design sensitivity analysis of hyperelastic structures using a meshless method a continuum based design sensitivity analysis method for hyperelastic structures is presented analysis is performed using a meshless method called the reproducing kernel particle method yeoh s energy density function is used to describe thehyperelastic structural behavior the meshless method eliminates mesh distortion orentanglement encountered in using e nite element analysis for large deformation structural analysis and structural shape design optimization both the adjoint variable and direct differentiation methods are developed for material and shape design variables an ine nitely long rubber tube a two dimensional rubber band and an engine mount are examples used to demonstrate the feasibility and accuracy of the method

shape optimization of piezoelectric devices using an enriched meshfree method we present an enriched reproducing kernel particle method for shape sensitivity analysis and shape optimization of two dimensional electromechanical domains this meshfree method incorporates enrichment functions for better representation of discontinuous electromechanical fields across internal boundaries we use cubic splines for delineating the geometry of internal external domain boundaries and the nodal coordinates and slopes of these splines at their control points become the design parameters this approach enables smooth manipulations of bi material interfaces and external boundaries during the optimization process it also enables the calculation of displacement and electric potential field sensitivities with respect to the design parameters through direct differentiation for which we adopt the classical material derivative approach we verify this implementation of sensitivity calculations against an exact solution to a variant of lame s problem and also finite difference approximations we follow a sequential quadratic programming approach to minimize the cost function and demonstrate the utility of the overall technique through a model problem that involves the shape optimization of a piezoelectric fan copyright 2008 john wiley sons ltd

the dynamics of repeated impacts with a sinusoidally vibrating table a deceptively simple difference equation is derived which approximately describes the motion of a small ball bouncing vertically on a massive sinusoidally vibrating plate in the case of perfect elastic impacts the equation reduces to the standard mapping which has been extensively studied by physicists in connection with the motions of particles constrained in potential wells it is shown that for sufficiently large excitation velocities and a coefficient of restitution close to one this deterministic dynamical system exhibits large families of irregular non periodic solutions in addition to the expected harmonic and subharmonic motions the physical significance of these and other chaotic motions which appear to occur frequently in non linear oscillations is discussed

shape sensitivity analysis and shape optimization in planar elasticity using the element free galerkin method abstract this paper demonstrates that the element free galerkin efg method can be successfully used in shape design sensitivity analysis and shape optimization for problems in 2d elasticity the continuum based variational equations for displacement sensitivities are derived and are subsequently discretized this approach allows one to avoid differentiating the efg shape functions the present formulation that employs a penalty method for imposing the essential boundary conditions can be easily extended to 3d and or non linear problems numerical examples are presented to show the capabilities of the current approach for calculating sensitivities the flexibility of the efg method that eliminates the element connectivity requirement of the finite element method fem permits solving shape optimization problems without re meshing the problem of shape optimization of a fillet is used to demonstrate this fact smoother stresses and better accuracy for points close to the boundary allow for a better efg solution compared to published results using the fem the boundary element method bem or the boundary contour method bcm furthermore for the efg approach grid optimization appears unnecessary

effect of nonlinear impact damping on the frequency response of a torsional system with clearance in this article we examine a particular nonlinear impact damping model that has been well accepted by the scientific community first we consider the damping element with a linear spring and examine the nonlinear frequency response characteristics of a torsional system second the impact damping is examined along with the clearance nonlinearity including the backlash problem three semi analytical methods namely the describing function method multi term harmonic balance method and stochastic linearization method are utilized to investigate the effect of impact damping feasibility of such methods is confirmed by comparing predictions with results yielded by a numerical method the differences between impact damping and linear viscous damping mechanism are studied in terms of frequency responses time histories and the minimum number of harmonics required to simulate the behavior given sinusoidal excitations furthermore the effect of impact damping on sub and super harmonic responses and quasi periodic regimes are examined

