a new boundary element method for bending of plates on elastic foundations abstract the bending of plates on a winkler foundation according to kirchhoff s theory is solved by using an original boundary integral equation method involving the fundamental solution for plate flexure problems an integral representation for the second member pressure of the foundation of the equation is given by discretizing the integral equation it is possible to eliminate the boundary unknowns so that one is reduced to solving a linear system the solutions of which are deflections inside the domain to illustrate the potentialities of this method several problems with various boundary conditions loads and values of the modulus of the foundation are successfully solved

a control theory for cartesian flexible robot arms in this article we first use a fourth order partial differential equation with boundary conditions to model a flexible robot arm on a moving base with a payload at the tip end through the state space formulation we show that such a system is both controllable and observable in an infinite dimensional hilbert space we also show that the system is stabilizable via a feedback control

wave interactions in nonlinear elastic strings we study a system modeling the dynamics of a nonlinear elastic string this is a 6 6 system of hyperbolic conservation laws which is degenerate in that two wave families have multiplicity two we construct the wave curves for this problem and solve the riemann problem we then give a detailed analysis of elementary wave interactions leading to a glimm theorem and describe features of the system when the total variation is large there are complicated wave patterns including infinitely many interactions in finite time and both three and four resonances may be present

green s functions of two dimensional anisotropic plates containing an elliptic hole abstract for a two dimensional anisotropic plate the green s function satisfying traction free boundary conditions around an elliptic hole is developed using stroh s formalism a combination of this function and the boundary element method shows that it is the most effective approach for solving hole problems the generality of the present green s function is shown by the broader meaning of the following words two dimensional includes not only in plane but also antiplane problems and the problems where in plane and anti plane deformations couple each other anisotropic which need not have any material symmetry restrictions means that it covers the solutions given in the literature which only deal with orthotropic or monoclinic materials elliptic includes the special case where the minor axis of the ellipse tends to zero i e the case of a griffith crack the accuracy of the numerical method presented is then verified by comparison with exact or accepted solutions of several examples such as an infinite or a finite plate with an elliptic hole or a crack under in plane or anti plane loading the materials used are isotropic orthotropic or laminated composites finally problems where the hole boundary is not traction free are solved such as rigid inclusions and pin loaded holes

sup norm stability for glimm s scheme we consider the cauchy problem for a general n n system of conservation laws existence of solutions was proved by glimm using his celebrated random choice scheme in this paper we obtain a third order interaction estimate analagous to that obtained by glimm for 2 2 systems by using this estimate and identifying a global cancellation effect we obtain l stability for solutions generated by glimm s scheme as an immediate consequence we have l1 stability and l decay obtained by temple for 2 2 systems 1993 john wiley sons inc

the non homogeneous biharmonic plate equation fundamental solutions abstract real materials and structural components are often non homogeneous either by design or because of the physical composition and imperfections in the underlying material thus analytical solutions for non homogeneous materials under mechanical loads are of considerable interest to engineers and have widespread applications given the prevalence of these materials in fields as diverse as aerospace construction electronics etc more precisely those are essentially composites with carefully manufactured properties that yield desirable mechanical characteristics and properties such as optimal arrangement of the material minimum weight etc to this end the displacement fundamental solution or green s function corresponding to a point force for the non homogenous biharmonic equation in two dimensions are derived in this work by employing a conformal mapping technique in conjunction with the radon transformation these functions besides being useful in their own right can also be used within the context of integral equation formulations for the solution of boundary value problems finally a series of numerical examples that deal with the non homogeneous plate on elastic foundation problem serve to illustrate the present method

blowup with small bv data in hyperbolic conservation laws we construct weak solutions of 3 3 conservation laws which blow up in finite time the system is strictly hyperbolic at every state in the solution and the data can be chosen to have arbitrarily small total variation this is thus an example where glimm s existence theorem fails to apply and it implies the necessity of uniform hyperbolicity in glimm s theorem because our system is very simple we can carry out explicit calculations and understand the global geometry of wave curves

