and can analyze virtually any roll geometry and roll combinations. Nonlinear Finite Element Method is applied to the contact problem of two layered cylinders compressing a paper with arbitrary initial shape. The analysis assumed plane strain condition, the paper can therefore be treated as a beam. The result from the contact problem is applied to predict the behavior of the paper as it is feeding through the roll system. The Total Lagrange Formulation with Piola-Kirchoff Stress and Green-Lagrange strained is used. The quasi-static solution at different time intervals is presented. It was found that they agreed favorably with experiments.

The mechanical behaviour of wood was studied from a micro up to a macro level. Wood is a cellular material possessing a high degree of anisotropy. Like other cellular solids, it often exhibits a highly nonlinear stress–strain behaviour. In the present study the mechanical properties of the cellular structure of wood are characterized and modelled, the irregular cell shape, the anisotropic layered structure of the cell walls and the periodic variations in density being taken into account. The continuum properties were derived by use of a homogenization procedure and the finite element method. Stiffness and shrinkage properties determined by this procedure are presented and are compared with measured data. The constitutive properties thus determined at various structural levels can be used in numerical simulations of the behaviour of wood in different industrially related areas. One such area is that of the refining process in mechanical pulp manufacture. Simulations of the deformation and fracturing of wood specimens loaded under conditions similar to those found in the refining process are presented. The numerical and experimental results obtained are compared.

In this paper we discuss the finite element modeling of Composite Overwrapped Pressure Vessels (COPVs) which are used in the aerospace industry, when high strength/weight ratios are required, for containers filled with pressurized fluids. The COPVs that we analyze are composed by a thin metallic liner and an external reinforcement made with high strength fibers that are wrapped around the liner embedded in an epoxy resin. It is shown in the paper that for a reliable description of the vessels behavior under internal pressure it is required to use a model that incorporates the mechanical behavior of the liner, of the fibers and of the resin matrix (micromechanical model).

This paper presents a numerically efficient tool for linear buckling predictions of perforated thin-walled bars within the framework of generalized beam theory (GBT). GBT-based beam finite element methods (GBT-FEM) have been well developed for eigenvalue buckling analyses of non-perforated thin-walled bars. The novelty of this paper consists in an extension of the standard GBT to the scope of thin-walled members with arbitrarily shaped and placed holes. This is achieved by combining the standard GBT and the extended finite element method (X-FEM). More specifically, insert a set of locally supported enrichment functions, accounting for the discontinuities on displacement fields arising from the cross-section cut-outs/holes, into the GBT-based finite element approximations of the member configuration spaces, using the partition of unity method (PUM), where a set of level-set functions are used to describe the geometric profiles of hole edges, i.e., with the hole edges being the zero level sets, and also used to construct the enrichment functions. The proposed approach makes it possible to calculate the deformation mode participations for any perforated thin-walled members as the classic GBT for non-perforated ones. Finally, the proposed approach is calibrated against the shell/solid finite element analysis with four illustrative examples. It can be found that the presented approach is of higher computation efficiency than the shell model.

Path planning of loaded pin-jointed bar mechanisms, typical of Pantadome, is discussed in this paper. In engineering, the path from the initial configuration to the target configuration generally cannot be determined easily because of the complicated constraint conditions. The basic kinematic equation of loaded pin-jointed bar mechanisms is hereby established based on FEA, and the driving condition of internal rigid-body (mechanism) displacements is presented for the length actuation of active members. A numerical strategy is proposed to trace the shortest path of pure mechanism displacement from the initial configuration to the given target configuration. With the emphasis on the constraints of structural stability and range of motion, the Rapidly-exploring Random Tree (RRT) method is adopted for the path planning of the loaded pin-jointed bar mechanisms. The RRT method is further modified to be applicable for the path planning when the target configuration is implicitly defined by its distance to be as close as possible to a geometrical boundary, at which the conventional RRT algorithm fails to track multiple feasible paths. An adaptive strategy is also suggested to improve the sampling efficiency of RRT. Considering loose and tight constraints of structural stability respectively, a loaded planar Pantadome is employed as the numerical example to investigate the validity of the path planning method proposed in this paper.

This work deals with the structural behaviour, ultimate strength and design of fixed-ended cold-formed steel (CFS) lipped channel columns experiencing various levels of local-distortional-global buckling mode interaction (more or less close critical local, distortional and global loads). First, a comparison between experimental results, obtained from three tests carried out at The University of Hong Kong (UHK), and the corresponding A baqus shell numerical simulations are presented and discussed – the UHK test campaign is reported in Part I of this two-part paper. The comparison (i) involves equilibrium paths, deformed configurations, failure loads and collapse mechanisms, and (ii) provides enough evidence to ensure that the numerical model developed may be deemed validated. Then, this numerical model is employed to perform a parametric study, aimed at obtaining numerical failure load data concerning lipped channel columns experiencing different levels of local-distortional-global interaction – 368 fixed-ended columns, exhibiting different geometries (cross-section dimensions and lengths) and various yield stresses, thus covering a wide slenderness range. Finally, the present (Part II) paper also assesses the quality of the failure load estimates provided by various design approaches, based on the Direct Strength Method (DSM), for CFS columns affected by the triple coupling phenomenon under consideration. This assessment is based on the comparison with both (i) experimental failure loads, namely those reported in Part I and others collected from the literature, and (ii) numerical failure loads, obtained from A baqus shell finite element analyses (SFEA) and either reported in this work or gathered from previous publications by the authors.