shape optimization using reproducing kernel particle method and an enriched genetic algorithm combining reproducing kernel particle method rkpm with the proposed multi family genetic algorithm mfga a novel approach to continuum based shape optimization problems is brought forward in this paper taking full advantage of the features of meshfree method and the merits of mfga the new method solves shape optimization problems in such a unique way that remeshing is avoided and particularly the computation burden and errors caused by sensitivity analysis are eliminated completely the effectiveness versatility and performance of the proposed approach are demonstrated via three 2 d numerical examples

effect of radial internal clearance of a ball bearing on the dynamics of a balanced horizontal rotor the response of a balanced horizontal rigid motor rotor supported by a deep groove ball bearing is theoretically simulated the effect of radial internal clearance of the ball bearing on the dynamic response of the rotor is studied the system equations have been numerically integrated the results of which have been validated with harmonic balance alternating frequency time domain method variation of radial internal clearance shifts the peak response as the speed is changed over a range the results of a parametric study done by taking radial internal clearance have resulted in the observation of a third region of instability which has not been reported in literature the appearance of regions of periodic subharmonic and chaotic behavior is seen to be strongly dependent on the radial internal clearance the system response is analyzed for stability and nature with the help of floquets method for stability analysis and generation of higher order poincare maps the bearing stiffness is estimated experimentally and the effect of variation in radial internal clearance on the bearing stiffness is studied

review of options for structural design sensitivity analysis part 1 linear systems the paper reviews options for structural design sensitivity analysis including global finite differences continuum derivatives discrete derivatives and computational or automated differentiation the objective is to put these different approaches to design sensitivity analysis in the context of accuracy and consistency computational cost and implementation options and effort linear static analysis and transient dynamic analysis are reviewed in a separate appendix special attention is paid to the semi analytical method a future paper will address design sensitivity analysis in nonlinear structural problems

non linear dynamics of gear pair systems with periodic stiffness and backlash the present work investigates dynamics of a gear pair system involving backlash and time dependent mesh stiffness in addition the system is under the action of external excitation caused by torsional moments and gear geometry errors first the equation of motion is established in a strongly non linear form then the emphasis is laid on a specific forcing frequency range corresponding to conditions of simultaneous fundamental parametric resonance and principal external resonance for these conditions several types of periodic steady state response are identified and determined by employing suitable methodologies including techniques applicable to piecewise linear systems and to oscillators with time periodic coefficients moreover these methodologies are complemented by appropriate procedures revealing the stability properties of the located periodic solutions in the second part of the work numerical results are presented these results verify the validity and effectiveness of the new analytical methodology and provide information on the gear pair dynamics first series of typical response diagrams are obtained illustrating the effect of the mesh stiffness variation the damping and the forcing parameters on the gear pair periodic response these response diagrams are accompanied by results obtained with direct integration of the equation of motion in this way it is demonstrated that for some parameter combinations the dynamical system examined can exhibit more complicated and irregular response including crises and intermittent chaos

vibration of plate with curvilinear stiffeners using mesh free method the element free galerkin method which is based on the moving least squares approximation is developed for vibration analysis of unitized structures e g a plate with curvilinear stiffeners the plate and stiffeners are modeled using the first order shear deformation theory and timoshenko beam theory respectively the moving least squares approximation does not satisfy the delta function property consequently an approximation method e g the well known penalty method must be used for imposing essential boundary conditions a key benefit of using element free galerkin for the vibration analysis of a stiffened panel is that the locations and curvatures of the stiffeners can be changed without modifying the plate nodes numerical results for different stiffeners configurations and boundary conditions are presented all results are verified using the commercial finite element software ansys excellent agreement is seen in all cases a comparison of the present formulations with other available results for stiffened plates is also made the mesh free approach yields highly accurate results for the plates with curvilinear stiffeners

the hilbert phenomenon in chaotic motions abstract it is proved that chaotic dynamical systems have d 1 singularity due to such singularity and its periodicity in hausdorff metric spaces a chaotic dynamical system induces a hilbert iterated system which was discovered at the end of the 19th century this implies that the most puzzling discovery in nature in the 20th century can be put into deep correspondence with that in thoughts in the 19th century all this is verified by the numerical experiments of chaotic vibrations of a beam and a tension slack oscillator