on the mathematical model for linear elastic systems with analytic damping in the present paper we investigate linear elastic systems with damping ddot y b dot y ay 0 in hilbert spaces where a is a positive definite unbounded linear operator and b is a closed linear operator related in various ways to a alpha frac 1 2 leqq alpha leqq 1 we discuss the spectral property of these systems and obtain some fundamental results for the holomorphic property and the exponential stability of the semigroups associated with these systems

a new symmetric and positive definite boundary element formulation for lateral vibrations of plates abstract a new symmetric and positive definite boundary element method in the time domain is presented for the dynamic analysis of thin elastic plates the governing equations of the problem are obtained from a variational principle in which a hybrid modified functional is employed the functional is expressed in terms of the domain and boundary basic variables in plate bending assumed to be independent of each other in the discretized model the boundary variables are expressed by nodal values whereas the internal displacement field is modelled by a superposition of static fundamental solutions the equations of motion are deduced from the functional stationarity conditions and they constitute a linear system of ordinary differential equations expressed in terms of nodal displacements the structural operators are frequency independent and preserve the symmetry and definiteness properties of the continuum moreover these operators are calculated by performing boundary integrations of regular kernels only some applications to free vibrations and self excited vibrations under aerodynamic loads have been worked out to test the accuracy of the proposed method the numerical results have been found in very good agreement with those obtained by using other solution techniques by which the accuracy of the present boundary element model is demonstrated

wave scattering by cracks in inhomogeneous continua using biem elastic wave scattering by cracks in inhomogeneous geological continua with depth dependent material parameters and under conditions of plane strain is studied in this work a restricted case of inhomogeneity is considered where poisson s ratio is fixed at one quarter while both shear modulus and density profile vary with depth but proportionally to each other furthermore time harmonic conditions are assumed to hold for this type of material the body wave speeds remain macroscopically constant and it becomes possible to recover exact green functions for the crack free inhomogeneous continuum by using an algebraic transformation method proposed in earlier work as a first step in a subsequent step the complete elastodynamic fundamental solution along with its spatial derivatives and an asymptotic expansion for small argument are all derived in closed form using the radon transform next a non hypersingular traction based boundary integral equation method biem formulation for solving boundary value problems with internal cracks is presented specifically the biem is used for computing stress intensity factors and scattered wave displacement amplitudes for an inclined line crack in an otherwise inhomogeneous continuum that is being swept by either pressure waves or vertically polarized shear waves at an arbitrary angle of incidence with respect to the horizontal direction the numerical results obtained herein reveal substantial differences between homogeneous and continuously inhomogeneous materials containing a crack in terms of their dynamic response where the latter case is assumed to give a more realistic representation of geological deposits compared to the former one finally these types of examples plus the benchmark case used for validation serve to illustrate the present approach and to show its potential for solving complex problems not just in geophysics but also in mechanics

a dual reciprocity boundary element solution method for the free vibration analysis of fluid coupled kirchhoff plates abstract a boundary element solution method is proposed for linear vibration analysis of fluid coupled thin plates the method is based on replacing the associated biharmonic operator with two successive harmonic operators leading to a coupled system of boundary integral equations with simpler properties the fundamental solution has an elementary form and complicated singularity removal techniques can be avoided the fluid flow due to the plate motion is taken as a potential field and its effect on the plate dynamics is incorporated into the analysis by invoking another boundary integral solution described over the fluid plate interface the body terms in the plate boundary integral equations are considered by the dual reciprocity boundary element formulation three different radial basis functions are employed as interpolation functions alone and augmented with polynomial and sine expansions to represent the body terms the performance of the method is investigated from several perspectives by adopting plates with different shapes and or boundary conditions excellent approximations are obtained in general the convergence behavior is consistent both dry and wet frequency parameters are predicted accurately and the mode shapes are captured even with rough models in some of the studied problems however deviated results are obtained for specific modes furthermore it is observed that the performance of the method depends on the implemented drm functions and combining radial basis functions with global expansions does not yield noticeable improvements