In this paper, a numerical formulation for the analysis of viscoelastic functionally graded materials under finite strains is presented. The general constitutive modeling is described within the context of Lagrangian and isotropic visco-hyperelasticity. The specific models selected are the compressible neo-Hookean hyperelastic law, the Zener rheological model and the isochoric evolution law described in terms of the rate of the viscous right Cauchy-Green stretch tensor. The material coefficients may vary smooth and continuously along one direction according to the power law. The viscous update is performed via the exponential rule. The main novelty of this paper is the use of gradually variable viscoelastic coefficients in the finite strain regime. Four numerical examples involving functionally graded materials and finite viscoelastic strains are originally analyzed to assess the formulation proposed: a bar under uniaxial extension, a block under simple shear, the Cook’s membrane and an elastomeric bridge bearing. Isoparametric solid tetrahedral finite elements of linear, quadratic and cubic orders are employed. The influence of the material viscoelastic parameters on the mechanical behavior is analyzed in detail. Results confirm that mesh refinement provides more accuracy and the present model can reproduce large levels of viscoelastic strains in functionally graded materials.

This paper proposes a computational approach for studying the overall behaviour and local stress state of strand-type structures. This method is based on the homogenization theory of periodic beamlike structures, with the local problem posed on the strand axial period being solved using the finite element method. This approach fully utilises the strand’s helical symmetry, thus minimising the size of the computational domain. Consequently, accounting for geometric complexity and contact interactions, which are of paramount importance for bending loads, is more straightforward. The numerical model mesh size can also be reduced thanks to the use of beam elements, and one objective of this paper is to assess the accuracy of such a model in comparison with solid element models and analytical results. These comparisons are performed on both single-layer and multi-layer strands. Results demonstrate the capability of the proposed computational approach to accurately capture the nonlinear bending behaviour stemming from the stick-slip transition as well as local stress distributions. As for the beam model, it apparently offers a very good compromise between accuracy and numerical efficiency.

Stiffness matrices of beams embedded in an elastic medium and subjected to axial forces are considered. Both the bending and the axial deformations have been incorporated. Two approaches for deriving the element stiffness matrix analytically have been proposed. The first approach is based on the direct force–displacement relationship, whereas the second approach exploits shape functions within the finite element framework. The displacement function within the beam is obtained from the solution of the governing differential equation with suitable boundary conditions. Both approaches result in identical expressions when the exact transcendental displacement functions are used. Exact closed-form expressions of the elements of the stiffness matrix have been derived for the bending and axial deformation. Depending on the nature of the axial force and stiffness of the elastic medium, seven different cases are proposed for the bending stiffness matrix. A unified approach to the non-dimensional representation of the stiffness matrix elements and system parameters that are consistent across all the cases has been developed. Through Taylor-series expansions of the stiffness matrix coefficients, it is shown that the classical stiffness matrices appear as an approximation when only the first few terms of the series are retained. Numerical results shown in the paper explicitly quantify the error in using the classical stiffness compared to the exact stiffness matrix derived in the paper. The expressions derived here gives the most comprehensive and consistent description of the stiffness coefficients, which can be directly used in the context of finite element analysis over a wide range of parameter values.

A field-enriched finite element method is proposed in this paper to simulate the failure process of rocks. According to the different types of defects, the proposed method can select the appropriate failure criteria for voids and cracks. Field variables are used to characterize the crack location and to realize the influence of cracks on the physical field of the numerical model. The main features and the capability of the field-enriched finite element method to efficiently simulate the failure process of rocks with different defects are illustrated with some numerical examples. The results show that the field-enriched finite element method proposed in this paper can obtain the crack propagation path which is consistent with other numerical methods and experimental observations. Moreover, the numerical method proposed in this paper has the advantages of simple implementation process and higher computational efficiency and accuracy in some cases. Therefore, it is a promising numerical simulation method.

A new paradigm of solution is considered.We give the formulation of new overlapping finite elements.The numerical integration of the element matrices is efficient.The new elements are quite distortion insensitive.We illustrate the complete solution scheme of the new paradigm. We present novel overlapping finite elements for a new paradigm of solution proposed in our previous papers, see Bathe (2016) and Bathe and Zhang (2017).We give the formulation of the new overlapping elements and the solutions of basic numerical examples to investigate the robustness and efficiency of the new finite elements. The results show that the new overlapping elements are quite distortion insensitive and the numerical integration of the element matrices is efficient. The computational effort to integrate the matrices is much less than in meshfree methods. Finally, we illustrate the complete solution scheme of the new paradigm using the overlapping finite elements in the analysis of the bracket problem already considered in Bathe and Zhang (2017).While the paper proposes and studies new overlapping elements, we conclude that further research is needed to fully harvest the potential of the new analysis approach.

A new paradigm is presented for finite element analysis in CAD environments.The focus is, firstly, on operating directly with clean-up on the CAD geometry.The focus is, secondly, on establishing efficiently a finite element mesh.Overlapping finite elements are used to achieve these aims.The theory of the new scheme and example solutions are given. A major difficulty in finite element analysis is the preparation of an effective mesh leading to a good response solution. In engineering analyses of complex components, oftentimes, much more time is spent to arrive at an adequate mesh than to obtain the solution of the established finite element model. The difficulty in meshing is due to the fact that finite elements need to abut each other and cannot overlap. This can lead to highly distorted elements, e.g. sliver elements, reducing the accuracy of solution. In practice, to establish an effective mesh, frequently, significant expertise in building meshes is needed, because great care must be taken in cleaning up the CAD geometry and preparing an effective mesh.The objective in this paper is to present a new finite element solution scheme including meshing in which the elements can overlap. The property that finite elements can overlap removes many of the meshing difficulties, leads to an effective meshing procedure and an overall easy-to-use solution scheme for an analyst or a designer.We first present the meshing scheme that we propose, which combines the use of traditional finite elements and overlapping finite elements. A particular feature is that the meshing procedure can be directly embedded in CAD driven solutions. We then present the theory used for the formulation of the overlapping finite elements and the coupling with traditional finite elements. We consider spherical and brick-shaped overlapping finite elements for which the theory is largely based on the formulation of the method of finite spheres. Finally, we illustrate the complete solution scheme in the analysis of some two-dimensional problems using the CAD geometry as the starting point.While the paper presents a new paradigm for analysis in CAD environments, with much potential, we realize that much further study and research is needed on some of the important ingredients of the method to render the complete procedure effective for general practical engineering analyses of static and dynamic problems.

