bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the mathematical foundations of hyperthermia therapy
Authors: Kremer Jüurgen , Louis Alfred K. 
Published: November 2005

AbstractHyperthermia is an aid to standard cancer therapy. The aim is to heat up a tumour region inside the patient's body with the help of microwave radiation. The microwayes are generated by some suitable antenna array. Here we investigate the control properties of such antenna configurations and determine their resolution capabilities. We will define the hyperthermia operator, which can produce every field of any antenna array up to any degree of accuracy. We shall see that this operator is compact and we are able to compute a singular system under general assumptions explicitly. This, together with a detailed knowledge of the decay of the singular values, constitutes the tools with which we treat the previously stated problems. We examine the propagation of microwave radiation in homogeneous media and then carry over the results obtained to the case of inhomogeneous media.
Mathematical problems of liquid crystal flows
Authors: Calderer M. Carme 
Published: November 2005

AbstractThis article deals with flow phenomena in liquid crystal materials. The model that I analyse is that due to Ericksen for liquid crystals with variable degree of orientation. One of the goals is understanding the role of the order parameter in the model. I examine the multiplicity of solutions, phases, that occur in shear flow regimes and analyse their stability under physically realistic conditions. In particular, I show that ellipticity of the linearized system of governing equations is a consequence of the Clausius–Duhem inequality.
On stationary flow of asymmetric fluids with diffusion
Authors: Krzyżanowski Piotr 
Published: November 2005

AbstractWe prove existence and uniqueness theorems for weak solutions of equations describing stationary isothermic motion of a mixture of two viscous incompressible fluids with asymmetric stress tensor, in a bounded subset of ℝ3. The model of the flow we consider here assumes that some of coefficients characterizing isotropic properties of the fluid equal zero.
Inverse scattering from an open arc
Authors: Kress Rainer 
Published: November 2005

AbstractA Newton method is presented for the approximate solution of the inverse problem to determine the shape of a sound‐soft or perfectly conducting arc from a knowledge of the far‐field pattern for the scattering of time‐harmonic plane waves. Fréchet differentiability with respect to the boundary is shown for the far‐field operator, which for a fixed incident wave maps the boundary arc onto the far‐field pattern of the scattered wave. For the sake of completeness, the first part of the paper gives a short outline on the corresponding direct problem via an integral equation method including the numerical solution.
On the bending of plates with transverse shear deformation and mixed periodic boundary conditions
Authors: Constanda Christian , Lobo Miguel , Pérez Eugenia 
Published: November 2005

AbstractThe method of matched asymptotic expansions is used to find a homogenized problem whose solution is an approximation to the solution of a mixed periodic boundary value problem in the theory of bending of thin elastic plates. A critical size for the fixed parts of the boundary is found such that the boundary condition of the homogenized problem is an intermediate case between that for the clamped edge plate and that for the free boundary plate.
On some second‐order non‐linear systems of a hyperbolic‐parabolic type
Authors: Chrzȩszczyk Andrzej 
Published: November 2005

AbstractWe consider local solutions to the Cauchy problem for a class of non‐linear hyperbolic‐parabolic systems generalizing the systems of elasticity and thermoelasticity. Our main purpose is to relax the usual regularity requirements to include the nonclassical solutions into considerations.
A method of computing numerically integrated stiffness matrices
Authors: Gupta Ajaya K. , Mohraz Bijan 
Published: November 2005

AbstractA method of formulating and computing numerically integrated stiffness matrices is presented. Through a better organization of the formulation which is easily achieved by the use of index notation, the computations for integrating and evaluating the element stiffness matrix are substantially reduced. For cases in which the terms of the material property tensor are not functions of position co‐ordinates (elastic isotropic and anisotropic materials), a further reduction in computation is achieved by multiplying the material property‐tensor after the numerical integration has been carried out.
Elastic‐plastic analysis of Saint‐Venant torsion problem by a hybrid stress model
Authors: Yamada Y. , Nakagiri S. , Takatsuka K. 
Published: November 2005

AbstractAn application of the finite element method to inelastic analysis of the Saint‐Venant torsion problem, using a triangular element formulated on the basis of the hybrid stress approach, is described. The stress field in the element is defined by a stress function which is assumed to vary linearly within the element. The warping function on the element boundary is also defined by a linear expression. Numerical results indicate that the method gives an accurate stress solution and is appropriate to the elastic‐plastic analysis of bars of arbitrary cross‐section which may include multiply connected regions. It is further shown that such phenomena as planar orthogonal plastic anisotropy, strain‐hardening and unloading of relevant twisted bar can be treated in a unified manner.
A finite element, linear programming methods for the limit analysis of thin plates
Authors: Faccioli E. , Vitiello E. 
Published: November 2005

