bluuebunny/crossref_metadata_2025_split huggingface dataset:
A new discrete Kirchhoff‐Mindlin element based on Mindlin–Reissner plate theory and assumed shear strain fields—part II: An extended DKQ element for thick‐plate bending analysis
Authors: Katili Irwan 
Published: August 2005

AbstractThis is the second part of a two‐part paper on plate bending elements with shear effects included.This paper presents a new four‐node, 12‐d.o.f. quadrilateral plate bending element valid for the analysis of thick to thin plates. The element called DKMQ, has a proper rank (contains no spurious zero‐energy modes), passes the patch test for thin and thick plates in an arbitrary mesh and is free of shear locking. Very good results have been obtained for thin and thick plates by the element. An extended DKT element for thick‐plate bending analysis is evaluated in Part I.19
Convex multilevel decomposition algorithms for non‐monotone problems
Authors: Stavroulakis G. E. , Panagiotopoulos P. D. 
Published: August 2005

AbstractA convex, multilevel decomposition algorithm is proposed in this paper for the solution of static analysis problems involving non‐monotone, possibly multivalued laws. The theory is developed here for a model structure with non‐monotone interface or boundary conditions. First the non‐monotone laws are written in the form of a difference of two monotone functions. Under this decomposition, the non‐linear elastostatic analysis problem is equivalent to a system of convex variational inequalities and to non‐convex min‐min problems for appropriately defined Lagrangian functions. The solution(s) of each one of the aforementioned problems describe the position(s) of static equilibrium of the considered structure. In this paper a multilevel optimization scheme, due to Auchmuty,1 is used for the numerical solution of the problem. The most interesting feature of this method, from the computational mechanics' standpoint, is the fact that each one of the subproblems involved in the multilevel algorithm is a convex optimization problem, or, in terms of mechanics, an appropriately modified monotone ‘unilateral’ problem. Thus, existing algorithms and software can be used for the numerical solution with minor modifications. Numerical results concerning the calculation of elastic and rigid stamp problems and of material inclusion problems with delamination and non‐monotone stick‐slip frictional effects illustrate the theory.
A lanczos‐based technique for exact vibration analysis of skeletal structures
Authors: Smith H. A. , Sorensen D. C. , Singh R. K. 
Published: August 2005

AbstractThis paper presents and discusses a Lanczos‐based eigensolution technique for evaluating the natural frequencies and modes from frequency‐dependent eigenproblems in structural dynamics. The new solution technique is used in conjunction with a mixed finite element modelling procedure which utilizes both the polynomial and frequency‐dependent displacement fields in formulating the system matrices. The method is well suited to the solution of large‐scale problems.The new solution methodology presented here is based on the ability to evaluate a specific set of parameterized non‐linear eigenvalue curves at given values of the parameter through an implicitly restarted Lanczos technique. Numerical examples illustrate that the implicitly restarted Lanczos method with secant interpolation accurately evaluates the exact natural frequencies and modes of the non‐linear eigenproblem and verifies that the new eigensolution technique coupled with the mixed finite element modelling procedure is more accurate than the conventional finite element models. In addition, the eigenvalue technique presented here is shown to be far more computationally efficient on large‐scale problems than the determinant search techniques traditionally employed for solving exact vibration problems.
A finite element procedure for axisymmetric elastomeric solids under general loading
Authors: Marusak Ronald E. , Becker Eric B. 
Published: August 2005

AbstractA finite element procedure, which utilizes Fourier series, is developed to compute the large deformations and deflections in axisymmetric elastomeric solids subjected to non‐axisymmetric loading. Nearly incompressible and incompressible, isotropic strain energy density functions describe the elastic properties. The nearly incompressible functions become compatible with an analytical integration scheme by using a novel variable to approximate the dilatation. A large spherical elastomeric bearing is analysed with this procedure.
Discontinuous displacement approximation for capturing plastic localization
Authors: Larsson Ragnar , Runesson Kenneth , Ottosen Niels Saabye 
Published: August 2005