a hybrid boundary node method a new variational formulation for boundary node method bnm using a hybrid displacement functional is presented here the formulation is expressed in terms of domain and boundary variables and the domain variables are interpolated by classical fundamental solution while the boundary variables are interpolated by moving least squares mls the main idea is to retain the dimensionality advantages of the bnm and get a truly meshless method which does not require a boundary element mesh either for the purpose of interpolation of the solution variables or for the integration of the energy all integrals can be easily evaluated over regular shaped domains in general semi sphere in the 3 d problem and their boundaries numerical examples presented in this paper for the solution of laplace s equation in 2 d show that high rates of convergence with mesh refinement are achievable and the computational results for unknown variables are most accurate no further integrations are required to compute the unknown variables inside the domain as in the conventional bem and bnm copyright 2001 john wiley sons ltd

orientation and stabilization of a flexible beam attached to a rigid body planar motion the author considers a flexible structure modeled as a rigid body which rotates in inertial space a light flexible beam is clamped to the rigid body at one end and free one is clamped at the other it is assumed that the flexible beam performs only planar motion the equations of motion are obtained by using free body diagrams two control problems are posed namely the orientation and stabilization of the system it is shown that suitable boundary controls applied to the free end of the beam and suitable control torques applied to the rigid body solve the problems posed above the proofs are obtained by using the energy of the system as a lyapunov functional

riesz basis approach to the stabilization of a flexible beam with a tip mass using an abstract condition of riesz basis generation of discrete operators in the hilbert spaces we show in this paper that a sequence of generalized eigenfunctions of an euler bernoulli beam equation with a tip mass under boundary linear feedback control forms a riesz basis for the state hilbert space in the meanwhile an asymptotic expression of eigenvalues and the exponential stability are readily obtained the main results of siam j control optim 36 1998 pp 1962 1986 are concluded as a special case and the additional conditions imposed there are removed

the boundary node method for three dimensional linear elasticity the boundary node method bnm is developed in this paper for solving three dimensional problems in linear elasticity the bnm represents a coupling between boundary integral equations bie and moving least squares mls interpolants the main idea is to retain the dimensionality advantage of the former and the meshless attribute of the later this results in decoupling of the mesh and the interpolation procedure for problems in linear elasticity free rigid body modes in traction prescribed problems are typically eliminated by suitably restraining the body however an alternative approach developed recently for the boundary element method bem is extended in this work to the bnm this approach is based on ideas from linear algebra to complete the rank of the singular stiffness matrix also the bnm has been extended in the present work to solve problems with material discontinuities and a new procedure has been developed for obtaining displacements and stresses accurately at internal points close to the boundary of a body copyright 1999 john wiley sons ltd

making the boundary element method less sensitive to changes or errors in the input data to solve a problem by the boundary element method requires a solution of an integral equation by discretizing the boundary the integral equation is reduced to a set of linear algebraic equations if the matrix in algebraic equation is not diagonal dominant or more precisely poorly conditioned then the accuracy of the numerical solution becomes very sensitive to small changes in the input data small errors in the input data or changes in the mesh description can change the solution drastically in this paper a scheme is described which improves the condition of the matrix furthermore it also reduces the sensitivity of the condition of the matrix to changes in the mesh description the ideas described are applicable to any boundary element formulation however the numerical examples are from two dimensional elastostatics solved by the indirect version of the boundary element method

reduction of nonhomogeneous quasilinear 2 2 systems to homogeneous and autonomous form by using the invariance with respect to suitable lie groups of point transformations necessary and sufficient conditions are determined allowing one to map through an invertible point transformation nonhomogeneous and nonautonomous quasilinear 2 2 systems to homogeneous and autonomous form the procedure is constructive and the new independent and dependent variables are obtained by determining the canonical variables associated with the lie groups of point symmetries admitted by the source system various examples of physical interest arising from different contexts are considered