a multiscale strategy for structural optimization this paper presents a multiscale strategy dedicated to structural optimization the applications concern the study of geometric details such as holes surface profiles etc within the structures with frictional contacts the first characteristic of the method is that it uses a micro macro approach this approach is based on a domain decomposition into substructures and interfaces which involves the resolution of independent micro problems in each substructure and transfers macro information only through the interfaces the second characteristic is the use of a multiresolution strategy in order to reduce the computation cost for problems with evolving design parameters the last characteristic is the capability to model the geometry of details without remeshing thanks to two features the use of a local enrichment method and the use of level set functions to easily modify the boundary of the detail during the optimization process

a periodically forced piecewise linear oscillator a single degree of freedom non linear oscillator is considered the non linearity is in the restoring force and is piecewise linear with a single change in slope such oscillators provide models for mechanical systems in which components make intermittent contact a limiting case in which one slope approaches infinity an impact oscillator is also considered harmonic subharmonic and chaotic motions are found to exist and the bifurcations leading to them are analyzed

stability and nonlinear dynamics of a vibration system with oblique collisions abstract two moving rigid bodies can contact with each other as the clearance between them is exceeded supposing that the contacting areas are two parallel planes with an oblique angle to the moving direction periodic responses of the system with oblique collision are determined by applying poincare mapping impulse momentum theorem and poisson s hypothesis in this paper first the relations of the body velocities before and after collisions are derived upon an instantaneous collision hypothesis then the existence condition and the stability criterion of the period n motion with single collision are deduced by using the poincare mapping and the floquet theory last numerical simulations are carried out and bifurcation diagrams poincare maps and phase portraits are adopted to prove the stability analysis and illustrate rich dynamical behaviors of the system over a rather broad range of frequency of the external excitation transitions from the single collision period n motion to chaotic one through three ways period doubling bifurcation hopf bifurcation and abruptly transition are revealed

reproducing kernel particle methods for large deformation analysis of non linear structures abstract large deformation analysis of non linear elastic and inelastic structures based on reproducing kernel particle methods rkpm is presented the method requires no explicit mesh in computation and therefore avoids mesh distortion difficulties in large deformation analysis the current formulation considers hyperelastic and elasto plastic materials since they represent path independent and path dependent material behaviors respectively in this paper a material kernel function and an rkpm material shape function are introduced for large deformation analysis the support of the rkpm material shape function covers the same set of particles during material deformation and hence no tension instability is encountered in the large deformation computation the essential boundary conditions are introduced by the use of a transformation method the transformation matrix is formed only once at the initial stage if the rkpm material shape functions are employed the appropriate integration procedures for the moment matrix and its derivative are studied from the standpoint of reproducing conditions in transient problems with an explicit time integration method the lumped mass matrices are constructed at nodal coordinate so that masses are lumped at the particles several hyperelasticity and elasto plasticity problems are studied to demonstrate the effectiveness of the method the numerical results indicated that rkpm handles large material distortion more effectively than finite elements due to its smoother shape functions and consequently provides a higher solution accuracy under large deformation unlike the conventional finite element approach the nodal spacing irregularity in rkpm does not lead to irregular mesh shape that significantly deteriorates solution accuracy no volumetric locking is observed when applying non linear rkpm to nearly incompressible hyperelasticity and perfect plasticity problems further model adaptivity in rkpm can be accomplished simply by adding more points in the highly deformed areas without remeshing

are the optimum problems in structural design well posed from the examples considered above it can be seen that the area of the cross section minimizing the total weight of a simple rod under a given load is in general not unique only under particular assumptions on the constraints and the distribution of axial loads is the optimal solution uniquely determined by the principle of minimum weight another feature of the optimal solutions is that their properties of regularity number and location of discontinuities of the solutions and its derivatives are in general not at all obvious from the beginning

the corresponding phenomena of mechanical and electronic impact oscillator a mechanical impact oscillator and a diode rectifier circuit of an impact oscillator are presented time series and phase portrait analysis are performed for both oscillators the results show that the proposed electronic impact oscillator is in agreement with the mechanical impact oscillator for varying the driving frequency a fixed harmonic input force can generate a periodic or non periodic impact oscillation the phenomena of bifurcation are also observed in both impact oscillators

