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Barlow was the first to propose a method to predict optimal stress recovery points in finite elements (FEs). Prathap proposed an alternative method that is based on the variational principle. The optimal points predicted by Prathap, called Prathap points in this paper, have been reported in the literature for linear, quadratic and cubic elements. Prathap points turn out to be the same as Barlow points for linear and quadratic bar elements but different for cubic bar element. Nevertheless, for all the three elements, Prathap points coincide with the reduced Gaussian integration points. In this paper, an alternative implementation of Prathap's best-fit method is used to compute Prathap points for higher-order (viz., 4–10th order) bar elements. The effectiveness of Prathap points as points of accurate stress recovery is verified by actual FE analysis for typical bar problems. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The phenomenon of failure by catastrophic crack propagation in structural materials poses problems of design and analysis in many fields of engineering. Cracks are present to some degree in all structures. They may exist as basic defects in the constituent materials or they may be induced in construction or during service life. Using the finite element method, a lot of papers deal with the calculation of stress intensity factors for two- and three-dimensional geometries containing cracks of different shapes under various loadings to elastic bodies. In order to increase the accuracy of the results, special elements have been used. They are described together with methods for calculating the stress intensity factors from the computed results. At the vicinity of a crack tip, the strains are not always small, but they may also be large. In this case, the J-integral can also be applied to characterize the cracks in elastic or elastic–plastic bodies. This paper describes the computation of the two-dimensional J-integral for large strains to elastic and elastic–plastic bodies and represents some numerical examples. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a hypersingular integral equation for curved cracks in plane elasticity is formulated and presented. This paper describes a new numerical technique for solution of deep curved cracks in plane elasticity. In this method, the crack curve length is taken as the co-ordinate in the hypersingular integral equation of the curved crack problems. The curved crack configuration maps on the real axis with interval (-a,a), where ‘2a’ is the arc length of the crack. The original hypersingular integral equation is converted into other hypersingular integral equation which is formulated on the curve length co-ordinate, or on (-a,a). The hypersingular integral equation is solved numerically. Numerical examples prove that higher efficiency has been achieved in the suggested method. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A simple method to satisfy the homogeneous boundary condition in the element-free Galerkin method is proposed in this paper. Effectiveness of the method is demonstrated, through free vibration problems of Timoshenko beams. Several case studies involving different slenderness ratios and end conditions are carried out. The results of the present study are compared with those obtained using classical Rayleigh–Ritz and conventional element-free Galerkin method wherein Lagrangian multipliers are employed to satisfy boundary conditions. Eventhough, a one-dimensional problem is considered in the present paper, the validity of the proposed method for the two-dimensional problems is demonstrated theoretically. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper presents a general method of large strain determination over the deformed surface of a sheet metal stamping. It is demonstrated that the conventional degenerated shell element with two normal rotation degrees of freedom is not suitable for large deformation, especially when large element rotation is present. This inaccuracy is primarily caused by the fact that the displacement field description used in the degenerated shell element is only a first-order approximation with respect to the two rotation degrees of freedom, and is therefore suitable only for small rotation angles. The new method presented in this paper replaces the two rotation DOFs with three new degrees of freedom to describe the rotation of the surface normal so that the element deformation can be accurately described with no limitation on the amount of deformation and rotation involved. The advantages of this new method are: (i) a linear and accurate expression of the displacement field in terms of nodal DOFs is obtained; (ii) the formulation is easily incorporated into any existing degenerated shell elements; (iii) the strain calculation is accurate for any amount of element rigid body rotation; (iv) if the method is used in surface grid analysis, the algorithm will not only provide correct surface strains, but also their variation through the thickness direction, i.e. the bending deformation. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A variant of the boundary element method, called the boundary contour method (BCM), offers a further reduction in dimensionality. Consequently, boundary contour analysis of two-dimensional (2-D) problems does not require any numerical integration at all. The method is thus very computationally effective and accurate as shown in previous related studies. This paper presents a further development of the BCM for multi-region problems in 2-D elasticity, and an application of this development, coupled with the displacement correlation technique, to evaluating the stress intensity factors K1 and K2 for bimaterial interface cracks. Some preliminary tests conducted within this work suggest that the proposed technique is robust and able to provide highly accurate results of both K1 and K2 for this challenging class of fracture problems. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a locally refined tetrahedral mesh generation algorithm based on advancing front technique using optimization scheme with a non-uniform trial height has been developed for three dimensional forming simulations to improve the quality of the local mesh system and computational efficiency. To generate locally refined surface elements, the refinement region was identified by checking the local effective strain rate and minimum interior angle of a surface element, respectively. In addition, a limiting value for the edge length of the tetrahedron was introduced to avoid generation of extremely small triangular surface elements. The developed scheme was applied for numerical simulations of indentation and spur gear and connecting rod forging. The computational results indicate that the currently developed algorithm was successful in generating better mesh system to finish numerical simulations with relatively shorter computation time compared to the previous scheme with a uniform trial height available in the literature. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A generalized finite element for buckling analysis of tapered columns with various cross sections is established by using Chebyshev polynomial approach to the governing differential equation in this paper. The proposed formulation involves the effects of shear deformation and is therefore applicable to lattice columns. The change of the sectional properties along the length direction can be calculated exactly in the FE analysis. Buckling of a tapered lattice column, with respective lace bars and batten plates, is studied in the numerical example. The effects of shear deformation on the buckling loads of tapered lattice columns are specified. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents the use of the hypersingular integral equation method for solving the flat crack problem in shear mode. In the method, the crack opening displacement (COD) functions are assumed to be polynomials with several undetermined coefficients. The involved hypersingular integral can be reduced into a repeat integral in a particular polar co-ordinate, and further integrated by a known quadrature rule. This technique considerably reduces the effort of derivation and computation to obtain the final solution. The undetermined coefficients in the COD functions are obtained from an algebraic equation. The stress intensity factors (SIF) along the boundary of the flat crack can then be easily calculated. Numerical examples are given to demonstrate the efficiency of the proposed method. Copyright 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Dynamic problems of active optimal vibration control of elastic structures are solved by applying ‘static’ beam elements from standard structural FEM software. The approach uses an analogy between the optimality equations for the vibration control problem and the equations for the static bending of certain beams. The computer implementation of the analogy, which was presented in Part I of the paper, is discussed here in detail. