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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]

This paper treats a united-form solution for a point force applied at the interior of an infinite transversely isotropic solid. Several heuristic functions are adopted to obtain the expressions of the solution based on the general solution. To exclude some indeterminate attributes, the expressions are rewritten. In the final expressions, unlike previous publications where the solutions are expressed in different forms, or when some individual constants have different definitions depending on the conditions satisfied by the elastic constants, we provide united solutions which are suitable for all stable transversely isotropic materials and isotropic materials. Thus accurate numerical evaluation of the boundary element method can be performed directly without the need to resolve the singularity algebraically. Some numerical examples with BEM are also presented in this paper. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The virtual contact loading method (VCLM), a highly efficient numerical method to solve elastic contact problems, is proposed in this paper. Having applied virtual loads on the possible contact region (PCR) of a structure system, we carried out the usual finite-element calculations only once and made a local iteration analysis in PCR then the contact region (shape and size), contact state (stick, slide or mixed), contact normal and shear stress distributions, and the stress and displacement fields in contact bodies were all obtained simultaneously. This method is very simple and easy to use. The elastic contact problems for cylinder-cylinder are solved in this paper and the results agree well with those in previous work. [ABSTRACT FROM AUTHOR]

Currently, there is major interest within the biomedical community in developing accurate non-invasive means for analyzing bone micro-structure. This paper presents a new approach for a multi-scale finite element (FE) analysis of a trabecular structure. Two domain decomposition approaches are investigated as a basis for computational analysis at the micro-scale level, which is then applied for solving a 2D elasticity FE problem. In addition, a homogenization procedure from micro- to macro-scale level is presented. The proposed new multi-scale FE method has the potential to provide new insights into bone structure and behavior. Moreover, it is expected that the outcomes of this research will develop into a computerized virtual biopsy system. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper describes the development of an efficient and accurate algebraic multigrid finite element solver for analysis of linear elasticity problems in two-dimensional thin body elasticity. Such problems are commonly encountered during the analysis of thin film devices in micro-electro-mechanical systems. An algebraic multigrid based on element interpolation is adopted and streamlined for the development of the proposed solver. A new node-based agglomeration scheme is proposed for computationally efficient, aggressive and yet effective generation of coarse grids. It is demonstrated that the use of appropriate finite element discretization along with the proposed algebraic multigrid process preserves the rigid body modes that are essential for good convergence of the multigrid solution. Several case studies are taken up to validate the approach. The proposed node-based agglomeration scheme is shown to lead to development of sparse and efficient intergrid transfer operators making the overall multigrid solution process very efficient. The proposed solver is found to work very well even for Poisson's ratio >0.4. Finally, an application of the proposed solver is demonstrated through a simulation of a micro-electro-mechanical switch. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper proposes a Trefftz method for evaluating the T-stress for cracks emanating from a hole in a rectangular plate. In this method, the displacement and the stress field are an elasticity solution, which is derived from complex potentials. The complex potentials are assumed in a series form with undetermined coefficients. After using the minimum potential energy principle, an algebraic equation for the undetermined coefficients can be formulated. The coefficients can be obtained from the equation, and the whole stress field is determined. Stress intensity factor and T-stress can be evaluated immediately from the known solution. Merit of the suggested method is addressed. For three particular cases, R=0, R/w=0.25 and R/w=0.5, the computed results are tabulated. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents the implementation of Reissner's (J. Appl. Math. Phys. 1972; 23:795–804) strain–displacement relations for a planar beam using a variable order secant matrix (VOSM) technique. The secant matrices are formed using a Taylor expansion of the strain energy and hence the order of the secant and tangent matrices to be included in the nonlinear analysis can be varied depending upon the degree of nonlinearity involved in the problem. Nevertheless, a maximum of 24 matrices is sufficient to obtain predicted internal stress resultants to within 0.2% of the converged solution in all the problems tested. Using a three-noded isoparametric beam element, the accuracy of the VOSM method is demonstrated for the elastic postbuckling of arches. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents an approach which allows the solution of elastic problems concerning a half-space (half-plane) with cavities by the boundary integral equation methods using Neumann's series. To evaluate the series terms at singular points, the regular representations of singular integrals for the external problems were proven and the regular recurrent relationships for the series terms, which can be calculated by any known quadrature rule, are obtained. The numerical proposed procedure was tested by comparison with known theoretical solution and the method convergence was studied for various depths of a buried cavity. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We developed in this paper a variational formulation of heat diffusion equation applicable to the flat shell context and cellular structures. For this purpose, we introduce the average mid-surface temperature field, through-the-thickness gradient and their dual generalized fluxes. Moreover, we introduced radiative heat exchange in the same way, which leads to a non-linear and unsymmetrical thermal discrete problem. The model performance is illustrated by several numerical examples concerning cellular structures like hollow clay bricks submitted to thermal loading. Thermo-mechanical coupling for such structure which is well adapted to the shell-like modelling approach, is presented in the elastic regime with the numerical results concerning temperature field and forces. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The computational significance of the case of two or three equal principal stretches in large deformation analysis is investigated in this paper. A detailed analytical study shows that the previously suggested solutions, based on numerical perturbations, are not adequate and might lead to erroneous results. A number of examples are presented to illustrate the approach. Copyright © 2005 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 presents an application of the boundary element method to the analysis of plate structures subjected to arbitrary loadings. Using a multi-region technique to assemble plate structures, boundary element formulation for a shear deformable plate bending are coupled with the formulation for plane stress elasticity. Additional equations required to solve the problem are obtained by imposing the compatibility and equilibrium conditions along interface edges. Several examples with different configurations and loadings are presented to demonstrate the effectiveness of the proposed method. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The main idea of the paper is to introduce the second-order perturbation second probabilistic moment extension of the finite difference method (FDM). The approach can be successfully applied to all these engineering analyses where FDM modelling is still useful and some structural parameters are treated as random variables or fields. The main advantage of the stochastic finite difference method (SFDM) proposed is relatively easy extension of the existing deterministic results in the classical theory of elasticity on the random or even stochastic problems. A very attractive aspect can be the usage of the SFDM in the stochastic signals processing in a conjunction with the wavelet optimized FDM. 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]