AbstractFinite elements having linear moment distributions and use of linearized yield criteria allow one to determine lower bounds to the collapse load of thin plates as solutions of linear programs.The method is quite general and rigorously meets the requirement of the lower bound theorem of limit analysis for concentrated or line load distributions. Ways of treating distributed surface loads are also discussed and tested.Actual bounds are computed for a variety of plate problems governed by Tresca yield criterion and compared with previous solution obtained from higher order stress elements and non‐linear optimization techniques. The comparison shows that the present method can yield accurate bounds with considerably shorter computer times and relatively small number of elements. Additional tests show that numerical convergence to the limit loads is assured by suitable refinement of the mesh pattern.
Design parameter variation and structural response
Authors: Romstad K. M. , Hutchinson J. R. , Runge K. H. 
Published: November 2005

AbstractA general power series method is developed to aid in obtaining changes in the response variable due to changes in design parameters. The approach is considered for eigenvalue problems and systems of simultaneous equations which may represent static, dynamic and stability response problems. Particular emphasis is placed upon the eigenvalue problem and techniques for improving the calculations form the power series are suggested utilizing modified Rayleigh quotient expressions. Each of the methods proposed is treated computationally by the formulation of a finite element solution of column elastic stability. Investigations of solution accuracy versus percentage variation in element stiffness, whether the method underestimates or overestimates the changes, and the required number of eigenvalue solutions are presented.
Stability criteria for explicit finite difference solutions of the parabolic diffusion equation with non‐linear boundary conditions
Authors: Milton James L. , Goss William P. 
Published: November 2005

AbstractThe criteria for stability of the explicit finite difference solution of the one‐dimensional, transient, conduction heat transfer problem with both radiant and convection heat transfer at the boundaries are considered in this paper. These criteria are governed by an inequality set from a functional relationship between the newly calculated and the old temperature at each node.From the node with the most stringent criteria, it is shown that setting the coefficient of the old temperature equal to zero in the governing difference equation is not sufficient for a general criterion. On the other hand, setting the derivative of the new temperature with respect to the old temperature equal to zero in the governing difference equation presents a simple, straightforward technique for obtaining a sufficient condition for a stable system. It is further shown that the second law of thermodynamics, written in explicit finite difference form, does present a necessary criterion for stability. However, the second law, because it is in the form of an inequality, does not present as simple a criterion as the derivative method does.The specific problem studied is a finite thickness slab, initially at a uniform temperature, but instantaneously subjected to both radiation and convection on its two surfaces. Temperature profiles were calculated on a digital computer and are presented in dimensionless graphical form over a range of five dimensionless parameters. A plot that relates stability to the maximum time‐step size for the entire range of practical conditions of radiation numbers is also presented.
Optimized prestressing by linear programming
Authors: Kirsch Uri 
Published: November 2005

AbstractThe problem of optimizing the prestressing force and the tendon configuration for an indeterminate prestressed structure with prescribed cross‐sectional dimensions is formulated in linear programming form, The structure is subjected to multiple load conditions and constraints are related to the structural behaviour and to the tendon configuration.It is shown that the number of behaviour constraints at each point in the structure can be reduced, as they represent parallel hyperplanes in the design space. Necessary conditions for feasible solutions are derived. The method based on transformation of the design variables, is suitable for beams, frames, grids and plates. Its application is illustrated for the case of a prestressed bridge.
Comparison of some penalty function based optimization procedures for the synthesis of a planar truss
Authors: De Silva B. M. E. , Grant G. N. C. 
Published: November 2005

AbstractThe present investigation examines the multibar truss optimization problem in the context of a general class of unconstrained optimization procedures in conjunction with various types of penalty function transformations. Specifically, the problem is transformed into a series of unconstrained minimization problems using the penalty function techniques of Heaviside and SUMT. These are solved using the methods of Rosenbrock (orthogonal directions), Powell (conjugate directions) and Nelder–Mead (Simplex). This resulted in many cases in substantial improvements being recorded over previously reported data. The paper includes a comparative study of the synthesis based on these procedures.
Transient shell response by numerical time integration
Authors: Krieg Raymond D. , Key Samuel W. 
Published: November 2005

