analytical and numerical study on spatial free vibration of non symmetric thin walled curved beams for spatial free vibration of non symmetric thin walled circular curved beams an accurate displacement field is introduced by defining all displacement parameters at the centroidal axis and three total potential energy functionals are consistently derived by degenerating the potential energy for the elastic continuum to that for thin walled curved beams the closed form solutions are newly obtained for in plane and out of plane free vibration analysis of monosymmetric curved beams respectively also two thin walled curved beam elements are developed using the third and fifth order hermitian polynomials in order to illustrate the accuracy and the practical usefulness of the present method analytical and numerical solutions by this study are presented and compared with previously published results or solutions by abaqus the shell element particularly effects of the thickness curvature as well as the inextensional condition are investigated on free vibration of curved beams with monosymmetric and non symmetric cross sections

influence of centerline extensibility on the in plane free vibrations of loaded circular arches free vibrations of circular arches about a prestressed static equilibrium state are investigated the equations of motion for the small amplitude free vibrations about the initial equilibrium state attained under distributed tangential and normal loading derived in a previous paper and specialized to constant curvature are used particular attention is given to the influence of centerline stretching during the vibratory motion the vanishing of the loaded free vibration frequencies signals static buckling and the load intensities at which the frequencies go to zero correspond to the static buckling loads free vibrations with no initial loading is treated as a special case of the problem considered it is shown that exact numerical values for the frequencies can be obtained in this case in general the presence of distributed initial loading precludes the possibility of obtaining closed form analytical solutions barring a few simple loading situations such as uniform constant directional pressure as the governing differential equations have variable coefficients in the present work numerical results are obtained for uniform arches subjected to gravity loading the galerkin method with polynomial trial functions that satisfy the geometric boundary conditions is employed in obtaining accurate values of free vibration frequencies convergence of the method with increasing number of terms in the assumed expansion representing the true solution is demonstrated arches with pinned and clamped end support conditions are considered considerably different frequencies are found depending upon whether one includes or ignores the influence of centerline stretching during the vibratory motion

a complete factorization of paraunitary matrices with pairwise mirror image symmetry in the frequency domain the problem of designing orthonormal paraunitary filter banks has been addressed in the past several structures have been reported for implementing such systems one of the structures reported imposes a pairwise mirror image symmetry constraint on the frequency responses of the analysis and synthesis filters around spl pi 2 this structure requires fewer multipliers and the design time is correspondingly less than most other structures the filters designed also have much better attenuation we characterize the polyphase matrix of the above filters in terms of a matrix equation we then prove that the structure reported in a paper by nguyen and vaidyanathan 1988 with minor modifications is complete this means that every polyphase matrix whose filters satisfy the mirror image property can be factorized in terms of the proposed structure

alternate bem formulations for 2 and 3 d anisotropic thermoelasticity abstract direct boundary element formulations are presented for the elastostatic analysis of two and three dimensional general anisotropic media subject to known temperature distributions the thermal effects are incorporated in the analysis through a volume integral or alternatively using particular integrals a multi region boundary element approach is adopted in which particular integrals are derived assuming a quadratic temperature distribution in each sub region a multiple regression scheme is used for the best fit quadratic temperature distribution in each sub region for temperature data given at discrete points the multi region analysis capability of the numerical implementation enhances its capacity to model discontinuous temperature fields as well as piecewise homogeneous media such as laminated composites the formulations presented are incorporated in a general purpose system and are illustrated with examples

transient heat conduction analysis of 3d solids with fiber inclusions using the boundary element method a boundary element formulation is presented in this work for transient heat conduction analysis of three dimensional 3d fiber reinforced materials the cylindrical shaped fibers in a 3d matrix are idealized by a system of curvilinear line elements with a prescribed diameter the variations in the temperature and flux fields in the circumferential direction are represented in terms of a trigonometric shape function together with a linear or quadratic variation in the longitudinal direction this approach significantly reduces the modeling effort and the computing cost the storage requirement for the convolution integrals is eliminated by adopting an accurate integration based convolution algorithm for the surface of the hole and the fibers as well as a fast convolution algorithm for the outer boundary recently developed by the present authors numerical examples are presented to demonstrate the accuracy and applicability of the proposed method of analysis of fiber reinforced materials copyright 2007 john wiley sons ltd

