bluuebunny/crossref_metadata_2025_split huggingface dataset:
Constrained minimization of vibrational magnitudes using a modal reduction method
Authors: Abrahamsson T. J. S. 
Published: August 2005

AbstractA numerically effective method is suggested and applied for evaluating objective and constraint functions when so‐called vibrational magnitudes of a mechanical structure are minimized. General damped linear structures under external harmonic loading are considered. The magnitude functions studied can relate to displacements, velocities and accelerations and also to sectional and reactive forces. Both magnitudes at a specific frequency and peak magnitudes and averaged magnitudes over a frequency range are investigated. An arbitrary set of magnitude functions can be used in the constraints. Design variables are masses, dampings and stiffnesses of discrete and discretized continuous elements contained in the structure. The objective and constraint functions are expressed by use of the modal parameters (generally complex‐valued) of the structural system. A reduced modal model is established and updated during the optimization process. Approximate derivatives (sensitivities) of the objective and constraint functions with respect to changes in design variables are calculated employing perturbed modal parameters. The optimization problem is solved by use of a primal method. Numerical examples demonstrate applications to the classical damped vibration absorber with two design variables and to a beam system used in a light‐weight machine foundation with 14 design variables.
A simple non‐layered finite element for the elasto‐plastic analysis of shear flexible plates
Authors: Shi Guangyu , Voyiadjis George Z. 
Published: August 2005

AbstractA simple and accurate non‐layered plastic element which is capable of capturing the development of plastic curvatures across the thickness of the plates is presented in this paper. The influence of transverse shear forces on the plastic behaviour of plates is also investigated here. This non‐layered plastic element is based on: (i) the four‐node quadrilateral strain element for shear flexible elastic plates given by the authors; (ii) the plastic hinge formulation outlined by Shi and Atluri; and (iii) the modified Ilyushin's yield function which can account for both the development of plastic deformations across the thickness of plates and the effect of transverse shear forces. The numerical examples given here demonstrate that the present non‐layered plastic element can achieve the results obtained by the layered element model and the transverse shear forces considerably affect the plastic behaviour of plates under certain load conditions.
Limitations to the large strain theory
Authors: Cheng Y. M. , Tsui Y. 
Published: August 2005

AbstractIn the formulation of a large strain problem, the Euler–Cauchy–Stokes decomposition and the Eulerian objective stress and strain rates used for the formulation of the problem are actually applicable only for some special cases and are not suitable for general large strain and rotation rates. In this paper, the limitations and applicabilities of the conventional large strain formulation under various deformation cases will be studied.
Free vibration of axisymmetric and beam‐like cylindrical shells, partially filled with liquid
Authors: Lakis Aouni A. , Sinno Marwan 
Published: August 2005

AbstractA theory is presented for the determination of the free vibration characteristics of anisotropic thin cylindrical shells, partially or completely filled with liquid, for two circumferential wave numbers, n = 0, axisymmetric and n = 1, beam‐like. The method used was a combination of finite element analysis and classical shell theory. The shell was subdivided into cylindrical finite elements and the displacement functions were obtained using the shell equations. Expressions for the mass and stiffness matrices for a finite element and for the whole structure were obtained. A finite element was developed for the liquid in cases of potential flow. The natural frequencies of the shell, both empty and partially filled, were obtained and compared with existing experiments and other theories.
Mesh generation/refinement using fractal concepts and iterated function systems
Authors: Bova S. W. , Carey G. F. 
Published: August 2005

AbstractA novel method of mesh generation is proposed which is based on the use of fractal concepts to derive contractive, affine transformations. The transformations are constructed in such a manner that the attractors of the resulting maps are a union of the points, lines and surfaces in the domain. In particular, the mesh nodes may be generated recursively as a sequence of points which are obtained by applying the transformations to a coarse background mesh constructed from the given boundary data. A Delaunay triangulation or similar edge connection approach can then be performed on the resulting set of nodes in order to generate the mesh. Local refinement of an existing mesh can also be performed using the procedure. The method is easily extended to three dimensions, in which case the Delaunay triangulation is replaced by an analogous 3‐D tesselation.
Improving finite element predictions of modes of vibration
Authors: Mackie R. I. 
Published: August 2005

AbstractA technique is presented whereby the standard finite element approximations used in vibration analysis are modified in order to allow them to accurately predict the frequencies of the higher modes. This is done by using the results of dispersion analysis of the numerical approximations. The method is applied to the longitudinal vibration of a bar, and is shown to give good results for a uniform bar, a bar with continuously varying properties, and a bar with a step change in properties. Dispersion correction gives improved accuracy for the flexural vibration of a beam. The results of the method are also applied to the mode superposition method of dynamic analysis, and again a marked improvement in performance is obtained.
A quadrilateral hybrid‐Trefftz plate bending element for the inclusion of warping based on a three‐dimensional plate formulation
Authors: Piltner R. 
Published: August 2005