double impact orbits of periodically forced impact oscillators we consider a periodically forced oscillator which impacts against a rigid constraint the forcing is both sinusoidal and non sinusoidal and is made up of a combination of the first and second harmonics of a fourier series a simple restitution law is used to describe the impact this paper centres around the analysis of double impact periodic solutions that is motions which repeat after every second impact solutions for these double impact orbits are found including non physical orbits and unstable orbits behaviour typical of nonlinear dynamical systems such as period doubling bifurcations are detected and grazing bifurcations which are unique to discontinuous dynamical systems are also observed a combination of analytical and numerical techniques are used to uncover the behaviour of the system at odd multiples of the natural frequency where numerical experiments tell us that stable double impact periodic solutions exist the persistence of these stable double impact orbits are also examined as parameters are varied we conclude by presenting some numerical calculations of two more general cases of impacting systems

type i periodic motions for nonlinear impact oscillators abstract in this paper a general class of nonlinear impact oscillators is considered for subharmonic bifurcation this system can be used to model an inverted pendulum impacting on rigid walls under external periodic excitation and its unperturbed system possesses a pair of homoclinic cycles via the identification given by the impact law and three separate families of periodic orbits inside and outside the homoclinic cycles by discussing the subharmonic orbits inside the homoclinic cycles the subharmonic melnikov method established for smooth dynamical systems is extended to be applicable to the non smooth system

homogenization of the three dimensional hall effect and change of sign of the hall coefficient the notion of a hall matrix associated with a possibly anisotropic conducting material in the presence of a small magnetic field is introduced then for any material having a microstructure we prove a general homogenization result satisfied by the hall matrix in the framework of the h convergence of murat tartar extending a result of bergman we show that the hall matrix can be computed from the corrector associated with the homogenization problem when no magnetic field is present finally we give an example of a microstructure for which the hall matrix is positive isotropic almost everywhere while the homogenized hall matrix is negative isotropic

change of sign of the corrector s determinant for homogenization in three dimensional conductivity in this paper we study the positivity of the determinant of the local electric field in a conducting composite we know by 1 that the positivity holds true in two dimensions for any periodic structure using a different approach from 11 we prove that is also the case for a laminate microstructure in any dimension however and this is the main result of the paper we provide an example of a two phase three dimensional periodic composite for which the determinant changes sign

low dimensional maps for piecewise smooth oscillators abstract dynamics of the piecewise smooth nonlinear oscillators is considered for which general methodology of reducing multidimensional flows to low dimensional maps is proposed this includes a definition of piecewise smooth oscillator and creation of a global iterative map providing an exact solution the global map is comprised of local maps which are constructed in the smooth sub regions of phase space to construct this low dimensional map it is proposed to monitor the points of intersections of a chosen boundary between smooth subspaces by a trajectory the dimension reduction is directly related to the dimension of the chosen boundary and the lower its dimension is the larger dimension reduction can be achieved full details are given for a drifting impact oscillator where the five dimensional flow is reduced to one dimensional 1d approximate analytical map first an exact two dimensional map has been formulated and analysed a further reduction to 1d approximate map is introduced and discussed standard nonlinear dynamic analysis reveals a complex behaviour ranging from periodic oscillations to chaos and co existence of multiple attractors accuracy of the constructed maps is examined by comparing with the exact solutions for a wide range of the system parameters