Eigenvalues of a Dynamic Stiffness Matrix are searched for using specialized methods.Polynomial and hyperbolic approximations of the DSM elements are pointed out.The proposed modifications successfully supplement the Wittrick-Williams algorithm.The methods are applicable to abstract differential systems on an oriented graph. The aim of this study is an alternative approach to structure response or modal analysis. The structure consists of one-dimensional bars with continuously distributed mass and stiffness. The analysis is considered on an abstract basis as a problem of a differential system on an oriented graph. This graph is a geometric representation of the investigated mechanical system, where elements of the graph are individual bars of the system, recti- or curvilinear. The system as a whole is fixed through boundary conditions or interconnected with other sub-systems. Hence the paper can be taken as a follow up to earlier works presented at the CC2013 and CST2014 Conferences, where full mathematical background dealing with a general problem has been discussed. This paper is focused on the problem of dynamics of a system with straight prismatic bars with uniformly distributed mass. Dissipation of energy is omitted in order to keep the formulation in the real domain. The detailed assembly procedure of the Dynamic Stiffness Matrix (DSM) and transformation from local to global coordinates is outlined and demonstrated. Conventional way of eigenvalue searching by means of discrete alternative of the Newton-Raphson method is sketched out and later two possibilities based on polynomial and hyperbolic approximations of the DSM elements are pointed out. Lambda matrices as a tool are introduced together with a couple of application possibilities.The Wittrick-Williams algorithm is discussed and applied to localize and facilitate the eigenvalues searching on the whole frequency interval investigated. Finally, an illustrative example of the eigenvalue analysis of a structure is included. Strengths and shortcomings of the approach are discussed. Some open problems and orientation of further investigation are briefly outlined.The rapid development of analytical and semi-analytical methods being based at DSM idea is commented and justified in comparison with FEM analysis. Even if a certain overlap exists, the DSM approach represents an irreplaceable alternative of analysis especially in broadband dynamic problems stemming from area of the stochastic dynamics, like wind, earthquake or traffic engineering. Problems of dynamic stability are easier to be managed as well, when using DSM oriented approaches together with related algorithms of the analytical and semi-analytical method family. Moreover, many problems of physics at the nano-scale emerged recently where these procedures are preferable to be used.

This paper presents a node-based free-form optimization method for two kinds of vibration problems of shell structures.We provide two optional approaches to avoid the repeated eigenvalue problem.The optimal smooth and natural curvature distribution can be determined without any shape design parameterization.It can be easily implemented in combination with a commercial FEM code. We have previously proposed a numerical node-based parameter-free shape optimization method for designing the optimal free-form surface of shell structures. In this paper, this method is extended to deal with two vibration problems including a vibration eigenvalue maximization problem and a frequency response minimization problem. To avoid the repeated eigenvalue problem when a specified vibration eigenvalue is maximized, we provide two optional approaches, i.e., tracking the specified natural mode or increasing all the repeated eigenvalues. Each vibration problem is formulated as a distributed-parameter shape optimization problem, and the derived shape gradient function is applied to the H1 gradient method for the shells proposed by the authors, where the shape gradient function is used as a distributed force function to vary the surface. With this method, the optimal and smooth free-form shape including a natural bead pattern can be obtained. Several calculated examples are presented to demonstrate the effectiveness of the proposed method for the free-form design of shell structures involving vibration problems.

Monitoring and predicting seismic responses of a civil structure can be used to assess its behavior under dynamic loading and to determine its structural health condition. In practice, the employed number of sensors is generally limited by the cost and functionality issues. This paper develops a practical solution of four-stage procedures, focusing on prediction of seismic displacement responses at all building floors using acceleration measurements at the optimized sensor locations. In this paper, a novel multi-scale attention-based recurrent neural network is proposed. In particular, the attention mechanisms in the network effectively focuses on more relevant input data among bidirectional ground accelerations and multivariate acceleration responses. The seismic response data for training the developed neural network is generated by performing nonlinear time historical analysis of a three-dimensional finite element model. A floor displacement warping loss is designed to numerically measure the discrepancy between the prediction and the ground truth. A case study is performed using the numerical and real-world data of a high-rise building to systematically evaluate the prediction performance of the proposed methodology. Results demonstrate that the proposed method outperforms the compared state-of-the-art methods in terms of prediction accuracy and reliability.

The paper describes various approaches for the mathematical modelling of Adaptive Inflatable Structures (AIS) along with the corresponding numerical methods. The introductory part presents a general idea of adaptive impact absorption (AIA) and the concept of inflatable structures equipped with controllable valves serving for internal pressure control. Application of AIS for adaptive absorption of the impact loading is briefly explained. The paper focuses on diverse methods of modelling of inflatable structures, which are based on interaction between solid walls and fluid enclosed inside. Modelling of the solid walls is based on rigid body dynamics or initial-boundary value problem of solid mechanics. In turn, modelling of the fluid utilizes either classical equilibrium thermodynamics or Navier-Stokes equations. Consequently, four possible combinations of the above approaches are distinguished, precisely analyzed and applied for the modelling of different types of inflatable structures. Each model takes into account controllable valves, which requires introducing additional coupling between parameters defining the valves and selected results of the analysis. Corresponding numerical methods include classical methods of solving ordinary differential equations, finite volume method (FVM) applied for problems with mobile boundaries, finite element method (FEM) applied for problems involving additional ODEs and, finally, FEM coupled with FVM. Proposed numerical methods and software tools are utilized for the simulation of adaptive pneumatic cylinders, adaptive pneumatic fenders and membrane valves.