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper concerns the determination of the singular stress fields in bonded bimaterial wedges under inplane loading. The mathematical complexity required for deriving the eigen solutions is avoided by an ad hoc developed one-dimensional finite element formulation. The computed eigen solutions are here adopted in the assumed stress fields of hybrid stress elements which are employed to determine the stress intensities. To illustrate the efficacy of the suggested procedure, stress intensities for cracks in homogeneous, interfacial cracks, bimaterial free edges and other configurations are computed and compared with the existing analytical/reference solutions. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper discusses algorithms for the computation of stresses and elasticity moduli for stored energy functions which are given in terms of a Seth–Hill-type generalized strain measure. The key contribution is distinct computational representations of a chain rule representation for the stresses and moduli which may serve as a basic tool for an effective numerical implementation of complex elasticity models. The representations are formulated in the Lagrangian geometric setting based on a spectral decomposition of the right Cauchy–Green tensor and contain particular representations for the case of equal eigenvalues. Two algorithmic boxes are pointed out for three- and two-dimensional problems, respectively. Furthermore, a distinct algorithmic setting is developed for applications of the Seth–Hill-type measures to the isochoric part of the deformation based on a spectral decomposition of the unimodular part of the right Cauchy–Green tensor. The computation of the stress response in connection with generalized Hookean laws is considered as a simple application. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper we consider a kinematically exact finite beam element in geometrically and materially non-linear structural analysis. The considered isoparametric plane beam element based on Reissner's stress resultant theory is capable of handling finite displacements, finite rotations and finite strains. The solution procedure used in the non-linear equilibrium path detection is based on the arc-length method with Fried's orthogonal trajectory constraint, (Fried I. Orthogonal trajectory accession to the nonlinear equilibrium curve. Computer Methods in Applied Mechanics and Engineering 1984; 47:283–297), and with the full Newton–Raphson iteration. The considered isotropically hardening elasto-plastic material model obeys the associative flow rule and a yield criterion expressed in terms of the stress resultants. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In element free Galerkin method (EFGM), only nodal data are necessary, there is no need to join nodes into elements; in addition, high accuracy can be achieved and postprocess is easy. In this paper, how to deal with point loads in EFGM is suggested and this is followed by related examples. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Based on energy functional and with the inclusion of high-order incompatible dynamic displacement modes, a formulation for 3-D finite dynamic element method (DEM) is developed and a new 8-node solid element is derived in this paper. Numerical results exhibit that the present method provides the most economical and efficient solution when compared with the usual FEM and DEM. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Based on Hellinger–Reissner functional and with the inclusion both of displacements and stresses, a hybrid stress formulation of dynamic finite element method is derived in this paper. In this formulation, the displacements are separated into zeroth displacement modes and high-order incompatible dynamic dis placement modes which are related to the dynamic characteristics. The rationality, feasibility and effec tiveness of the present method are also numerically justified. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The so-called enhanced strain finite elements are based on the enrichment of the standard compatible strain field by the introduction of additional, non-compatible strains. This class of elements can be derived starting from a partial Hu–Washizu variational principle. However, since in the original enhanced strain formulation the stress field is eliminated from the formulation, a separate least-squares procedure had to be implemented for a variational derivation of the stress field. A three-field generalized variable approach incorporating strain enhancement is proposed in the present paper within the context of linear elastic structural problems. It is shown how the original two-field enhanced strain method can be naturally recovered by suitably choosing the strain model. For this case a straightforward, but still variationally consistent stress recovery is proposed. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A triangular plate bending element, based on the generalized conforming element theory, has been formulated. The variations of the rotation and shear strain along each side are determined based on Timoshenko's beam theory. The rotation and shear strain fields within the element are then obtained using interpolation. As the plate becomes progressively thinner, the shear strain field approaches zero automatically, and thus the proposed element type is free of shear locking. The excellent performance of the proposed element type in the analysis of both thick and thin plates has been clearly illustrated in the numerical examples presented. Moreover, the formulation method presented in this paper is general, and thus can be used to develop quadrilateral elements. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper discusses an iterative scheme for solving large-scale three-dimensional linear elasticity problems, discretized on a tensor product of two-dimensional and one-dimensional meshes. A framework is chosen of the additive AMLI method to develop a preconditioner of a ‘black-box’ type which is robust with respect to discontinuities of the problem coefficients and imposes only weak (and acceptable in practice) restrictions on the choice of the meshing procedure. The preconditioner works on a hierarchical sequence of nested finite element spaces to solve the problem with arithmetic cost, nearly proportional to the number of degrees of freedom on the finest mesh. It is particularly well suited for the case when the solution is known to be strongly varying in certain subregions of the domain and the mesh is locally prerefined there to reduce the discretization error. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the relation between the incremental right stretch tensor by the total Lagrangian (T.L.) description and that by the updated Lagrangian (U.L.) description is obtained. The incremental polar decomposition method without drilling degrees of freedom is developed. The non-linear shell elements using the Biot strain tensor as the strain measure are established. The non-linear finite element formulation based on the polar composition theorem is developed with respect to the U.L. description. As a by-product the material time derivative of the right stretch tensor is given by a new form suitable for numerical evaluations. Two examples demonstrate the feasibility of the proposed incremental polar decomposition method. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a quadratic polynomial expression is used as the displacement shape function to develop the Boundary Contour Method. In this work, the divergence free property of the J integral is proved; the evaluation of the J integral is transformed, through an application of Stokes' theorem, into a linear combination of the displacement and traction at the boundary point that have been calculated by the Quadratic Boundary Contour Method such that numerical integrals are not needed at all. Numerical results are presented for two-dimensional problems, and these are compared against conventional solutions. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a six-node triangular C0 plate bending element is developed by the assumed natural strain method. In the element, all the sampled natural transverse shear strains are chosen such that the latter has a favourable constraint index and the strains are optimized with respect to a linear pure moment field. The element passes the patch tests, yields satisfactory accuracy and shows no sign of shear locking in all the problems considered. Copyright © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a simple linear tetrahedron element that can be used in explicit dynamics applications involving nearly incompressible materials or incompressible materials modelled using a penalty formulation. The element prevents volumetric locking by defining nodal volumes and evaluating average nodal pressures in terms of these volumes. Two well-known examples relating to the impact of elasto–plastic bars are used to demonstrate the ability of the element to model large isochoric strains without locking. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