development of a boundary element method for time dependent planar thermoelasticity abstract a new boundary element method is developed for two dimensional quasistatic thermoelasticity this time domain formulation involves only surface quantities consequently volume discretization is completely eliminated and the method becomes a viable alternative to the usual finite element approaches after presenting a brief overview of the governing equations boundary integral equations for coupled quasistatic thermoelasticity are derived by starting with existing fundamental solutions along with an appropriate reciprocal theorem details of a general purpose numerical implementation are then discussed next boundary element methods for the two more practical theories uncoupled quasistatic and steady state thermoelasticity are developed directly from limiting forms of the coupled formulation several numerical examples are provided to illustrate the validity and attractiveness of the boundary element approach for this entire class of problems

a boundary element method for axisymmetric soil consolidation abstract the development of a time domain boundary element method for axisymmetric quasistatic poroelasticity is discussed this new formulation for the complete biot consolidation theory has the distinct advantage of being written exclusively in terms of boundary variables thus no volume discretization is required and the approach is ideally suited for geotechnicul problems involving media of infinite extent in the presentation the required axisymmetric integral equations and kernel functions are first developed from the corresponding three dimensional theory in particular emphasis is placed on the analytical and numerical treatment of the kernels this is followed by an overview of the numerical implementation and a demonstration of its merits via the consideration of several examples

multi domain two and three dimensional thermoelasticity by bem a computationally advantageous multi domain boundary element formulation is presented for uncoupled thermoelastic analysis of two and three dimensional isotropic media particular integrals capable of representing exactly a quadratic temperature distribution in both two and three dimensions are employed these particular integrals are derived using an orderly approach when temperature data are provided at discrete points the best fit quadratic distribution is generated in the least square error sense which together with a multi domain approach makes it possible to represent an arbitrary temperature distribution within acceptable bounds numerical examples are given to show the efficiency and effectiveness of the present formulation which is now incorporated in a general purpose boundary element code named gpbest

free vibration analysis of three dimensional solids by bem in practical applications it is often necessary to determine the natural frequencies and mode shapes of a solid in addition to the static response under a variety of loading conditions this paper discusses the calculation of natural frequencies and mode shapes of three dimensional solids using the boundary element method the method developed is based on the use of particular integrals of the elastic equilibrium equations and employs only real arithmetic it represents an extension to three dimensions of work previously carried out for two dimensional problems in references 1 and 15 the method has been incorporated for multiregion analysis in the best3d boundary element solution technology three dimensional computer program 11 results of the boundary element calculations are compared with analytical finite element and experimental results

a fast multi level convolution boundary element method for transient diffusion problems a new algorithm is developed to evaluate the time convolution integrals that are associated with boundary element methods bem for transient diffusion this approach which is based upon the multi level multi integration concepts of brandt and lubrecht provides a fast accurate and memory efficient time domain method for this entire class of problems conventional bem approaches result in operation counts of order o n 2 for the discrete time convolution over n time steps here we focus on the formulation for linear problems of transient heat diffusion and demonstrate reduced computational complexity to order o n 3 2 for three two dimensional model problems using the multi level convolution bem memory requirements are also significantly reduced while maintaining the same level of accuracy as the conventional time domain bem approach

two and three dimensional transient heat conduction and thermoelastic analyses by bem via efficient time convolution abstract efficient re integration based convolution algorithms are presented for a large class of problems involving transient two and three dimensional heat conduction and uncoupled thermoelastic analyses based on the earlier works of dargush and banerjee g f dargush p k banerjee application of boundary element method to transient heat conduction int j numer methods engrg 31 1991 1231 1248 g f dargush p k banerjee development of a boundary element method for time dependent planar thermoelasticity int j solids struct 25 1989 999 1021 the main motivation behind the current development is the fact that the storage based convolution approach used in earlier developments was not found to be very suitable for solving large scale practical problems because of substantial computer disk space requirement and the inability to handle time dependent boundary conditions in this paper a re integration based full convolution as well as an efficient and simplified re integration based fast convolution algorithms are presented in which all of the time convolution steps have been calculated by preserving the energy balance as expressed in the convolution while assuming equivalent values of variables to represent the total effect the accuracy and efficiency of the developed algorithms are demonstrated via numerical examples