AbstractIt is proposed to capture localized plastic deformation via the inclusion of regularized displacement discontinuities at element boundaries (interfaces) of the finite element subdivision. The regularization is based on a kinematic assumption for an interface that resembles that which is pertinent to the classical shear band concept. As a by‐product of the regularization, an intrinsic band width is introduced as a ‘constitutive’ property rather than a geometric feature of the finite element mesh. In this way the spurious mesh sensitivity, which is obtained when the displacement approximation is continuous, can be avoided. Another consequence is that the interfacial relation between the elements is derived directly from the conventional constitutive properties of the continuously deforming material. An interesting feature is that the acoustic tensor will not only play a role for diagnosing discontinuous bifurcation but will also serve as the tangent stiffness tensor of the interface (up to within a scalar factor). An analytical investigation of the behaviour of the interface is carried out and it is shown that dilatation may indeed accompany slip within a ‘shear’ band for a general plasticity model. The significance of proper mesh alignment is demonstrated for a simple problem in plane strain and plane stress. It is shown that a unique structural post‐peak response (in accordance with non‐linear fracture mechanics) can be achieved when the plastic softening modulus is properly related to the bandwidth. The paper concludes with a numerical simulation of the gradual development of a shear band in a soil slope.
On a finite element method for dynamic contact/impact problems
Authors: Taylor Robert L. , Papadopoulos Panayiotis 
Published: August 2005

AbstractThis paper addresses the formulation and discrete approximation of dynamic contact/impact initial‐value problems. The continuous problem is presented in the context of non‐linear kinematics. Standard semi‐discrete time integrators are introduced and are shown to be unsuccessful in modelling the kinematic constraints imposed on the interacting bodies during persistent contact. A procedure that bypasses the aforementioned difficulty is proposed by means of a novel variational formulation. Numerical simulations are conducted and the results are reported and discussed.
Adaptively shifted integration technique for finite element collapse analysis of framed structures
Authors: Toi Yutaka , Isobe Daigoro 
Published: August 2005

AbstractThe present study is concerned with the improvement of the previously proposed ‘shifted integration technique’ for the plastic collapse analysis of framed structures using the linear Timoshenko beam element or the cubic beam element based on the Bernoulli‐Euler hypothesis. In the newly proposed ‘adaptively shifted integration technique’, the numerical integration points for the evaluation of the stiffness matrices are automatically shifted immediately after. the occurrence of plastic hinges according to the previously established relations between the locations of numerical integration points and those of plastic hinges. By using the adaptively shifted integration technique, sufficiently accurate solutions can be obtained in the non‐linear frame analysis by two‐linear‐element or only one‐cubic‐element idealization for each structural member. The present technique can easily be implemented in the existing finite element codes utilizing the linear or the cubic beam element.
A Hermite interpolation algorithm for hypersingular boundary integrals
Authors: Gray L. J. , Soucie Carol San 
Published: August 2005

AbstractThis paper presents a conforming C1 boundary integral algorithm based on Hermite interpolation. This work is motivated by the requirement that the surface function multiplying a hypersingular kernel be differentiable at the collocation nodes. The unknown surface derivatives utilized by the Hermite approximation are determined, consistent with other boundary values, by writing a tangential hypersingular equation. Hypersingular equations are primarily invoked for solving crack problems, and the focus herein is on developing a suitable approximation for this geometry. Test calculations for the Laplace equation in two dimensions indicate that the algorithm is a promising technique for three‐dimensional problems.
Numerical simulation of ultrasonic transmission through curved interface
Authors: Goswami P. P. , Rudolphi T. J. 
Published: August 2005