a feedback control and a simulation of a torsional elastic robot arm a feedback control is designed for a torsional elastic robot arm to be exponentially stable and to arrive at any designated position an eigenvalue problem is discussed and a finite dimensional approximation theorem is proposed and proved based on the numerical analysis and the approximation theorem we can simulate the system and show that the bending vibration the torsional vibration the rigid turning angle and the bending moment of the robot arm can be controlled in a short period of time

robust control of flexible structures a case study a comparison is made between three partial differential equation models for a flexible beam with different types of damping and varying parameter values robust controllers can be designed to stabilize all linear systems whose transfer functions lie within a ball in the l norm given a nominal model for our flexible beam we calculate which sets of models can be stabilized by the same finite dimensional robust controller by stabilize we mean here that the poles of the system are moved to the left of the line re s 0

stabilization of beams by pointwise feedback control a flexible structure consisting of serially connected euler bernoulli beams with co located sensors and actuators is considered controls are point forces and point bending moments applied at the nodes it is known that uniform exponential stability can be achieved with linear velocity feedback a sensitivity analysis of the system s spectrum with respect to feedback coefficients is set up it is also proved that in a particular case exponential decay rate can be obtained from the spectrum of the system

a boundary integral equation method for bending of orthotropic plates abstract a boundary integral equation method for bending of thin orthotropic linear elastic plates with polygonal planform under quasistatic pressure loading is presented a change from huber s differential equation for the deflection to the simpler biharmonic equation of kirchoff s isotropic plate theory by means of a linear transformation of the plate domain renders a non classical boundary value problem the transformed plate is embedded in a basic rectangular domain coincidence of boundaries is applied as far as possible using green s matrix of the basic isotropic plate a vectorial boundary integral equation for a fictitious density function vector is developed which has to be defined on part of the actual boundary only solution generally is achieved by a numerical procedure and green s matrix is split into a regular and a singular part analytic integrals of the latter are independent of the special choice of the basic domain having solved the integral equation all interesting state variables within the isotropic domain are evaluated by means of integration and may be transformed back to the original orthotropic plate in a simple manner method is tested in example problems

harmonic reproducing kernel particle method for free vibration analysis of rotating cylindrical shells abstract a meshfree approach the harmonic reproducing kernel particle method is proposed for the free vibration analysis of rotating cylindrical shells the reproducing kernel particle estimation is employed in hybridized form with harmonic functions to approximate the two dimensional displacement field this is the first instance in which a meshless technique has been adopted for rotating shell dynamics this technique provides ease of enforcing various types of boundary conditions and concurrently is able to capture the traveling modes the effects of centrifugal and coriolis forces as well as the initial hoop tension due to rotation are all taken into account in the present formulation this study examines in detail the effects of different boundary conditions on the frequency characteristics of rotating shells the present results wherever possible are verified by comparison against results available in the open literature in general close agreement between the authors results and those of others has been found further results presented here in selective parametric studies may be used as benchmarks for future related works

asymmetric boundary value problems for a transversely isotropic elastic medium abstract this paper considers general boundary value problems displacement traction mixed related to a transversely isotropic elastic half space the geometry of the problems considered is axisymmetric but the load is asymmetric a cylindrical coordinate system is employed in the analysis and fourier expansion and hankel integral transforms are applied with respect to circumferential and radial coordinates respectively the boundary value problems are formulated in terms of a system of non singular integral equations for each fourier harmonic the kernels of the integral equations are displacement and traction green s functions corresponding to buried ring loads with appropriate circumferential dependence in general a total of 18 green s functions are required for each fourier harmonic explicit solutions for green s functions corresponding to an arbitrary fourier harmonic are presented in terms of infinite integrals of lipschitz hankel type the versatility of the solution scheme is illustrated by solving a traction boundary value problem corresponding to a pressurized hemispherical cavity displacement boundary value problems related to an embedded rigid cylindrical body and a non linear mixed boundary value problem corresponding to an embedded rigid hemisphere with an elastic perfectly plastic interface