boundary element methods for three dimensional thermoplasticity abstract a new boundary element formulation is presented for quasistatic thermoplasticity the governing integral equations utilize kernel functions based upon the fundamental solutions of uncoupled thermoelasticity thereby eliminating volume discretization except in regions where plasticity occurs as a result the boundary element approach becomes an attractive alternative to finite element methods particularly for problems involving localized plastic effects in addition the present work introduces a temperature dependent strain hardening material model and includes the body heat sources due to inelastic dissipation the entire three dimensional formulation has been implemented in a general purpose boundary element code details of this numerical implementation are provided along with results of several illustrative examples

closed form solutions of a multi cracked circular arch under static loads abstract generalised functions have been widely adopted in structural mechanics to treat singularities of beam like structures however due to the curved geometry that couples axial and transversal displacements their use has never been explored for curved beams in this paper the capability of distributions of leading to closed form exact solutions for multi cracked circular arch is shown the exact closed form solution of a circular euler arch in presence of any number of discontinuities due to concentrated damage and subjected to an arbitrary distribution of static loads is obtained damage under the form of concentrated cracks has been modeled through the widely adopted and validated equivalent elastic hinge concept and has been introduced in the governing differential equations by making use of dirac s delta functions the resulting nontrivial generalised six order differential equations have been derived and solved in closed form independently of the number of along arch concentrated cracks the solution is expressed as a function of six integration constants only in which the damage positions and intensities are given data appearing explicitly in the solution expression this latter aspect constitutes a fundamental aid towards the resolution of the static damage inverse identification problem the results have been validated through some comparisons with finite element numerical simulations examples referred to multi cracked euler arches with different boundary conditions damage and load scenarios are presented

time dependent axisymmetric thermoelastic boundary element analysis a 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

the use of stokes fundamental solution for the boundary only element formulation of the three dimensional navier stokes equations for moderate reynolds numbers this paper presents a boundary element formulation for the permanent navier stokes equations in which the well known closed form fundamental solution for the steady stokes equations is employed in this way from the integral representation formulae for the stokes equations an integral equation is found in which the original non linear convective terms of the navier stokes equations appear as a domain integral additionally the method of dual reciprocity is used to transform the domain integral to boundary integrals this method is closely related to the method of particular integrals also used in the literature to transform domain integrals to boundary integrals numerical results are presented for the three dimensional internal flow in a cylindrical container with a rotating cover in which the accuracy of the method is shown

a time domain boundary element method for poroelasticity the development of a general boundary element method bem for two and three dimensional quasistatic poroelasticity is discussed in detail the new formulation for the complete biot consolidation theory operates directly in the time domain and requires only boundary discretization as a result the dimensionality of the problem is reduced by one and the method becomes quite attractive for geotechnical analyses particularly those which involve extensive or infinite domains the presentation includes the definition of the two key ingredients for the bem namely the fundamental solutions and a reciprocal theorem then once the boundary integral equations are derived the focus shifts to an overview of the general purpose numerical implementation this implementation includes higher order conforming elements self adaptive integration and multi region capability finally several detailed examples are presented to illustrate the accuracy and suitability of this boundary element approach for consolidation analysis

boundary element methods in three dimensional thermoelasticity abstract a boundary element method is developed for the solution of time dependent problems in three dimensional thermoelasticity the time domain boundary only formulation represents the first of its kind for quasistatic analysis which by definition considers transient heat conduction but ignores the effects of inertia by eliminating the need for volume discretization the method becomes an attractive alternative to finite element analysis for this class of problems additionally because an exact green s function is used in the interior steep thermal gradients can be captured much more readily than with standard domain based methods the presentation includes details of the fundamental solution a derivation of the boundary integral equations and an overview of a general purpose numerical implementation this implementation permits the solution of large multiregion problems with arbitrary geometry and boundary conditions several examples are included to validate the proposed method as well as to highlight its usefulness