AbstractA plate formulation, for the inclusion of warping and transverse shear deformations, is considered. From a complete thick and thin plate formulation, which was derived without ad hoc assumptions from the three‐dimensional equations of elasticity for isotropic materials, the bending solution, involving powers of the thickness co‐ordinate z, is used for constructing a quadrilateral finite plate bending element. The constructed element trial functions, for the displacements and stresses, satisfy, a priori, the three‐dimensional Navier equations and equilibrium equations, respectively. For the coupling of the elements, independently assumed functions on the boundary are used. High accuracy for both displacements and stresses (including transverse shear stresses) can be achieved with rather coarse meshes for thick and thin plates.
Boundary formulations for shape sensitivity of temperature dependent conductivity problems
Authors: Kane James H. , Wang Hua 
Published: August 2005

AbstractUsed in concert with the Kirchhoff transformation, implicit differentiation of the discretized boundary integral equations governing the conduction of heat in solids with temperature dependent thermal conductivity is shown to generate an accurate and economical approach for computation of shape sensitivities. For problems with specified temperature and heat flux boundary conditions, a linear problem results for both the analysis and sensitivity analysis. In problems with either convection or radiation boundary conditions, a non‐linear problem is generated. Several iterative strategies are presented for the solution of the resulting sets of non‐linear equations and the computational performances examined in detail. Multi‐zone analysis and zone condensation strategies are demonstrated to provide substantive computational economies in this process for models with either localized non‐iinear boundary conditions or regions of geometric insensitivity to design variables. A series of non‐linear example problems is presented that have closed form solutions. Exact anaytical expressions tor the shape sensitivities associated with these problems are developed and these are compared with the sensitivities computed using the boundary element formulation.
Time dependent axisymmetric thermoelastic boundary element analysis
Authors: Dargush G. F. , Banerjee P. K. 
Published: August 2005

AbstractA boundary element method is developed for problems of quasistatic axisymmetric thermoelasticity. Unlike previous approaches, this new time domain formulation is written exclusively in terms of surface quantities, thereby eliminating the need for volume discretization. Furthermore, since the exact three‐dimensional infinite space fundamental solutions are employed, very accurate solutions are obtainable, including the determination of surface stresses.In the integral formulation, the fundamental solutions are separated into steady‐state and transient components. The steady‐state portion, which contains all of the singularities, is integrated analytically in the circumferential direction, yielding the familiar axisymmetric kernels. The remaining non‐singular transient integrands are treated by a combination of analytical and numerical quadrature.The method is implemented in a general purpose boundary element code, which includes multiregion capability along with higher order conforming surface elements. Several numerical examples are provided to illustrate the validity of the formulation and the attractiveness of this approach for practical engineenring analysis.
Coupled bending–torsional dynamic stiffness matrix for axially loaded beam elements
Authors: Banerjee J. R. , Fisher S. A. 
Published: August 2005

AbstractAnalytical expressions for the coupled bending–torsional dynamic stiffness matrix elements of an axially loaded uniform beam element are derived in an exact sense by solving the governing differential equations of motion of the beam. The influence of axial force on the coupled bending–torsional frequencies of a cantilever and hinged–hinged beam of thin‐walled section is demonstrated by numerical results. Application of the developed theory includes coupled bending–torsional frequency and mode calculations of helicopter, turbine and propeller blades, plane and space frames, and grillages consisting of axially loaded beam elements with non‐coincident mass centre and shear centre.
Vibration of shear‐deformable beams using a spline‐function approach
Authors: Dawe D. J. , Wang S. 
Published: August 2005

AbstractB‐spline functions are used as trial functions in a Rayleigh‐Ritz analysis of the free vibration of shear‐deformable Timoshenko beams. In a first approach it is demonstrated in numerical applications that when the lateral deflection and the cross‐sectional rotation are represented by functions of equal order the calculated natural frequencies are of good accuracy for stocky beams but can overestimate the true frequencies very considerably for slender beams. This is identified as a shear‐locking difficulty and consideration of its causes points clearly to the adoption of a new displacement field in which the deflection is represented by a B‐spline function which is one order higher than that used to represent the rotation. Numerical results using this new displacement field demonstrate good accuracy for both stocky and slender beams: the shear‐locking difficulty is completely eliminated. This has clear significance for the analysis of shear‐deformable plates and shells when using B‐spline functions.
Large displacement analysis of thin‐walled beams with generic open section
Authors: Conci Aura 
Published: August 2005