For a cracked orthotropic torsion bar, the torsion compliance C is evaluated numerically in this paper. The dependence of the compliance C with respect to the crack length A will give the stress intensity factor at the crack tip. Numerical examples are given to demonstrate the influence of the elastic material constants of orthotropic materials. ©1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The major difficulty in applying the finite element method to practical problems is the design of a suitable mesh and the assessment of discretization errors. To overcome this difficulty considerable effort has been made in developing adaptive finite element methods, but most of the work has been limited to linear problems. In this paper, fundamental concepts related to error estimates and mesh refinement strategies for non-linear problems are addressed. A simple, but reliable, path-dependent error estimator is proposed. Based on the errors estimated by the present method, a mesh refinement strategy is also suggested. Numerical examples of two ideal plasticity plane stress problems are shown. The non-linear plasticity model is based on an incremental theory using the von Mises yield criterion. © 1997 by John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In the paper a mathematical formulation for embedding reinforcements in 3D brick concrete elements is presented. The computational aspects and the implementation process of the model have been discussed. The proposed algorithm may be implemented in 3D finite element programs for stress analysis of reinforced concrete structures. [ABSTRACT FROM AUTHOR]

This is a presentation of a quadrilateral finite element for wrinkled curved elastic membranes. A modified form of the deformation gradient enables us to avoid the spurious compressive stresses generated by a classical model. It results in non-linear relations for the eigeneomponents of the Cauchy stres.'; tensor. which are solved by means of a secant method. The application of the element to sail design is presented in this paper. [ABSTRACT FROM AUTHOR]