application of the boundary element method to transient heat conduction an advanced boundary element method bem is presented for the transient heat conduction analysis of engineering components the numerical implementation necessarily includes higher order conforming elements self adaptive integration and a multiregion capability planar three dimensional and axisymmetric analyses are all addressed with a consistent time domain convolution approach which completely eliminates the need for volume discretization for most practical analyses the resulting general purpose algorithm establishes bem as an attractive alternative to the more familiar finite difference and finite element methods for this class of problems several detailed numerical examples are included to emphasize the accuracy stability and generality of the present bem furthermore a new efficient treatment is introduced for bodies with embedded holes this development provides a powerful analytical tool for transient solutions of components such as casting moulds and turbine blades which are cumbersome to model when employing the conventional domain based methods

2d and 3d transient heat conduction analysis by bem via particular integrals abstract particular integral formulations are presented for 2d and 3d transient potential flow heat conduction analysis the results of the analysis are compared with an alternative formulation developed using the volume integral conversion approach although the mathematical foundation of the two methods are different both formulations are shown to produce almost identical results for the particular integral formulation the steady state heat conduction equation is used as the complementary solution and two global shape functions gsfs are considered to approximate the transient term of the heat conduction equation the numerical results for three example problems are given and compared with their analytical solutions

a new bem formulation for tow and three dimensional elastoplasticity using particular integras new two and three dimensional bem formulations are developed for elastoplastic stress analysis these new procedures differ from previous work in that volume integration is not required to incorporate the nonlinear effects in the analysis instead initial stress rates are introduced in the bem system via particular integrals the present formulation is implemented in a general purpose multi region system and examples are presented to demonstrate the accuracy and versatility of the method

analytical and numerical results for vibration analysis of multi stepped and multi damaged circular arches this paper investigates the in plane linear dynamic behaviour of multi stepped and multi damaged circular arches under different boundary conditions cracked cross sections are modelled as massless elastic rotational hinges in damaged configuration cracks can be located both at the interface between two adjacent portions as well as inside the portion itself for each arch portion bounded by two cracks the differential equations of motion have been established considering axial extension transverse shear effects and rotatory inertia the equilibrium equations of arch portions are combined in the coupled fundamental system in terms of radial displacement tangential displacement and rotation analytical and numerical solutions for multi stepped arches in undamaged as well as in damaged configurations are proposed the analytical solution is based on the euler characteristic exponent procedure involving the roots of characteristic polynomials while the numerical method is focused on the generalized differential quadrature gdq method and the generalized differential quadrature element gdqe technique numerical results are shown in terms of the first 10 analytical and numerical frequencies of multi stepped and multi damaged arches with different boundary conditions finally convergence and stability characteristics of the gdqe procedure are investigated the convergence rate of the natural frequencies is shown to be very fast and the stability of the numerical procedure is very good

free vibration of elastically coupled dual span curved beams the free vibration response of dual span extensional and inextensional circular curved beams constrained by an intermediate elastic support is studied the elastic constraint consists of a transverse and rotational spring as well as a tangential spring which couples the extensional motion of one span with the other wave propagation techniques are used to formulate the eigenvalue problem which result in exact eigensolutions the effects of the support type and stiffness on the transverse and tangential modes are examined in addition the influence of the curvature on the free response of the extensional curved beam is also addressed for certain support conditions the extensional and inextensional curved beams have similar behavior in general however the behavior of the system is shown to depend strongly on the type of support the modeling of the beam as extensional or inextensional and whether the natural frequencies are above or below the cut off frequency

a new boundary element formulation for two and three dimensional thermoelasticity using particular integrals new two and three dimensional boundary element formulations are developed for steady state and transient uncoupled thermoelasticity these new procedures differ from previous work in that additional surface or volume integration is not required to incorporate thermal loads in the analysis instead thermal body forces are introduced in the boundary element system via particular integrals the present formulation is implemented in a general purpose multi region system and examples are presented to demonstrate the accuracy and versatility of the method