AbstractA finite element formulation for geometric non‐linear analysis of elastic straight thin‐walled beams is presented. The updated Lagrangian procedure is used for a stiffness matrix derivation‐to analyse large displacements or buckling behaviour of space frames. The stiffness matrix is developed for a generic cross‐section and is equally efficient for symmetric, monosymmetric or asymmetric open sections. Some non‐linear strain terms usually neglected in the literature have been considered, resulting in a formulation which also includes the initial bimoment and torsion effect for all cross‐sections analysed. The proposed method has been implemented and the results of sample problems are presented.
Boundary element analysis of two‐dimensional elastoplastic contact problems
Authors: Karami G. 
Published: August 2005

AbstractIn this paper a boundary element method for two‐dimensional elastoplastic stress analysis of frictional contact problems is presented. The bodies in contact are treated as separate regions. The contact conditions are used to join the different system of equations for different regions of contacted bodies and, hence, an overall system of equation is obtained. An incremental and iterative procedure can be used to find the contact load, or the contact extent and the proper contact conditions. To include the plastic deformation in the analysis, the initial strain algorithm is employed. Elastic‐perfectly plastic or work‐hardening material behaviour can be assumed. For the numerical analysis, an isoparametric three‐noded line elements are used to represent the boundary and eight‐noded quadrilateral or six‐noded triangular elements are used for the interior of the domain. The displacement rates and traction rates are assumed to vary quadratically and the shape functions for the interior strain rates are also of quadratic type. As an example, the behaviour of an elastic and elastoplastic body with a smooth, circular inclusion under the increasing load is presented.
Non‐singular boundary integral equation implementation
Authors: Cruse T. A. , Aithal R. 
Published: August 2005

AbstractThe basis of the boundary integral equation (BIE) development is the singular field solution for the Kelvin point load problem. The presence of the mathematical singularity in an otherwise non‐singular problem has created over the years a variety of numerical coping strategies. The current paper extends some of the earlier works in a simple manner that eliminates the mathematical singularity through analytical integration of the critical terms. The resulting formulation is fully non‐singular and is shown to be amenable to simple, low‐order Gaussian integration. The critical class of problems involving thin sections and/or highly graded BIE meshes now can be solved without previous problems and concerns the accuracy of the numerical integrations used in creating the linear BIE equations. Extension of the formulation approach to remove hypersingular formulation problems in fracture mechanics is seen to be a future beneficiary of the semi‐analytical BIE implementation reported herein.
Application of block Lanczos method for analysis of cyclic symmetric structures
Authors: Balasubramanian P. , Jagadeesh J. G. , Suhas H. K. , Ramamurti V. 
Published: August 2005

AbstractIn this study the free vibration of circumferentially periodic structures has been analysed using the block Lanczos method in a semi complex domain for extracting real natural frequencies and complex mode shapes. The influence of the number of vectors in the block and also the effect of renumbering of nodes, depending on whether they are internal, adjacent or boundary nodes, on the CPU time are studied. The efficiency of the present method is compared with the subspace iteration schemes.
An efficient implementation of stress resultant plasticity in analysis of Reissner‐Mindlin plates
Authors: Ibrahimbegović Adnan , Frey François 
Published: August 2005

AbstractAn efficient solution procedure for elasto‐plastic analysis of Reissner‐Mindlin plates has been proposed in this work. The main ingredients which render efficiency are: what appears to be an optimally tuned four‐node plate element with assumed shear strains and incompatible bending modes; an elasto‐plastic constitutive model given directly in terms of stress resultants; and efficient computation of plastic flow which simplifies to a solution of a single scalar equation and remaining state update computation. The performance of the element has been proved very satisfying in both elastic singularity‐dominated and elasto‐plastic problems.
Solution of the Helmholtz eigenvalue problem via the boundary element method
Authors: Kirkup S. M. , Amini S. 
Published: August 2005

AbstractThe numerical solution of the Helmholtz eigenvalue problem is considered. The application of the boundary element method reduces it to that of a non‐linear eigenvalue problem. Through a polynomial approximation with respect to the wavenumber, the non‐linear eigenvalue problem is reduced to a standard generalized eigenvalue problem. The method is applied to the test problems of a three‐dimensional sphere with an axisymmetric boundary condition and a two‐dimensional square.
Quartz resonator frequency shifts computed using the finite element method
Authors: Clayton Larry D. , Eernisse Errol P. 
Published: August 2005