The method of finite spheres enriched for transient wave propagation problems.Implicit time integration, the Bathe method.Monotonic convergence of calculated solutions with smaller time step sizes.Dispersion analysis of solution schemes.Numerical solutions to demonstrate the important attributes of the solution schemes. In the paper by Ham et al. (2014), the method of finite spheres enriched for transient wave propagation problems was used and a monotonic convergence of the calculated solutions with decreasing time step size was seen. This is an important property for practical analyses and different from what is seen in traditional finite element solutions. In this paper we explicitly show and study this characteristic through a dispersion analysis of the solutions calculated by the method of finite spheres using an implicit time integration method, the Bathe method. Another important property identified is that in uniform spatial discretizations for the problems solved, the calculated solution accuracy is almost independent of the solution direction considered. Numerical solutions of some wave propagation problems are given to demonstrate these attributes and show that with the schemes discussed very accurate response predictions can be obtained.

A newly developed X-SBFEM based on the LSM is proposed in this paper for fracture mechanics.The level set method algorithm further develops the X-SBFEM and is used to solve the crack propagation problem.Large structure engineering practice based on XSBFEM.The numerical implementation of XSBFEM. The extended scaled boundary finite element method (X-SBFEM) based on the level set method (LSM) is proposed in this paper to combine the advantages of the scaled boundary finite element method (SBFEM) and the extended finite element method (XFEM). The level set method (LSM) algorithm is applied to further develop the X-SBFEM, especially for the crack propagation problem. The Heaviside enrichment function is used to represent a jump across a discontinuity surface in a split element, and the non-smooth behavior around the crack tip is described using the semi-analytical SBFEM. The stiffness of the region containing the crack tip is computed directly, and the generalized stress intensity factors of many types of singularities are obtained directly from their definitions using consistent formulas. In the numerical simulations, a square plate with an edge crack under tension, a three-point bending beam, a four-point shear beam and a dam (the Koyna dam) with a single propagating crack are modeled. The results show that the proposed X-SBFEM is capable of calculating the stress intensity factors of cracks and predicting crack trajectories and load-displacement relations accurately. An analysis of the sensitivity of the parameters is employed to demonstrate that various mesh densities and crack propagation step lengths led to consistent results.

Depending on the required solution, this paper presents results for the state of stress and buckling of a uniformly pressurized elastic toroidal vessel of four segments. In the first part of the paper, a closed-formed stress solution is formulated for the novel shell form, by adopting the membrane solution as the particular solution of the Reissner-Meissner general bending-theory equations, and an approximate bending solution is used to quantify discontinuity effect at the shell junctions. In the second part of the paper, linearized stability equations are formulated and simplified for the segmented toroidal vessel buckling problem. The membrane results obtained in the first part is used to predict the pre-buckling state and the stability equations are approximately solved for the segments in the middle regions of the toroidal vessel, using the Galerkin’s scheme. This leads to an expression for estimating the critical buckling pressures of pressurized isotropic toroids. Numerical results from the proposed methods are presented and compared with those from a finite element method solution.

This paper describes a macro model for a shallow foundation. The macro model represents the non-linear soil structure interaction (SSI) exemplified by a suspension bridge anchor-block. The model can be adjusted and used for other structures. The formulation uses an elasto-plastic framework to calculate the foundation response. A yield surface in the V – M - H (Vertical, Moment and Horizontal loading) load-space defines the yield and failure envelopes. A non-associated potential surface and a simple bi-linear hardening law describe the magnitude as well as the direction of the plastic displacements. Calibration of model parameters are performed through 2D and 3D finite element calculations. The model is suited for integration in a program for structural design. Compared to a full finite element model, the macro model simplifies the soil structure interaction analyses significantly. The yield and potential surfaces include the option to modify the shape in the H − V plane versus the M − V plane. Allowing for this flexibility in the formulation improves modeling of foundation uplift behavior. The paper demonstrates calibration of macro model parameters through a calculation example. Validation of the model by prototype testing in a sand bin is also performed and presented. © 2017. This is the authors’ accepted and refereed manuscript to the article. Locked until 8.8.2019 due to copyright restrictions. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

In this paper, a reduced order coupled finite element/boundary element method (FEM/BEM) for control of noise radiation and sound transmission of vibrating structure by viscoelastic and passive piezoelectric treatments is presented. The system consists of a sandwich structure composed of elastic faces and a viscoelastic core (with surface mounted piezoelectric patches) and coupled to external/internal acoustic domains. The passive shunt damping strategy is employed for vibration attenuation in the low-frequency range while dissipative viscoelastic materials are used for the higher-frequency domain. The originality of the present paper lies (i) in evaluating the classically used FEM/BEM methods for structural-acoustics problems when taking account smart systems at the fluid-structure interfaces and viscoelastic interlayers and (ii) in development of a reduced-order model, based on a normal mode expansion, able to capture the main characteristics of the system dynamical behavior.