AbstractIn using the finite element method to compute a transient response, two choices must be made. First, some form of mass matrix must be decided upon. Either the consistent mass matrix prescribed by the finite element method can be employed or some form of diagonal mass matrix may be introduced. Secondly, some particular time integration procedure must be adopted. The procedures available divide themselves into two classes: the conditionally stable explicit schemes and the unconditionally or conditionally stable implicit schemes. The choices should be guided by both economy and accuracy. Using exact discrete solutions compared to the exact solutions of the differential equations, the results of these choices are displayed. Concrete examples of well‐matched methods, as well as ill‐matched methods, are identified and demonstrated. In particular, the diagonal mass matrix and the explicit central difference time integration method are shown to be a good combination in terms of accuracy and economy.
The efficient finite element analysis of rectangular and skew laminated plates
Authors: Kolář V. , Němec I. 
Published: November 2005

AbstractVarious solutions of laminated plates by the finite element method are analysed. An efficient solution of skew (or rectangular) laminated plates with small effect of σz and ϵz stress and strain components is developed. It can be used with an arbitrary number of layer elements (sub‐elements) in different plate elements. Some remarks to the possible modification of solution are presented. Numerical examples with a short discussion and conclusions complete the paper.
On the generalization of equicofactor matrices
Authors: Kardestuncer H. 
Published: November 2005

AbstractEguicofactor properties of the entities occurring in electric networks and discrete elastic systems extend beyond the present definition of such entities. For instance, the zero‐sum property of these matrices is, in fact, a particular version of a broader definition. The generalization is accomplished in using higher order submatrices as opposed to scalars (submatrices of order 1) in the present literature.
Rate of convergence for the iterative approach in elastic‐plastic analysis of continua
Authors: Yamamoto Yoshiyuki 
Published: November 2005

AbstractIn connection with the finite element method, the iterative approach has been commonly used for the analysis of elastic‐plastic continua. The rate of convergence of iteration is investigated in the present paper; it depends largely upon the ratio of tangent modulus to Young's modulus, accuracy of the first guess for the exact solution and occurrence of unloading. In the case of finite displacements the rate of convergence is closely related to the stability characteristics of the continua in the sense of Shanley.
Fluid‐structure dynamic interaction and wave forces. An introduction to numerical treatment
Authors: Zienkiewicz O. C. , Bettess P. 
Published: November 2005

AbstractThe paper presents an introduction to two general approaches used in the soluation of coupled structures and fluid systems in which effects of large scale flow are excluded. In the first approach, the Lagrangian, the fluid is simply treated as a ‘solid’ with a negligible shear modulus. In the second method, Eulerian, a single pressure variable is used in the fluid.The numerical problems posed, discretization methods used and possible simplifications are discussed.
A displacement method for the analysis of vibrations of coupled fluid‐structure systems
Authors: Hamdi Mohamed Ali , Ousset Yves , Verchery Georges 
Published: November 2005

AbstractA variational principle in terms of displacements in the fluid and the structure with a penalty for irrotationality of displacement in the fluid is developed for the analysis of harmonic vibrations of ideal compressible fluid and elastic structure systems. Its Discretization by the finite element method leads to an algebraic eigenvalue problem with a positive definite symmetric banded matrix. Numerical examples obtained for pure acoustic cases and coupled cases show the efficiency of the method.
Optimum design of prestressed concrete slabs using primal geometric programming
Authors: Ramamurthy S. 
Published: November 2005

AbstractPrestressed concrete members, because of the use of high strength materials and the efficient disposition of tensile forces, need considerably less material. This and other advantages, however, are offset by the high unit costs of materials and the associated specialized labour. Thus, it is important to make the most of the savings in materials through the application of optimum design procedure. Among the available optimization techniques, generalized geometric progamming (GGP) is ideally suited because the design equations of prestressed concrete members are expressible in the form of polynomials. Using the GGP, in this study, a set of minimum prestress force designs are obtained for various depths of one‐way slab. From the data thus obtained a minimum cost design procedure is explained. Moreover, the need for supplementary non‐prestressed reinforcement to obtain economical designs for depths of slab beyond a certain depth is also shown.
On the efficient time integration of systems of second‐order equations arising in structural dynamics
Authors: Enright W. H. 
Published: November 2005

AbstractFixed stepsize low‐order methods are the most widely used technique for solving the second‐order initial value problems that arise in structural dynamics. In this paper we shall describe the special stability difficulty that arises with this class of problem and we will outline how variable stepsize techniques can cope with this difficulty and result in efficient numerical methods.
Large deflections and large‐amplitude free vibrations of straight and curved beams
Authors: Reddy J. N. , Singh I. R. 
Published: November 2005