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

period one motions of a mechanical oscillator with periodically time varying piecewise nonlinear stiffness the dynamic behavior of a piecewise nonlinear mechanical oscillator with parametric and external excitations is investigated the viscously damped single degree of freedom oscillator is subjected to a periodically time varying piecewise nonlinear restoring function defined by a clearance surrounded by continuously nonlinear quadratic and cubic regions typical applications represented by this oscillator are highlighted a multi term harmonic balance formulation is used in conjunction with discrete fourier transforms and a parametric continuation scheme to determine steady state period 1 motions of the system due to both parametric and external excitations the accuracy of the analytical solutions is demonstrated by comparing them to direct numerical integration solutions floquet theory is applied to determine the stability of the steady state harmonic balance solutions at the end detailed parametric studies are presented to quantify the combined influence of clearance quadratic and cubic nonlinearities within reasonable ranges of all other system parameters a comparison between time varying and time invariant systems is also provided to demonstrate the influence of the parametric and external excitations on a piecewise nonlinear system

a continuous lagrangian sensitivity equation method for incompressible flow a continuous lagrangian sensitivity equation method clsem is presented as a cost effective alternative to the continuous eulerian sensitivity equation method cesem in the case of shape parameters boundary conditions for the clsem are simpler than those of the cesem however a mapping must be introduced to relate the undeformed and deformed configurations thus making the pdes more complicated we propose the use of pseudo elasticity equations to provide a general framework to generate this mapping for unstructured meshes on complex geometries the methodology is presented in details for the incompressible navier stokes and sensitivity equations in variational form the pdes are solved with an adaptive fem sensitivity data obtained with both approaches for a flow around a naca 4512 are used to obtain estimates of flows around nearby geometries results indicate that the clsem produces significant improvements in terms of both accuracy and cpu time

the mapping dynamics of periodic motions for a three piecewise linear system under a periodic excitation in this paper the mapping dynamics of periodic motions for a three piecewise linear system under a periodic excitation is developed and the mapping structures for specified periodic motions are constructed based on the mapping structures an analytical prediction of all possible stable and unstable periodic motions is given the symmetry for the stable asymmetrical periodic motions of such a system is observed however the unstable periodic motions do not have such symmetry the methodology presented in this paper is applicable to other non smooth systems such as friction induced vibration impact oscillator and power control systems in addition the mapping dynamics provides a useful and efficient tool for the co existence of periodic motions and or chaotic motions in nonlinear dynamical systems

large amplitude non linear normal modes of piecewise linear systems a numerical method for constructing non linear normal modes nnms for piecewise linear autonomous systems is presented these nnms are based on the concept of invariant manifolds and are obtained using a galerkin based solution of the invariant manifold s non linear partial differential equations the accuracy of the constructed non linear modes is checked by the comparison of the motion on the invariant manifold to the exact solution in both time and frequency domains it is found that this construction approach can accurately capture the nnms over a wide range of amplitudes including those with strong non linear effects several interesting dynamic characteristics of the non linear modal motion are found and compared to those of linear modes a two degree of freedom example is used to illustrate the technique the existence stability and bifurcations of the nnms for this example are investigated

estimation of clearances and impact forces using vibroimpact response sinusoidal excitation abstract a novel clearance estimation approach has been developed for a randomly excited vibroimpact system the clearance estimates based on this approach were obtained using data from the mechanical analogue of an impact oscillator and simulation using a digital computer and they reasonably agree with the actual clearances

asymmetric type ii periodic motions for nonlinear impact oscillators abstract in this paper a general class of nonlinear impact oscillators is considered for type ii periodic motions this system can be used to model an inverted pendulum impacting on rigid walls under external periodic excitation the unperturbed system possesses a pair of homoclinic cycles and three separate families of periodic orbits inside and outside the homoclinic cycles via the identification given by the impact law by approximating the poincare map to o e directly a general method of melnikov type for detecting the existence of asymmetric type ii subharmonic orbits outside the homoclinic cycles is presented

shape optimization directly from cad an isogeometric boundary element approach using t splines abstract we develop a t spline isogeometric boundary element method igabem simpson et al 2012 scott et al 2013 simpson et al 2014 to shape sensitivity analysis and gradient based shape optimization in three dimensional linear elasticity contrary to finite element based isogeometric analysis iga approaches no parametrization of the volume is required hence the iterative optimization algorithm can be implemented directly from cad without any mesh generation or postprocessing step for returning the resulting structure to cad designers t splines also guarantee a water tight geometry without the manual geometrical repair work as with non uniform rational b splines nurbs we demonstrate the worth of the method by analysing problems with and without analytical solutions including engineering examples involving complex shapes additionally we provide all the derivations of the required sensitivities and the details pertaining to the geometries examined in the benchmarking to provide helpful reference problems for 3d shape optimization