Large deformation analysis of functionally graded elastoplastic materials under finite strains.High order solid tetrahedral finite elements fully integrated.General locking-free behavior for mechanical problems. In this paper, a solid finite element formulation applied to the analysis of functionally graded materials (FGMs) under finite elastoplastic deformation with mixed hardening is presented.The main novelty of this paper is the use of gradually variable material coefficients in finite elastoplastic strain regime.The numerical simulations are performed with the same constitutive models but with different variations of the material coefficients. Full integration and high order tetrahedral elements are used. Results show that high order elements and mesh refinement avoids general locking problems. Finally, the differences (regarding final results) between the homogeneous and the FG cases are depicted.

A well known approach for stabilization of mixed finite triangular elements are volume bubble functions. In this paper a new concept of area bubble functions in geometrically linear (elastic and elasto-plastic) and geometrically non-linear elastic regimes is presented. These functions are used in order to enrich the displacement field. In the numerical examples, simulations for Cook’s membrane problem and a block under central pressure demonstrate, that the proposed formulation avoids locking and reduces stress oscillations for incompressible materials. Furthermore, the results reveal that area bubble functions are superior to volume bubble functions. This paper is an extension of the works published by the authors regarding tetrahedral elements.

Corrosion defects which occur in oil and gas pipelines may compromise the safety of such structures. This paper makes an assessment of the accuracy of some of the analytical procedures commonly employed by industry to calculate the failure pressure of corroded pipelines via finite element analyses (FEA). Second, this paper studies the stress distribution on isolated pit corrosion defects also via FEA. Analytical procedures to calculate the failure pressure associated to isolated pits are not available yet. Thus, based on the stress analysis results, such a procedure is devised and proposed here.

In a previous paper (Kim and Bathe, 2013) [1], we introduced a scheme to improve finite element displacement and stress solutions by the use of interpolation covers. In the present paper we show how the scheme can be used to automatically improve finite element solutions. As in Ref. (Kim and Bathe, 2013) [1], we focus on the use of the low-order finite elements for the analysis of solids, namely, the 3-node triangular and 4-node tetrahedral elements with the use of interpolation covers. An error indicator is employed to automatically establish which order cover to apply at the finite element mesh nodes to best improve the accuracy of the solution. Some two- and three-dimensional problems are solved to illustrate the procedure.

The free flexural vibration behaviour of a range of tapered beams is investigated by making use of the exact solutions of the governing differential equations and then imposing the necessary boundary conditions. This research is prompted by a recently published paper in Computers and Structures which used the Frobenius method of series solution but needed 130 to 300 terms in the series when solving the free vibration problem of tapered beams using the transfer matrix method. This paper investigates the same problem using a direct approach, but with a twofold purpose. The first is to show that an exact solution for the problem is possible by using Bessel functions rather than relying on a series solution which is somehow unnecessary and from a computational standpoint inefficient. The second reason for writing this paper is to broaden the scope of the recently published paper by not focusing on only one type of cross-section, but on a range of cross-sections and yet retaining the exactness of the results. The application of Bessel functions is demonstrated when developing the theory and computing the numerical results. The results presented can be used as an aid to validate the finite element and other approximate methods.

In this paper, a new geometrically exact beam formulation is presented, aiming at calculating buckling (bifurcation) loads of Euler-Bernoulli/Vlasov thin-walled beams with deformable cross-section. The resulting finite element is particularly efficient for problems involving coupling between lateral-torsional buckling and cross-section distortion/local-plate buckling. The kinematic description of the beam is geometrically exact and employs rotation tensors associated with both cross-section rotation and the relative rotations of the cross-section walls in the cross-section plane. Moreover, arbitrary deformation modes, complying with Kirchhoff's assumption, are also included, which makes it possible to capture local/distortional/global buckling phenomena. Load height effects associated with cross-section rotation/deformation are also included. The examples presented throughout the paper show that the proposed beam finite element leads to accurate solutions with a relatively small number of degrees-of-freedom (deformation modes and finite elements).

Bird strikes are a major threat to aircraft structures, as a collision with a bird during flight can lead to serious structural damage. Computational methods have been used for more than 30 years for the bird-proof design of such structures, being an efficient tool compared to the expensive physical certification tests with real birds. At the velocities of interest, the bird behaves as a soft body and flows in a fluid-like manner over the target structure, with the high deformations of the spreading material being a major challenge for finite element simulations. This paper gives an overview on the development, characteristics and applications of different soft body impactor modeling methods by an extensive literature survey. Advantages and disadvantages of the most established techniques, which are the Lagrangian, Eulerian or meshless particle modeling methods, are highlighted and further topics like the appropriate choice of impactor geometry or material model are discussed. A tabular overview of all bird strike simulation papers covered by this survey with detailed information on the software, modeling method, impactor geometry, mass and velocity as well as the target application of each study is given in the appendix of this paper.

This paper presents the development and illustrates the application of a beam finite element based on Generalised Beam Theory (GBT) and intended to analyse the elastic post-buckling behaviour of thin-walled steel members exhibiting arbitrary open cross-section and with non-standard support conditions (e.g., in-span bracing systems). After briefly reviewing the main concepts and procedures required to obtain the GBT system of non-linear equilibrium equations, the paper describes the steps involved in the numerical implementation (incremental-iterative strategy) of a non-linear beam finite element that incorporates the influence of the non-standard support conditions. Finally, the application and capabilities of the proposed GBT-based beam finite element are illustrated by means of the presentation and discussion of numerical results concerning the post-buckling behaviour of lipped I-section columns and lipped channel columns and beams with and without localised displacement restraints. For validation purposes, most GBT-based results are compared with values yielded by shell finite element analyses carried out in the commercial code Ansys.