In the paper the application of the dual boundary element method to three-dimensional crack growth problems is presented. A procedure for remeshing of the free surfaces is presented to allow the simulation of surface breaking crack growth. [ABSTRACT FROM AUTHOR]

The geometrically non-linear response of a circular plate is investigated by means of a `deformation map'. The plate is subjected to static radial forces and bending moments, both uniformly distributed along the supported edges, in addition to a transverse load. The deformation map gives the complete picture for the investigated structure. The classical formulation of large deformation for the above-mentioned problem goes back to Timoshenko (1940). To create a deformation map, it is necessary to convert the boundary value problem into an initial value problem (Cauchy's problem). The Runge-Kutta (RK) method can then be used to solve numerically the equilibrium equations for the above-mentioned circular plate. In the paper several kinds of transverse loading are considered and their influence on the plate response is examined. It is shown that in some cases the plate's behavior is chaotic-like (unpredictable), in the sense that various equilibrium states are possible for a certain given set of loads. Yet, it is shown that the viscoelasticity reduces the range of the possible equilibrium states, and thus stabilizes the system. [ABSTRACT FROM AUTHOR]

The paper describes the influence of contact area on the service life of dynamically loaded gears with a crack in a tooth root. Numerical results obtained with the finite element method using the program package BERSAFE are compared with the experimental results obtained on the universal testing machine INSTRON 1255. Numerical and experimental results are in good agreement. The analysis shows that the contact area directly influences the speed and direction of the crack propagation and the service life of the gear with a crack in a tooth root. [ABSTRACT FROM AUTHOR]