AbstractThe direct boundary integral equation formalism is used to model reflected and transmitted wave fields due to a bounded ultrasonic beam incident upon an arbitrarily curved interface separating a fluid and a solid media. The numerical procedure involves application of point collocation with quadratic isoparametric approximation that reduce the integral equations to a discrete set of linear algebraic equations. Numerical results are provided for plane, concave and convex interfaces for incident beam profiles which are Gaussian or approximately rectangular. The case of surface wave excitation on a plane interface is considered and features of their numerical solution are discussed. Constraints on the various parameters of the numerical model and their effects on the accuracy of the solution are investigated in detail.
A numerical investigation of the effect of boundary motion on viscous channel flow
Authors: Abdulnour Bashar S. 
Published: August 2005

AbstractThe steady, laminar, incompressible flow past a moving boundary in the entry region of a two‐dimensional channel is considered in this study. The formation of a separated region during the upstream motion of a section of the lower boundary is of particular interest. The size of the separated region depends on the Reynolds number, and on the velocity and length of the moving boundary as well. A numerical solution is obtained from the continuity and the complete Navier‐Stokes equations, subject to the appropriate boundary conditions. The describing equations are expressed in terms of the vorticity and the stream function. The alternating‐direction implicit method is used to solve the vorticity equation while the successive over‐relaxation method is used to solve, the stream function equation. The present numerical scheme is second‐order‐accurate since both the finite‐difference equations and boundary conditions have second‐order accuracy.
A boundary element analysis of metal matrix composite materials
Authors: Mammoli A. A. , Bush M. B. 
Published: August 2005

AbstractThe numerical modelling of metal matrix composites is an important part of the research now being conducted on these materials. Due to the numerical complexity of a fully three‐dimensional analysis, two‐dimensional approximations are normally used with finite element methods. While these analyses are informative, they cannot treat complex particle shapes or examine three‐dimensional effects in the composite. The use of boundary element methods in place of the more widely used finite element methods significantly reduces the computing power necessary to obtain a solution to a given problem, making it possible to simulate fully three‐dimensional geometries. In the present paper a two‐dimensional form of the BEM is applied to the study of metal matrix composite materials, and its performance compared with that of similar FEM stadies. We also compare the predicted composite properties with existing and new experimental results. We conclude that the BEM is an effective tool for the analysis of this class of problems.
A novel isoparametric finite element displacement formulation for axisymmetric analysis of nearly incompressible materials
Authors: Yu H. S. , Houlsby G. T. , Burd H. J. 
Published: August 2005

AbstractIt is well accepted that severe numerical difficulties arise when using the conventional displacement method to analyse incompressible or nearly incompressible solids. These effects are caused by the kinematic constraints imposed on the nodal velocities by the constant volume condition. In elastic‐plastic analysis, these effects are due to a conflict between the plastic flow rule and the finite element discretization. Although several methods have been proposed to cope with this problem, none has been based on the appropriate choice of displacement interpolation functions to minimize the constraints. The theoretical formulation of a new six‐noded isoparametric displacement finite element, which is well suited for elastic‐plastic analysis of axisymmetric constrained solids by using a rational displacement interpolation function, is presented in this paper. The proposed displacement interpolation function implies that the displacement in the axial direction and the product of the displacement in the radial direction and the radius should be treated as two independent basic variables. Alternatively, the proposed displacement interpolation function can also be implemented in a conventional displacement formulation simply by using a modified shape function matrix. The suitability of the proposed formulations is first studied theoretically by assessing the number of degrees of freedom per constraint and then verified by performing numerical experiments on typical boundary value problems which involve incompressible behaviour.
Exact integration of constitutive equations in elasto‐plasticity
Authors: Ristinmaa Matti , Tryding Johan 
Published: August 2005