In this paper the use of mixed time integration is proposed to increase the efficiency of welding simulation. A technique similar to the one commonly used in sheet metal forming is applied to the welding of steel plates. The welding procedure can be divided into two very distinguishable parts with significantly different characteristics. The first part, the phase of the actual welding, is a fast paced, rapidly changing process that involves highly nonlinear material behavior. The second part, the phase of cooling down, is a slow paced, slowly changing process that does not result in dramatic changes in the material behavior. In this project, explicit time integration was used for the thermo-mechanical analysis of welding and implicit time integration was proposed for the subsequent cooling phase. This paper presents examples based on the conventional fully implicit solution and the proposed explicit integration solution using the finite element codes ABAQUS/Standard and ABAQUS/Explicit, respectively.

This work deals with the numerical evaluation of the structural response of simply supported (transversally loaded at mid-span) and cantilever (subjected to tip point loads) beams built from a commercial pultruded I-section GFRP profile. In particular, the paper addresses the beam (i) geometrically linear behaviour in service conditions, (ii) local and lateral-torsional buckling behaviour, and (iii) lateral-torsional post-buckling behaviour, including the effect of the load point of application location. The numerical results are obtained by means of (i) novel Generalised Beam Theory (GBT) beam finite element formulations, able to capture the influence of the load point of application, and (ii) shell finite element analyses carried out in the code Abaqus. These numerical results are compared with (i) the experimental values reported and discussed in the companion paper (Part 1) and (ii) values provided by analytical formulae available in the literature.

The objective in this paper is to present the method for the calculation of improved stresses published by Payen and Bathe in [1] for the 4-node three-dimensional tetrahedral element. This element is widely used in engineering practice to obtain, in general, only ''guiding'' results in the analysis of solids because the element is known to be poor in stress predictions. We show in this paper the potential of this novel approach to significantly enhance the stress predictions with the 4-node tetrahedral element at a relatively low computational cost.

In this paper, a novel orthotropic layer based failure criterion for modelling progressive failure of non-crimp fabrics is presented. The strength parameters and stiffnesses needed for this failure criterion are obtained from virtual material tests. Therefore, a finite element multiscale algorithm is used to model the effect of lower scale inhomogeneities on macroscale material behavior. With this multiscale approach it is possible to make predictions for one single layer within a textile preform solely from the knowledge of the mechanical behavior of the constituents fiber and matrix and from the textile fiber architecture. The obtained stiffnesses and strengthes for one textile layer are used as input data for the novel orthotropic failure criterion presented in this paper. In order to show the workability of this failure criterion, finite element simulations of coupon tests and of a three-point bending test of a textile composite are shown and compared to experimental data.

Discontinuous behaviour provides substantial obstacles to the efficient application of mesh based numerical techniques. Accounting for strong discontinuities is presently of particular interest to the finite element research community with for example the development of cohesive and enriched elements to cater for material separation. Although strong discontinuities are of importance, of equal if not of greater interest and the focus in this paper, are weak discontinuities, which are present at any material change. A recent innovation for accounting for weak discontinuities has been the discovery of non-physical variables which are founded and defined using transport equations. This paper is concerned with the application of the non-physical approach to solidification modelling in the presence of more than one material discontinuity. A typical feature of the enthalpy-temperature response in solidification is discontinuities at phase transition temperatures as a consequence of phase change and latent heat release. In these circumstances, depending on the conditions that prevail, an element in a finite element mesh can have more than one discontinuity present. Presented in the paper is a methodology that can cater for multiple discontinuities. The non-physical approach permits the precise removal of weak discontinuities arising in the governing transport equations. In order to facilitate the application of the approach the finite element equations are presented in the form of weighted transport equations. The method utilises a non-physical form of enthalpy that possesses a remarkable source distribution like property at a discontinuity. It is demonstrated in the paper that it is through this property that multiple discontinuities can be exactly removed from an element so facilitating the use of continuous approximations. The new methodology is applied to a range of simple problems to provide an in-depth treatment and for ease of understanding to demonstrate the methods remarkable accuracy and stability.

We present in this paper a novel approach to stress calculations in finite element analysis. Rather than using the stress assumption employed in establishing the stiffness matrix, the element nodal point forces are used, in a simple way, to enhance the finite element stress predictions at a low computational cost. While this paper focuses on the improvement of the stress accuracy, the proposed procedure can also be used as a basis for error estimation. Moreover, the procedure is quite general, and has the potential for many applications in finite element analysis.

In stochastic finite element problems the solution of a system of coupled linear random algebraic equations is needed. This problem in turn requires the calculation of the inverse of a random matrix. Over the past four decades several approximate analytical methods and simulation methods have been proposed for the solution of this problem in the context of probabilistic structural mechanics. In this paper we present a new solution method for stochastic linear equations. The proposed method is based on Neumann expansion and the recently developed joint diagonalisation solution strategy. Unlike the classical Neumann expansion, here only the inversion of a diagonal matrix is needed. Numerical examples are given to illustrate the use of the expressions derived in the paper.

This paper presents a new and efficient methodology for 3D frictional contact problems based on the Generalized Newton Method with line search (GNMls). The influence coefficients modeling the behavior of solids are approached by means of the Finite Element Method (FEM) and/or the Boundary Element Method (BEM). The contact problem is based on an Augmented Lagrangian formulation and the use of projection functions to establish the contact restrictions. A new and more simplified projection operator is presented, which makes it possible to obtain a quasi-complementarity of the contact variables. As a consequence, the number of contact problem unknowns is reduced. This, together with the use of iterative resolution techniques for computing the Newton line search, results in a fast and reliable algorithm, as shown in the examples solved in this paper.