The paper presents an application of the spline prism method to analyze vibration of isotropic, thick rectangular plates with two opposite edges simply supported. Three-dimensional spline prism models are formulated by combining B-spline functions with beam eigenfunctions. Because of the orthogonality of the beam functions, three-dimensional problems are reduced to a series of two-dimensional ones. To demonstrate the accuracy and convergence of the semi-numerical method, the results are compared with those obtained by other numerical methods. Good convergence and accuracy are obtained. The effects of the ratio of thickness to width and the aspect ratio on the frequencies of thick rectangular plates with several boundary conditions are analyzed, and the results are compared with those calculated by the Mindlin plate theory. [ABSTRACT FROM AUTHOR]

The paper presents boundary integral equation to two-dimensional elasticity with the stress component σijtitj as one of the boundary values, where t1 are direction cosines of the tangent on the boundary. This form of BEM has an advantage in that the stress component σijtitj on the boundary can be calculated directly from the numerical solution. The present formulation for planar problems uses two kernels, one of which is logarithmic singular and the other is 1/r singular. The effectiveness of the approach is also discussed through some test examples. [ABSTRACT FROM AUTHOR]

In the paper the experimental results considering the effects of temperature on the elastic modulus and creep of concrete arc introduced into the mathematical models of the three-dimensional finite-element method to improve the calculation of creep stresses in mass concrete structures. The Unite-element implementation of the exponential algorithm for concrete creep at variable temperatures is studied. The numerical solution procedure for thermal creep stresses in mass concrete structures with temperature effects is presented and a three-dimensional finite-element program is developed. [ABSTRACT FROM AUTHOR]

The paper reports some numerical experiments on the effectivity of the Zienkiewicz-Zhu error estimate (1987) and comparisons of two adaptive mesh generators: ADMESH, developed by Jin and Wiberg (1990) and MAD2D by Peraire et al. (1987) and Zhu et al. (1990-91). From the experiments we observe that: (1) without any empirical correction, the effectivity of the error estimate for linear triangular elements is good if post-processed continuous stresses are obtained by adequately using an iterative stress recovery procedure (Zienkiewicz et al., 1985), and is also acceptable by using a simple `averaging' procedure; (2) these two mesh generators are basically comparable. [ABSTRACT FROM AUTHOR]

The symmetric boundary-element method for mixed boundary-value problems is currently gaining increasing interest as it permits the derivation of symmetric matrices. It is even possible to obtain positive-definite finite-element stiffness matrices for BEM subregions, and therefore the method provides a very straightforward coupling to the finite-element method (FEM). The BEM subregions can be handled like FEM substructures in a domain decomposition context. The symmetric BEM uses the full set of integral representations for the 2n types of boundary data for self-adjoint problems of order 2n and solves them in a weighted residual (Galerkin) sense. The main difficulty of the method is caused by the need to compute hypersingular integrals arising from the integral representations of the Neumann boundary data. It is the object of the paper to show that, for 2-D problems on polygonal domains, these hypersingular integrands pose no problem at all, even for higher-order approximations. The present approach makes use of analytical integrations as far as possible. The integrals of the hypersingular expressions are derived completely within the framework of simple engineering mathematics. The problem is reduced to the computation of weakly singular integrals even for C0 continuous approximations. [ABSTRACT FROM AUTHOR]

This paper examines the behavior of various time-stepping schemes used in structural dynamic analysis when applied to models with negative stiffness. It is found that under such circumstances the accuracy of the numerical solution is greatly affected by the choice of integration parameters of the scheme. Optimal parameters for the Newmark family and the SS32 family have been investigated. [ABSTRACT FROM AUTHOR]

The paper describes the numerical method for calculating the crack propagation in the tooth root of a case-hardened and hardened gear. The method is based on the linear elastic fracture mechanics taking into account the total values of loadings and properties of the individual layers of the gear material. The main points are the determination of the stress intensity factor and the numerical calculations of the crack propagation, crack speed and path. [ABSTRACT FROM AUTHOR]