The paper presents an extension of a stress resultant based axisymmetric shell element by Reissner to the elasto-plastic computations. In the elastic range, the element exhibits exact kinematics for large displacements and rotations thus enabling the use of large increments in the global equilibrium path continuation. In order to preserve this desired property also in the elasto-plastic range, the general closest point projection algorithm is utilized for the elasto-plastic stress increment computation. In the case of the used element, consistent linearization of the stress updating algorithm results in a very simple form so that the element offers an efficient and computationally cheap approach to the large deflection elasto-plastic axisymmetric shell problems. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper revisits the real variable fundamental solution approach to the Boundary Integral Equation (BIE) method in two-dimensional orthotropic elasticity. The numerical implementation was carried out using quadratic isoparametric elements. The strong and weakly singular integrals were directly evaluated using Euler's transformation technique. The limiting process was done in intrinsic coordinates and no separate numerical treatment for strong and weak singular integrals was necessary. For strongly singular integrals a priori interpretation of the Cauchy principal value is not necessary. Two problems from plane stress and strain are presented to demonstrate the numerical efficiency of the approach. Excellent agreement between BEM results and exact solutions was obtained even with relatively coarse mesh discretizations. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The conventional boundary integral equation in two dimensions is non-equivalent to its corresponding boundary value problem when the scale in the fundamental solution reaches its degenerate scale values. An equivalent boundary integral equation was recently derived. This equation has the same solution as the boundary value problem of differential equations. This paper presents the boundary contour method based on the equivalent boundary integral equation for two-dimensional linear elasticity. The method requires only numerical evaluation of potential functions and gives correct equivalent results to the boundary value problem of differential equations in two dimensions. Numerical results are presented for some examples. The present approach is shown to give excellent results in illustrative examples. Meanwhile, the traction results from the BCM based on the conventional displacement boundary integral equation are incorrect. 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]