AbstractA new solution technique has been developed to calculate the frequency shifts arising from mechanical stresses in the case of quartz resonators. This solution technique utilizes finite element analysis as an initial step to calculate mechanical stress distributions in quartz resonators. Output from the finite element solution is used in a recently developed program to calculate resonator frequency shifts as the final step. Frequency shifts are calculated via numerical integration of the perturbation integral derived by Tiersten.36The solution technique is general in that any combination of mount and resonator geometries may be modelled. Any crystallographic orientation may be chosen and any load or combination of loads may be applied to the resonator. The frequency perturbation calculation includes movement of the mode to any position in the general vicinity of the resonator centre. Experimental results for AT‐ and SC‐cut quartz resonators subjected to diametric forces and inertial loading verify the accuracy of frequency shifts calculated using the new solution technique.
A numerical method for solving the two‐dimensional unsteady solidification problem with the motion of melt by using the boundary‐fitted co‐ordinate system
Authors: Saitou Masatoshi , Hirata Akira 
Published: August 2005

AbstractA numerical method for solving the two‐dimensional unsteady solidification problem with the motion of melt is proposed. The boundary‐fitted co‐ordinate system is applied to a treatment for the moving solid‐liquid interface in cylindrical co‐ordinates with a symmetry axis. An alternating‐direction‐implicit (ADI) method is used to solve the transformed equations of motion and energy, which are expressed in terms of the vorticity and stream function. Several examples are displayed.
Boundary element method solutions for elastic wave scattering in 3D
Authors: Schafbuch P. J. , Rizzo F. J. , Thompson R. B. 
Published: August 2005

AbstractTime‐harmonic elastic wave scattering problems such as those encountered in ultrasonic non destructive evaluation are solved by the boundary element method (BEM). Selected results for spherical and spheroidal shaped voids and inclusions are compared with analytical and other numerical solutions. Results for ellipsoids, which require a full three‐dimensional formulation, are provided as a benchmark for comparison when other numerical methods would be developed for this problem class in the future. The modelling of cracklike defects with this formulation is discussed. Recent theoretical findings regarding the fictitious eigenfrequency difficulty (FED) are confirmed by a numerical study.
An approach to optimal design of structures with non‐linear response
Authors: Oblak M. M. , Kegl M. , Butinar B. J. 
Published: August 2005

AbstractA commonly adopted procedure to solve a structural optimum design problem is to improve the design iteratively by solving a sequence of simpler problems, where each of these is obtained as an approximation of the original problem. Considering structures with linear response, this procedure works very well and can be implemented quite straightforwardly. However, considering structures with non‐linear response, the situation is more sophisticated since structural stability properties have to be taken into account.The paper presents an approach to optimal design of statically loaded structures with non‐linear response. It is proposed to replace the original problem with a sequence of similar problems from which corresponding approximate problems can easily be obtained. These similar problems additionally contain an estimation of the critical load constraint while other constraints are imposed at some properly chosen load level, which is lower or at most equal to the critical load level. By this approach, the structural stability requirements are taken into account in an effective manner. The efficiency is illustrated with several examples involving kinematic as well as material non‐linear effects.
Boundary stress calculation using regularized boundary integral equation for displacement gradients
Authors: Matsumoto Toshiro , Tanaka Masataka , Hirata Hideki 
Published: August 2005

AbstractAccurate computation of boundary stress components is important in stress‐base shape optimization. The boundary element method usually gives us more accurate solutions of them compared with those obtained by the finite element method. In the present paper we propose a new approach to calculate the boundary stress components by using the regularized boundary integral equation relating the boundary displacement gradients to the tractions. Although the original integral equation must be evaluated in the sense of the Cauchy principal value, it can be regularized by subtracting and adding the displacement gradients at the source point from and to the original integral equation. When the displacement gradients satisfy the Hölder continuity at the source point, the regularized integral equation becomes non‐singular and can be evaluated numerically by using the standard Gaussian quadrature formula. The numerical implementation of the proposed integral equation is presented and the effectiveness of the approach is also discussed through some numerical demonstrations.
Finite element simulation of adaptive bone remodelling: A stability criterion and a time stepping method
Authors: Harrigan Timothy P. , Hamilton James J. 
Published: August 2005

AbstractAdaptive bone remodelling simulations which use finite element analysis can potentially aid in the design of orthopedic implants and can provide examples which test specific bone remodelling hypotheses in a quantitative manner. By concentrating on remodelling algorithms in which the geometry is fixed but the tissue stiffness changes based on strain energy density, we have predicted stability conditions for bone remodelling and we have tested the applicability of these conditions using numerical simulations. The stability requirements arrived at using a finite element formulation are similar to the requirements arrived at in an earlier analytical study. In order to test the stability conditions, we have developed an Euler backward time stepping technique which uses the derivation for stability. These simulations arrived at solutions which were impossible using Euler forward time stepping as applied in this study. Cases in which a simplified version of the derived Euler backward method are unstable or marginally stable have also been seen, but when the Euler backward method is applied using the full derived matrices, no instabilities are apparent. The results of the stability tests indicate that the converged density distributions in the examples studied are stable. Although a priori conditions which ensure stability are not found, a test for stability is provided, given an assumed density distribution.