AbstractA unified approach is presented for establishing exact integration of the constitutive equations in elastoplasticity, assuming the total strain‐rate direction to be constant. This unified approach includes all previous exact integration procedures as special cases and, in addition, some new closed‐form solutions are derived for combined kinematic and isotropic hardening. Special emphasis is laid on combined kinematic and isotropic hardening for von Mises' material and on isotropic hardening for Mohr‐Coulomb and Tresca materials.
A two‐dimensional frost‐heave model for buried pipelines
Authors: Shah Ketan R. , Ghani Razaqpur A. 
Published: August 2005

AbstractThe rigid‐ice model of frost heave is one of the most comprehensive frost‐heave models but is restricted to one‐dimensional cases in its present form. In this paper, the model is extended to two‐dimensional problems. The complete formulation of the partial differential equations governing heat, moisture and ice transport in freezing soils is provided. The equations are subsequently solved using the Galerkin finite element method in space and the finite difference method in time. A computer program is developed for the two‐dimensional rigid‐ice model. A case of freezing around chilled gas pipeline is solved and the numerical results are compared with experimental values, with good agreement between the two sets of results.
A dynamic infinite element for three‐dimensional infinite‐domain wave problems
Authors: Zhao Chongbin , Valliappan S. 
Published: August 2005

AbstractA three‐dimensional dynamic infinite element which satisfies the following requirements: (1) displacement compatibility on the interface between finite and infinite elements; (2) definition of the wave propagation and amplitude attenuation behaviours in the infinite element using wave propagation functions; (3) convergence of the generalized integrals related to mass and stiffness matrices of the infinite element: and (4) displacement continuity along the common boundary of neighbouring infinite elements in the case of simulating multiple material layers or multiple wave numbers within the foundation, is presented in this paper. Since P‐waves, S‐waves and R‐waves in the foundation can be simulated Simultaneously in the present infinite element, the seismic response of an arch‐dam‐foundation system, especially a thin double‐curvature arch‐dam‐foundation system where the boundary element loses its competitive capacity with the finite element, can be economically calculated by coupling this infinite element with conventional finite elements. The good accuracy obtained using the present infinite element and finite element coupling model to simulate foundation wave problems has been proven by comparing the current numerical results with previous analytical results.
Finite element mesh control by integer programming
Authors: Tam T. K. H. , Armstrong C. G. 
Published: August 2005

AbstractA novel technique is presented for the control of mapped quadrilateral and hexahedral meshes generated inside a collection of connected subregions. Target division numbers on the subregion edges are given as input. By allowing these numbers to vary, meshes can be found which satisfy both the subregion constraints imposed by the mesh patterns being employed, and the compatibility constraints on edges shared by two or more adjacent subregions. Among all such feasible solutions the optimal one is obtained by minimizing the changes to the division numbers, using an integer programming technique.
High‐order hierarchical A‐ and L‐stable integration methods
Authors: Möller Peter W. 
Published: August 2005

AbstractNumerical integration of stiff first‐order systems of differential equations is considered. It is shown how a C0‐continuous polynomial time discretization, in conjunction with a weighted residual method, can be used to derive methods corresponding to the diagonal and first subdiagonal Padé approximants. In this manner A ‐stable schemes of order 2k and L‐stable schemes of order 2k ‐ l are obtained, at least for k ⩽ 4. The methods are hierarchical in the sense that a scheme with a given accuracy embraces the equations of all lower‐order methods that have the same stability type. We show how this feature may be utilized to perform partial refinements in the integration process, and how an error estimation by an embedding approach naturally follows. An adaptive algorithm based on the error estimator is suggested. Some numerical experiments that illustrate the ideas are included.
Some notes on singular integral techniques in boundary element analysis
Authors: Huang Q. , Cruse T. A. 
Published: August 2005

AbstractThe paper presented here reviews the numerical techniques used currently to calculate the singular integrals and nearly singular integrals in the boundary element analysis. Some incorrect algorithms published before are discussed and a new numerical technique to calculate the nearly singular integral is developed. The numerical results show a significant improvement in both accuracy and efficiency compared to the traditional adaptive Gaussian quadrature and subdivision techniques.
Patch recovery based on superconvergent derivatives and equilibrium
Authors: Wiberg Nils‐Erik , Abdulwahab Fethi 
Published: August 2005