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 dual reciprocity boundary element method traditionally uses the linear radial basis function r for interpolation. Recently, however, the use of the r function has been questioned both in relation to accuracy and in relation to the number and position of internal nodes required to obtain satisfactory solutions. Much research has been done in an attempt to fix criteria for choosing which approximation function should be used. One of the alternatives recently suggested is the augmented thin plate spline function, which consists of a thin plate spline function, r2 log(r), augmented with the first three terms of a Pascal triangle expansion. In this paper families of similar functions are obtained by augmenting radial basis functions with appropriate global expansions: these functions will be called hybrid approximate functions. It will be shown that using an appropriate hybrid function accurate results can be obtained for many body forces or pseudo body forces in elasticity without the need for internal nodes.© 1997 John Wiley & Sons, Ltd. [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]

The paper deals with the symbolic integration of a 4-noded isoparametric finite element for plane elasticity. An efficient approach to generate explicit formulas for computing the elementary stiffness matrix is discussed. The procedure is based on the use of the Derive symbolic manipulation code as well as in a posteriori manipulation of the expressions obtained. The accuracy of the results is tested in extremely distorted and geometrically ill-conditioned elements. Three practical engineering models are presented and the accuracy of the results is discussed. A computer time comparison between both numerical and symbolic integration approaches is also included, showing that relevant CPU savings are obtained when applying symbolic integration. [ABSTRACT FROM AUTHOR]

This paper presents a novel dual reciprocity formulation for elasticity problems with body forces in which the approximating functions are given in terms of augmented thin plate splines (ATPS). It is shown that the ATPS approximation is capable of correctly representing gravitational and centrifugal body forces, and provides superior accuracy for general load cases. [ABSTRACT FROM AUTHOR]

The paper investigates the convergence of the h-, p- and hp-versions of a variational symmetric boundary element method (BEM) in plane elasticity by numerical experiments. The study discusses mixed boundary value problems on polygonal domains, i.e. problems for which the exact solution is analytic except in a finite number of points. The convergence of the error in energy norm is displayed for all versions of the BEM. All results are also compared with those obtained by the corresponding finite element methods. The theoretically predicted asymptotic convergence rates for all versions of the method can be observed in the numerical experiments. A comparison of computer times is given as well. [ABSTRACT FROM AUTHOR]

An essential requirement for a satisfactory curved shell finite element is a capability for exact representation of rigid body movements: otherwise serious difficulties can occur, as is well known from early developments in shell finite element analysis. It is shown in this paper that appropriate assumed displacement fields for a particular shallow curved shell finite element with 18 degrees of freedom can be obtained in a very simple, yet apparently novel, way which permits the exact recovery of all rigid body movements. The shallow curved shell finite element considered here is constructed on a triangular flat facet approximation to a general thin elastic shell; it has quadratic middle surface geometry to allow for accurate modeling of arbitrary curvatures. [ABSTRACT FROM AUTHOR]

Mindlin-type plate and shell finite elements are the most widely used ones in the analysis of laminated composite structures. In the commercially available finite element programs, the transverse shear correction factors for these elements are usually the same as for structures made of isotropic materials. In the paper the shear correction factors are determined using energy principles for general laminates in cylindrical bending. Results for various materials and laminates are presented. [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]

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]

Reports on the award received by assistant professor Sanjay Govindjee for his paper "Computational Methods for Inverse Deformations in Quasi-incompressible Finite Elasticity," published in the November 15, 1998 issue of the "International Journal for Numerical Methods in Engineering." Award prizes; Purpose of the award.