This paper presents the outcome of a large parametric numerical analysis of solid and hollow reinforced concrete piers taken from actually constructed bridges, based on a consistent three-dimensional nonlinear finite element methodology that was presented in a companion paper. Various transverse reinforcement arrangements and spacings were examined, as well as the effect of high-strength concrete on confinement effectiveness. The interpretation of numerical results mainly focuses on identifying the most convenient confinement configurations in terms of enhanced strength and ductility, as well as ease of construction and cost effectiveness. Furthermore, issues regarding confinement arrangements (often used in practice) that result in reduced section ductility are investigated and possible remedies are suggested. Finally, the broad applicability of the proposed methodology is established by application to a particularly complex (in terms of geometry and reinforcement detailing) hollow pylon section.

The paper presents an efficient way of implementing general multi-point constraint conditions in a finite element solver. The proposed method of applying and processing the multi-point constraints on the primary unknown variables of finite element method is computationally efficient and memory economical, because all constrained degrees of freedoms (DOFs) are already eliminated during the assembly of the global stiffness matrix and right-hand side vectors. The adopted concept has a wide range of use, and several of its possibilities are discussed. At the end of the paper, sample analyses of reinforced concrete structures are presented that demonstrate the advantages of the developed form for modelling discrete reinforcement bars in non-linear FE calculation in engineering practice.

This paper presents a direct integration formulation for damped structural systems in which damping is characterised by exponential law models. In effect, for non-viscously damped systems the damping forces appearing in the equation of motion are represented by convolution integrals, which take into account the complete history of the load. The proposed formulation employs the Laplace transformation of the motion equation to transform it into a differential equation with time derivative orders higher than two, in contrast to the classical M-C-K-F equation of structural dynamics. Due to the difficulty to manipulate these high order derivatives, the particular case of a damping model with only two kernel functions is taken into account. Then, an implicit direct integration scheme is proposed to discretize the motion equation, which becomes an equivalent second-order M"e"q-C"e"q-K"e"q-F"e"q equation. In contrast with other methods revised in the literature, the proposed formulation does not employ internal variables, which normally enlarge the size of the system. Besides, standard direct integration schemes such as those of Newmark's family can be employed. In the last part of the paper two numerical examples are presented: one for a three degrees-of-freedom system, and another one for a finite element application.

This paper presents a straightforward and generally applicable method for detection and elimination of errors in semi-analytical design sensitivities for any kind of FE-formulation. The basic property of the semi-analytical approach is that derivatives of the stiffness matrix and the load vector are approximated by finite differences. Obviously, truncation errors occur by this method which depend on the chosen step size and the kinematic assumptions of the mechanical model. The accuracy problems in the semi-analytical sensitivity analysis result from these approximation errors [Barthelemy B, Haftka RT. Accuracy analysis of the semi-analytical method for shape sensitivity calculation. Mech Struct Mach 1988;18:407-32]. In this contribution two beam elements (Euler-Bernoulli kinematics, Timoshenko kinematics) are utilized to emphasize the consequences of the approximation errors by an analytical computation of the error terms. These two elements show serious differences in the errors of the sensitivities. The ideas gained by these simple 1-d elements are extended further to 3-d elements with Reissner-Mindlin and Kirchhoff kinematics. The errors of the finite difference approximation of the derivatives may become serious, so it is necessary to correct them to obtain exact sensitivities. There exists a great variety of methods in the literature which try to eliminate the errors in the design sensitivities. Important contributions are published by Haftka and Adelmann, Mlejnek, Cheng and Olhoff, V. Keulen and De Boer among many others. In this paper, a method for the computation of correction factors based on product spaces of rigid body rotation vectors is presented. A straightforward derivation yields to a rigid body condition for the stiffness matrix derivative. The approximation of this derivative violates this rigid body condition due to the changed basis of the perturbed element. By the proposed method one obtains a set of correction factors related to the rigid body rotation vectors of the specific finite element. Due to the modification of the approximated stiffness matrix derivative by this set of factors one finally gets 'exact' sensitivities. The improved approximation of the stiffness matrix derivative satisfies the above mentioned rigid body condition. The basic advantage of the proposed method is the efficiency and the independence on the Finite Element formulation. In contrast to many other correction methods published so far, this approach is applicable to all kind of Finite Elements without major modifications. This gives rise to general shape optimization algorithms for a huge amount of finite elements without the necessity to derive each single element analytically.

This paper introduces an algorithm for coupling the boundary element method and the scaled boundary finite element method. Although the particular application concerns the determination of stress intensity factors at crack tips, the approach is general in nature. The motivation for the work is the combination of the semi-analytical solution accuracy of the SBFEM with the geometric flexibility of the BEM for general engineering usage. The paper presents the development of the algorithm along similar lines to FEM/BEM coupling approaches. Example problems verify the accuracy of the approach, even for coarse discretisations, and demonstrate excellent convergence properties of the algorithm.

This paper describes a response surface based optimisation technique for the calculation of envelope frequency response functions (FRFs) of imprecisely defined structures using the interval and fuzzy finite element method.The authors developed a hybrid - global optimisation and interval arithmetic - procedure for interval and fuzzy envelope FRF calculation. This hybrid approach reduces the computational cost of the analysis compared to a full global optimisation approach and reduces the conservatism on the envelope FRF compared to a full interval arithmetic approach.Still, the optimisation step is the computationally most expensive part of the algorithm. To handle industrially sized applications, a very efficient optimisation procedure is imperative. The response surface based procedure described in this paper decreases the computational cost of a fuzzy envelope FRF calculation with a factor 50 or more compared to the commonly used two-level full factorial design of experiments, while giving a comparable accuracy.