AbstractThis paper is concerned with the large‐deflection (bending and free vibration)analysis of thin elastic curved beams by conventional and mixed finite element methods. The conventional finite element method is based on the total potential energy expression, whereas the mixed method is based on a Reissner‐type variational statement and involves the bending moments and deflections as primary dependent variables. Incremental and direct formulations are presented for both methods. The nonlinearity is included in the numerical method via an iterative procedure (i.e. the in‐plane force due to the large deflection is not treated as constant but included under the integral in the energy expression). In the case of vibrations, the transverse shear and rotary inertia effects are also included. A number of numerical examples of beams with various edge conditions are analysed for deflections and natural frequencies, and the results are compared with those reported in the literature.
Derivation of geometrically nonlinear finite shell elements via tensor notation
Authors: Harte R. , Eckstein U. 
Published: November 2005

AbstractTo develop geometrically nonlinear, doubly curved finite shell elements the basic equations of nonlinear shell theories have to be transferred into the finite element model. As these equations in general are written in tensor notation, their implementation into the finite element matrix formulation requires considerable effort. The present paper will demonstrate how to derive the nonlinear element matrices directly from the incrementally formulated nonlinear shell equations using a tensor‐oriented procedure. This enables the numerical realization of all structural responses, e.g. the calculation of pre‐ and post‐buckling branches in snap‐through analysis and especially in bifurcation analysis, including the detection of critical points and the consideration of geometric imperfections. To avoid loss of accuracy care is taken for a realistic computation of the geometric properties as well as of the external loads. Finally, the developed family of shell elements will be presented and its efficiency will be demonstrated by some applications to linear and geometrically nonlinear structural phenomena.
Shape design sensitivity analysis for non‐linear anisotropic heat conducting solids and shape optimization by the BEM
Authors: Meric R. A. 
Published: November 2005

AbstractShape design sensitivity analysis (SDSA) expressions have been derived for non‐linear anisotropic heat conducting solid bodies by following the material derivative concept and adjoint variable method of optimal shape design given in the literature. The variation of a general integral functional has been described in terms of primary and adjoint quantities evaluated at the varying boundaries. As an example problem in shape optimization, optimal outer boundary profiles of an orthotropic solid body are obtained by the boundary element method (BEM), after reformulating the SDSA equations in a form which is most suitable for the BEM.
An element‐by‐element method for heat conduction CAE including composite problems
Authors: Buratynski Edward K. 
Published: November 2005

AbstractMechanical computer aided engineering (CAE) implies large finite element problems due to the geometric complexity of the ‘true’ 3D designs. Application of the standard finite element technique is not practical for such problems because the direct solution of the global matrix equations is too costly. This paper considers the element‐by‐element implicit algorithm for the CAE application of transient heat conduction. The direct solution is avoided by an operator splitting or approximate factorization technique. This results in both the execution time and storage requirements for each time step being linearly proportional to the number of elements while retaining unconditional stability. However, the approximate factorization introduces additional truncation error and incorrect jump conditions at material interfaces. Detailed analyses and numerical experiments are carried out in one dimension to assess the nature and mechanism of these inaccuracies. A three dimensional implementation is then compared with one dimensional results. The need for an additional predictor–corrector element‐by‐element algorithm for 3D composite problems is also presented.
Ill‐Conditioned equations in kinematics and dynamics of machines
Authors: Park Taewon , Haug Edward J. 
Published: November 2005

AbstractDuring mechanical system kinematic and dynamic analysis, linear and non‐linear algebraic equations must be solved. Algebraic equations are often ill‐conditioned, due either to physical singularities or large numerical errors, in which case solutions may have large errors or analysis methods may fail. Causes of ill‐conditioned problems are studied and illustrated with examples. Ill‐conditioned matrices and matrix condition numbers are discussed and an efficient and reliable indicator of ill‐conditioned matrices is suggested. In constrained kinematic and dynamic analysis, equations are solved repetitively, so symbolic factorization is used. The ill‐conditioning problem due to symbolic factorization is discussed and methods of detecting ill‐conditioning are suggested. Three examples are studied to demonstrate the effectiveness and use of condition numbers and ill‐conditioned system detection methods.
A numerical study of laminar and turbulent flows in a two‐dimensional bend with or without a guide vane
Authors: Kotb N. A. E. , Mokhtarzadeh‐Dehghan M. R. , Ward‐Smith A. J. 
Published: November 2005

AbstractA numerical study of the flow in a two‐dimensional 90° circular‐arc bend is presented. The study is based on the solution of the governing equations using a finite volume technique. Both laminar and turbulent flows are considered. Particular attention is given to the occurrence and size of the separation regions and, in this respect, the effects of Reynolds number and bend radius to height ratio are discussed. The study includes the effect of a guide vane, placed in the bend, on the flow characteristics. It is shown that the emerging velocity distribution is more uniform than that associated with flow in a bend without a guide vane. The presence of a guide vane is shown to suppress the formation of regions of flow separation. Comparisons are made between the effects on the flow of two different designs of guide vane.