AbstractIn this paper a postprocessing technique is developed for determining first‐order derivatives (fluxes, stresses) at nodal points based on derivatives in superconvergent points. It is an extension of the superconvergent patch recovery technique presented by Zienkiewicz and Zhu. In contrast to that technique all flux or stress components are interpolated at the same time, coupled by equilibrium equations at the superconvergent points. The equilibrium equations and use of one order higher degree of interpolation polynomials of stress give a dramatic decrease in error of recovered derivatives even at boundaries.
Elastic interactions of a fatigue crack with a micro‐defect by the mixed boundary integral equation method
Authors: Lua Yuan Jie , Liu Wing Kam , Belytschko Ted 
Published: August 2005

AbstractIn this paper, the mixed boundary integral equation method is developed to study the elastic interactions of a fatigue crack and a micro‐defect such as a void, a rigid inclusion or a transformation inclusion. The method of pseudo‐tractions is employed to study the effect of a transformation inclusion. An enriched element which incorporates the mixed‐mode stress intensity factors is applied to characterize the singularity at a moving crack tip. In order to evaluate the accuracy of the numerical procedure, the analysis of a crack emanating from a circular hole in a finite plate is performed and the results are compared with the available numerical solution. The effects of various micro‐defects on the crack path and fatigue life are investigated. The results agree with the experimental observations.
Sweepline algorithm for unstructured‐grid generation on two‐dimensional non‐convex domains
Authors: Fang Jiunn , Parpia Ijaz. H. , Kennon Stephen R. 
Published: August 2005

AbstractThe sweepline algorithm has been modified to triangulate a set of nodes on a non‐convex domain. The new method is based on a fragile sweepline which is split and rejoined in a manner which ensures that boundaries are preserved. Both the original and the modified algorithms are introduced using simple examples. It is shown that a set of N nodes is triangulated in O(N log N) time. The validity of the new method has been confirmed through testing on a variety of problems, and two test cases are presented in this paper.
A non‐linear numerical method for accurate determination of limit and bifurcation points
Authors: Chan Siu Lai 
Published: August 2005

AbstractThis paper presents a numerical procedure for accurate determination of a limit or a bifurcation point. The method minimizes simultaneously the first and the second variations of an admissible functional or iterates to satisfy the equilibrium and the semi definite condition for the tangent stiffness matrix. It can be readily incorporated into a computer program for non‐linear finite element analysis to improve its accuracy in the location of critical points.
Static and dynamic analysis of wind turbine blades using the finite element method
Authors: El Chazly N. M. 
Published: August 2005

AbstractAnalysis of forces and stresses of horizontal axis propellers and turbines has been the subject of increased interest in recent years because of the need to develop adequate analytical tools for the design and evaluation of‐wind turbine rotors.Most of the structural failures of wind turbines occur in the blade root section. Hence, a three‐dimensional analytical model to compute the deflection, stresses and eigenvalues in the rotor blades is proposed using bending triangular plate finite elements.Both membrane and bending stiffness are considered in deriving the element stiffness matrix. The consistent mass matrix is used in generating the overall mass matrix. Lift and drag forces created in steady wind conditions are analysed as normal and tangential forces on the blade sections at certain angles of attack. These forces are applied as boundary loads to the computer program to analyse statically and dynamically rotor blades of symmetrical aerofoil NACA 0015 series. Constant chord, tapered and twisted blades were analysed at rated and survival wind speeds.The validity of the computer program used was verified by applying it to a standard cantilever box beam using the beam theory.The results showed that maximum stresses occurred at the root of the blades for all configurations in the spanwise direction and that a tapered blade, in addition to saving material weight, diminished the stresses obtained. The twisting of the blade leads to an increase in stiffness and a decrease in the stresses.