direct strain feedback control of flexible robot arms new theoretical and experimental results this paper addresses control problems for flexible robot arms by using direct strain feedback the purpose is to make clear why direct strain feedback can damp out vibration of flexible arms satisfactorily we concentrate on one link flexible robot arms whose dynamic models can be represented by linear partial differential equations with appropriate boundary conditions which have been well examined in a number of papers a key contribution of this paper is the introduction of the concept of strict a dependent operators which allows us to prove rigorously the closed loop stability of direct strain feedback and the existence and uniqueness of nonstandard second order abstract differential equations in hilbert spaces several control experiments are performed verifying the main theoretical points of this paper demonstrating satisfactory control results of direct strain feedback and leading to potential application of this simple control method for flexible robot control

elasto plasticity revisited numerical analysis via reproducing kernel particle method and parametric quadratic programming aiming to simplify the solution process of elasto plastic problems this paper proposes a reproducing kernel particle algorithm based on principles of parametric quadratic programming for elasto plasticity the parametric quadratic programming theory is useful and effective for the assessment of certain features of structural elasto plastic behaviour and can also be exploited for numerical iteration examples are presented to illustrate the essential aspects of the behaviour of the model proposed and the flexibility of the coupled parametric quadratic programming formulations with the reproducing kernel particle method copyright 2002 john wiley sons ltd

stress analysis in plane orthotropic material by the boundary element method abstract the boundary element method is a more suitable technique than the finite element method for problems having large stress gradients one such problem is the stresses around mechanical fasteners to solve a problem by the boundary element method requires a solution of an integral equation the integrand of the integral equation is a product of a known green s function and an unknown function unlike isotropic material the plane orthotropic material can have three forms of green s function depending upon the relationship of the four material constants to solve the integral equations numerically the unknown function is approximated by a piecewise continuous linear function the boundary is approximated by a sum of straight line segments the result of the two approximations is integrals over straight line segments the integrand of which is a product of linear polynomials and one of the three green s functions these integrals arc evaluated analytically by exploiting the common features in the three forms of green s function a very efficient algorithm can be designed numerical results arc presented for a circular hole in an infinite medium and in a coupon the results show good correlation with analytical results for all kinds of orthotropic materials

a meshless method for kirchhoff plate bending problems in this work a meshless method for the analysis of bending of thin homogeneous plates is presented this meshless method is based on the use of radial basis functions to build an approximation of the general solution of the partial differential equations governing the kirchhoff plate bending problem in order to obtain a symmetric and non singular linear equation system the hermite collocation method is used to assess the formulation a series of plates with different boundary conditions are analysed comparisons are made with other results available in the literature copyright 2001 john wiley sons ltd

a meshfree method for transverse vibrations of anisotropic plates a meshfree approach called displacement boundary method for anisotropic kirchhoff plate dynamic analysis is presented this method is deduced from a variational principle which uses a modified hybrid functional involving the generalized displacements and generalized tractions on the boundary and the lateral deflection in the domain as independent variables the discretization process is based on the employment of the fundamental solutions of the static problem operator for the expression of the variables involved in the functional the stiffness and mass matrices obtained for the dynamic model are frequency independent symmetric and positive definite and their computation involves boundary integrals of regular kernels only due to its features the final resolving system can be solved with the classical approaches by using standard numerical procedures to assess the formulation the free vibrations of some anisotropic plates were calculated and the results compared with those obtained using other solution techniques the present results are in good agreement with those found in the literature showing the accuracy and effectiveness of the proposed approach

block diagonalizability problem for hydrodynamic type systems the necessary and sufficient conditions are derived for the reducibility of a hydrodynamic type system into a block diagonal form with k mutually interacting blocks applications to the perturbations of the benney system and to the hamiltonian systems of partial differential equations are presented the algebraic identities connecting the nijenhuis tensors nb a u v and na u v and haantjes tensors hb a u v and ha u v are discovered