homogenization of high contrast two phase conductivities perturbed by a magnetic field comparison between dimension two and dimension three abstract homogenized laws for sequences of high contrast two phase non symmetric conductivities perturbed by a parameter h are derived in two and three dimensions the parameter h characterizes the antisymmetric part of the conductivity for an idealized model of a conductor in the presence of a magnetic field in dimension two an extension of the dykhne transformation to non periodic high conductivities permits to prove that the homogenized conductivity depends on h through some homogenized matrix valued function obtained in the absence of a magnetic field this result is improved in the periodic framework thanks to an alternative approach and illustrated by a cross like thin structure using other tools a fiber reinforced medium in dimension three provides a quite different homogenized conductivity

shape optimization of 2d structures using simulated annealing the goal of this study is to obtain globally optimum shapes for two dimensional structures subject to quasi static loads and restraints for this purpose a technique is proposed using which the volume or weight of a structure can be minimized the emphasis is on how one can define the shape precisely and find a shape that accurately reflects the globally optimum shape as design constraints stresses developed in the structure should not exceed the maximum allowable stress and connectivity of the structure should not be lost during shape changes optimization is achieved by a stochastic search algorithm called direct simulated annealing dsa which seeks the global minimum through randomly generated configurations in order to obtain random configurations a boundary variation technique is used in this technique a set of key points is chosen and connected by cubic splines to describe the boundary of the structure whenever the positions of the key points are changed in random directions a new shape is obtained thus coordinates of the key points serve as design variables in order to apply the optimization procedure a general computer code was developed using ansys parametric design language a number of cases were examined to test its effectiveness the results show that this technique can be applied to two dimensional shape optimization problems with high reliability even for cases where the entire free boundary is allowed to vary 2007 elsevier b v all rights reserved

bem first order regularisation method in linear elasticity for boundary identification in this paper we study the identification of an unknown portion of the boundary of a two dimensional domain occupied by an isotropic linear elastic material from additional cauchy data on the remaining known portion of the boundary this inverse problem is approached using the boundary element method bem in conjunction with the tikhonov first order regularisation procedure the choice of the regularisation parameter is based on the l curve criterion the numerical results obtained show that the proposed method produces a convergent and stable solution

frequency response characteristics of a multi degree of freedom system with clearances abstract in an earlier study the frequency response characteristics of a single degree of freedom system with a clearance non linearity were studied the current study an extension of the earlier work is concerned with the frequency response characteristics of a multi degree of freedom system with clearances the method of harmonic balance is used to develop approximate analytical solutions of the undamped equations of motion of a multi degree of freedom system composed of three coupled non linear oscillators for primary resonances and a harmonic excitation general formulations are presented which can be used to study both the existence and the stability of the solutions these general formulations are used to discuss a number of modal spacing and modal coupling issues an analysis methodology for multi degree of freedom systems is introduced and illustrated by two special but practical cases a strongly non linear system and a weakly non linear system the results of the analysis of the special cases are validated by using analog simulation it is shown that an analysis of the special cases of the general multi degree of freedom non linear formulation can provide not only an improved understanding of the dynamic behavior of non linear systems but also can be used as the basis for the development of simplified approximate solutions the limitations of the current study and areas for further research are discussed