This paper brings together the principles, equations, and applications of damage modelling and elastic waves propagation, both traditional and state-of-the-art in a review form. It begins with the relevant fundamentals of damage modelling, derives the basic equations of fracture mechanics and elastic wave propagations, and covers advanced topics and applications of Lamb waves that are at the forefront of today's research. The results obtained indicate that the current approach is capable of detecting cracks and delaminations of very small size, even in the presence of considerable measurement errors. The sections are filled with case studies, worked examples and exercises that make this paper an outstanding resource.

This paper presents a coupled particle and finite element method for fluid-shell structure interaction analysis. The Moving Particle Semi-Implicit (MPS) method is used to analyze fluid flow and the MITC4 shell element is used in the FEM analysis of the structure. This paper considers partitioned coupling between the fluid and structural solvers. In order to satisfy compatibility in the employed partitioned coupling scheme, the Neumann-Dirichlet condition is applied to both the fluid and the structure. A symplectic time integration scheme is used to preserve energy when analyzing the shell structure. If the frequencies of the shell analysis are much higher than those of the MPS fluid solver, its time integration scheme is sub-cycled. When the presented coupling scheme was applied to simulate the sloshing phenomenon in an elastic thin shell structure, fluid fragmentation and large structural deformations were observed.

This paper studies the effect of the initial configurations of the governing equations on flows in a collapsible channel where the upper elastic wall is replaced by a pre-stretched beam. The aim is to check the existence of a ''tongue'' shaped neutral stability curve in the Reynolds number-tension space from a fluid-beam model [Luo XY, Cai ZX. Effects of wall stiffness on the linear stability of flow in an elastic channel. In: de Langre E, Axisa F, editors. Proceedings of the eighth international conference on flow-induced vibrations, FIV2004, vol. II. Paris, France: 2004. p. 167-70], in a properly formulated initial strain configuration. It was found that, for a given Reynolds number, as the tension is lowered to a critical value, the system becomes unstable, which is to be expected. However, a further decrease of the tension re-stabilizes the system before it becomes unstable again. It was possible that this puzzling finding was an artefact since the elastic equations used in the model were not properly derived from the zero initial stress configuration (Ogden, private communication). To check this, in this paper, a range of steady solutions are studied with both zero and non-zero initial wall tension. These are compared with the results using the finite element package Adina 8.3 using both the initial strain and initial stress configurations. As expected, the fluid-beam model agrees with Adina when using the initial stress configuration, but not when using the initial strain configuration. For cases with a small initial tension or small deformation (very large initial tension), both initial stress and initial strain configurations lead to very similar results, however, when the initial tension is comparable with the stretching induced tension, there are obvious differences in these two configurations. The ''tongue'' stability curve is then re-calculated with a zero initial tension, and re-plotted in the Reynolds number-effective tension space. It is interesting to see that though slightly different in shape, the ''tongue'' stable zone appears again when the zero initial tension is used. Thus it is highly likely that the puzzling ''tongue'' in the neutral stability curve is not due to the modelling approximation, but indicating a real, interesting physical phenomenon.

This paper presents an identification method for material parameters using the observational boundary conditions and the wavelet analysis. The material parameter identification methods which belong to the deterministic approaches are classified into the inverse and direct approaches. The proposed method combines the inverse approach and the direct approach [Swoboda G, Ichikawa Y, Dong Q, Zaki M. Back analysis of large geotechnical models. Int J Numer Meth Geomech 1999;23:1455–72, Ichikawa Y, Ohkami T. A parameter identification procedure as a dual boundary control problem for linear elastic materials. Soils Foundat 1992;32(2):35–44], and by applying the discrete wavelet transform to the system matrix of the iteration equation, we estimate unknown material parameters for the case in which the number of unknown parameters exceeds the observed data. The validity of this method is examined for geotechnical engineering problems. This paper is a revised and extended version of reference [Ohkami T, Nagao J, Koyama S. Parameter identification method using wavelet transform. In: Topping B.H.V., editor, Proceedings of the ninth international conference on civil and structural engineering computing. Civil-Comp Press, Stirling (UK); 2003; Paper 116].

In this paper, the concept that adds the interior nodes of the Lagrange elements to the serendipity elements is described and a family of enriched elements is presented to improve the accuracy of finite element analysis. By the use of the static condensation technique at the element level, the extra computation time in using these elements can be ignored. Plane stress problems are used as examples in this paper. The numerical results show that these enriched elements are more accurate than the traditional serendipity elements. The convergence rate of the proposed elements is the same as the traditional serendipity elements. The error norm of the second and third order proposed elements can be reduced from 40% to 60% when compared with the use of the traditional serendipity elements. In the numerical examples, the use of the second and third order proposed elements not only give an improvement in element accuracy but also save computation time, when the precondition conjugate gradient method is used to solve the system of equations. The saving of computation time is due to the decrease of iteration number in iteration method.

This paper investigates ways to have a computational implementation of a lower bound approach for the buckling of imperfection-sensitive shells using general purpose finite element codes. This approach was developed by Croll and others, and has been mainly employed by developing special purpose programs or analytical solutions. However, it is felt that this limits the possibilities of the user, and this shortcoming is addressed in the paper. First, the formulation is presented in a way to highlight what computations can be done following a reduced energy approach. Then, a methodology is implemented in conjunction with a general purpose program to compute the lower bound buckling load for cylindrical shells with different geometric configurations under uniform pressure. The accuracy of the procedure and the difficulties in the implementation, depending on the finite element chosen for the discretization are shown. Results demonstrate that the proposed reduced energy model can predict the lower bound load for cylindrical shells under uniform pressure distributions.