analysis and control of a two link and three joint elastic robot arm a robot system composed of two link arm and three joint is considered in this paper an evolution equation corresponding to the robot system formulated by partial differential equations with initial and boundary conditions is established in an appropriate hilbert space the spectral properties of the main operator of the evolution equation is first discussed and then its semigroup generation is presented based on the resulting spectral properties of finally an asymptotical behavior of the robot system under a designed feedback control is shown in terms of semigroup approach

on the exponential stability of an initial boundary equation arising from strain feedback control of flexible robot arms with rigid offset this paper is concerned with an initial boundary value equation arising from direct strain feedback control of flexible robot arms with a revolute joint and rigid offset by analyzing the spectrum and by estimating the norm of the resolvent of the system operator associated with the equation it is verified that the equation admits a unique solution and furthermore the solution is exponentially stable no matter how long is the rigid offset

new concepts in meshless methods meshless methods have been extensively popularized in literature in recent years due to their flexibility in solving boundary value problems two kinds of truly meshless methods the meshless local boundary integral equation mlbie method and the meshless local petrov galerkin mlpg approach are presented and discussed both methods use the moving least squares approximation to interpolate the solution variables while the mlbie method uses a local boundary integral equation formulation and the mlpg employs a local symmetric weak form the two methods are truly meshless ones as both of them do not need a finite element or boundary element mesh either for purposes of interpolation of the solution variables or for the integration of the energy all integrals can be easily evaluated over regularly shaped domains in general spheres in three dimensional problems and their boundaries numerical examples presented in the paper show that high rates of convergence with mesh refinement are achievable in essence the present meshless method based on the lswf is found to be a simple efficient and attractive method with a great potential in engineering applications copyright 2000 john wiley sons ltd

on the decoupling problem of general quasilinear first order systems in two independent variables abstract the paper deals with the decoupling problem of general quasilinear first order systems in two independent variables we consider either the case of homogeneous and autonomous systems or the one of nonhomogeneous and or nonautonomous systems necessary and sufficient conditions for the partial or full decoupling of the systems at hand are provided the conditions involve the properties of eigenvalues and eigenvectors of the coefficient matrix and provide the differential constraints whose integration leads to the decoupling transformation some applications of physical interest are also given

a new numerical method for the analysis of anisotropic thin plate bending problems abstract a new method is presented for the analysis of anisotropic thin plate bending problems this method appears to enjoy several advantages over other numerical methods for linear problems in concept the present method is quite simple using the influence function for an infinite plate of the same material the solution to the problem of interest is expressed as the superposition of the effect of the actual lateral load plus 2n unknown point loads located outside the region occupied by the plate these 2n loads are then determined through imposition of the boundary conditions at n selected locations an interesting numerical question arises regarding the selection of the 2n external points it is shown that proper distribution of these points leads to excellent results with minimal computer effort several example problems are presented demonstrating the ability of the method to deal with difficult geometries and boundary conditions and with material anisotropy

a meshfree hermite type radial point interpolation method for kirchhoff plate problems a meshfree computational method is proposed in this paper to solve kirchhoff plate problems of various geometries the deflection of the thin plate is approximated by using a hermite type radial basis function approximation technique the standard galerkin method is adopted to discretize the governing partial differential equations which were derived from using the kirchhoff s plate theory the degrees of freedom for the slopes are included in the approximation to make the proposed method effective in enforcing essential boundary conditions numerical examples with different geometric shapes and various boundary conditions are given to verify the efficiency accuracy and robustness of the method copyright 2005 john wiley sons ltd

control and stability of a torsional elastic robot arm a mathematical model for a long elastic torsional robot beam is determined the above system can be expressed as an evolution equation on a hilbert space furthermore the system is shown to be stable and controllable and we design a controller for the system

modeling stabilization and control of serially connected beams many flexible structures consist of a large number of components coupled end to end in the form of a chain in this paper we consider the simplest type of such structures which is formed by n seri

decoupling problem for systems of quasi linear pde s the necessary and sufficient conditions for the decoupling of a quasi linear system of partial differential equations into k non interacting subsystems are derived several necessary conditions for the decoupling are found and applied to the benney system