analytical and differential quadrature results for vibration analysis of damaged circular arches the present paper focuses on in plane linear free vibrations of circular arches in undamaged and damaged configurations for the model herein utilized the equations of motion in terms of displacements and rotation take into account shearing and axial deformations and rotary inertia the cracked section of the arch is modeled with an elastic spring an exact analytical method of solution and an approximate numerical one are presented the first method solves the fundamental system in closed form by means of a characteristic polynomial the second one is based on a simple and efficient differential quadrature and domain decomposition technique natural frequencies and mode shapes are computed for some significant cases showing very good agreement between the two approaches

a bem formulation for transient dynamic elastoplastic analysis via particular integrals abstract this paper presents the particular integral formulation for two 2d and three 3d dimensional transient dynamic elastoplastic analyses the elastostatic equation is used for the complementary solution the particular integrals for displacement traction and stress rates are obtained by introducing the concept of a global shape function to approximate acceleration and initial stress rate terms of the inhomogeneous equation the houbolt time integration scheme is used for the time marching process the newton raphson algorithm for plastic multiplier is used to solve the system equation the developed program is integrated with the pre and post processor numerical results for four example problems are given to demonstrate the validity and accuracy of the present formulation

free vibrations of spatial timoshenko arches abstract this paper addresses the evaluation of the exact natural frequencies and vibration modes of structures obtained by assemblage of plane circular arched timoshenko beams the exact dynamic stiffness matrix of the single circular arch in which both the in plane and out of plane motions are taken into account is derived in an useful dimensionless form by revisiting the mathematical approach already adopted by howson and jemah 1999 18 for the in plane and the out of plan natural frequencies of curved timoshenko beams the knowledge of the exact dynamic stiffness matrix of the single arch makes the direct evaluation of the exact global dynamic stiffness matrix of spatial arch structures possible furthermore it allows the exact evaluation of the frequencies and the corresponding vibration modes for the distributed parameter model through the application of the wittrick and williams algorithm consistently with the dimensionless form proposed in the derivation of the equations of motion and the dynamic stiffness matrix an original and extensive parametric analysis on the in plane and out of plane dynamic behaviour of the single arch for a wide range of structural and geometrical dimensionless parameters has been performed moreover some numerical applications relative to the evaluation of exact frequencies and the corresponding mode shapes in spatial arched structures are reported the exact solution has been numerically validated by comparing the results with those obtained by a refined finite element simulation

bem analysis of free vibration problems using polynomial particular integrals abstract the development of a boundary element method for free vibration analysis using particular solutions is discussed the formulation presented is based on treating the forcing function in the governing differential equation as an initially unknown distributed body force within the domain the volume integral due to this body force is then eliminated by approximating the inertia force by global interpolation and polynomial function representations and finding particular solutions for the governing inhomogeneous equations the resulting non symmetric system matrix is solved by using a modified arnoldi s algorithm that takes advantage of the special structure of the substructured boundary element method the techniques described here are embedded in a computer program gpbest and the numerical examples arc solved by using this computer code

geometrically exact planar beams with initial pre stress and large curvature static configurations natural frequencies and mode shapes abstract within this paper an analytical formulation is provided and used to determine the natural frequencies and mode shapes of a planar beam with initial pre stress and large variable curvature the static configuration mode shapes and natural frequencies of the pre stressed beam are obtained by using geometrically exact euler bernoulli beam theory the beam is assumed to be not shear deformable and inextensible because of its slenderness and uniform closed cross section as well as the boundary conditions under consideration the static configuration and the modal information are validated with experimental data and compared to results obtained from nonlinear finite element analysis software in addition to the modal analysis about general static configurations special consideration is given to an initially straight beam that is deformed into semi circular and circular static configurations for these special circular cases the partial differential equation of motion is reduced to a sixth order differential equation with constant coefficients and solutions of this system are examined this work can serve as a basis for studying slender structures with large curvatures