cad inspired hierarchical partition of unity constructions for nurbs based meshless design analysis and optimization in this paper we develop a unified representational paradigm for design and analysis that is inspired by the set theoretic boolean operations of the constructive solid geometry csg procedure of computer aided design cad we develop the notion of a primitive design state corresponding to a csg primitive region which is characterized by a description of the geometrical shape of the primitive and by a description of the material distribution within the primitive we analogously define a primitive behaviour state that is associated with a primitive design state and that is determined through a global analysis problem we define a global multi level design problem to determine the primitive design states we define boolean operations on the fields belonging to primitive design and behaviour spaces and show that the compositions of these fields amount to a hierarchical partition of unity construction we propose to use non uniform rational b splines nurbs to discretize the geometry material and behavioural fields local approximations defined on the primitive regions we show that this leads to recursive partition of unity constructions on the knot spaces sub local approximations due to the partition of unity property of nurbs basis functions since the primitive shapes are parametrically defined using nurbs the numerical quadrature is carried out on the parametric sub regions of the nurbs entities this eliminates the need for either a background mesh or a pseudo mesh for quadrature the developed methodology is implemented in a symbolic meshless computational framework written using the java language jnurbs and was demonstrated on two classes of problems the first class is the simultaneous optimal design of shape and multi material distributions the procedure is argued as being a generalization of classical topology optimization to designing objects made of functionally graded materials with pre defined geometrical constraints such as holes or fixed boundary shape the second class of problems demonstrated in the paper is optimal design to mitigate the effects of cracks here we identify the optimal locations of holes introduced to reduce the stress intensity factor of an edge crack copyright 2007 john wiley sons ltd

global dynamics of a vibro impacting linear oscillator abstract the steady state vibro impacting responses of one dimensional harmonically excited linear oscillators are studied by using a modern dynamical systems approach allied with numerical simulation the steady state motions are attracting sets in the system phase space and capture initial conditions in their domains of attraction unlike the free harmonically excited oscillator the phase space of a vibro impacting system may be inhabited by many attracting sets for example there are sub harmonic multi impact periodic orbits and chaotic steady state responses in order to build a qualitative understanding of vibro impact response an attempt is made to build generic topological models of their phase spaces for physically significant parameter ranges use is made of the poincare section or stroboscopic mapping technique essentially following an initial impact forwards or backwards in time to subsequent or previous impacts using a computer the qualitative understanding gained from the analysis and simulations is discussed in an engineering context

grid optimization for the boundary element method the quality of solution obtained using the boundary element method bem is dependent on how the boundary is discretized this is particularly true in domains of complex geometry a rule for grid optimization for the bem is derived on the bases of an asymptotic measure of the boundary element error that preserves the number of elements degrees of freedom three example problems are provided to show the advantages of grid optimization in terms of accuracy and cost

a meshless integral method based on regularized boundary integral equation a meshless integral method based on the regularized boundary integral equation is developed and applied to two dimensional linear elasticity the governing integral equation is obtained from the weak form of elasticity over a local sub domain and the moving least squares approximation is used for meshless function approximation the method is built on the lbie method proposed by atluri and co workers and several key improvements are introduced in this work that significantly enhance the accuracy and robustness of the method the most critical improvement is the use of the subtraction technique to remove the strong singularity that results in a regularized governing integral equation the technique is straightforward and efficient and is much simpler and easier compared to other singularity removal techniques a special numerical integration is employed for the calculation of integrals with weak singularity which further improves accuracy the collocation method is employed to enforce the essential boundary conditions exactly which is simple and computationally efficient the natural boundary conditions are incorporated in the system governing equation and require no special handling numerical tests show that the meshless integral method is accurate and robust the effects of weight function support domain sub domain and monomial basis are investigated and discussed

super and sub harmonic response calculations for a torsional system with clearance nonlinearity using the harmonic balance method abstract this article presents a new multi term harmonic balance method hbm for nonlinear frequency response calculations of a torsional sub system containing a clearance type nonlinearity the ability of the simplified subsystem to capture the salient behavior of the larger system is verified by the comparison of results to experimental data unlike previous analytical and numerical methods the proposed hbm includes adaptive arc length continuation and stability calculation capabilities to find periodic solutions in multi valued nonlinear frequency response regimes as well as to improve convergence essential steps of the proposed hbm calculations are introduced and it is validated by comparing time and frequency domain predictions with those yielded by numerical solutions experimental studies or analog simulations for several examples then nonlinear frequency response characteristics of an oscillator with clearance nonlinearity are examined with focus on super and sub harmonics we also explore some issues that are not fully resolved in the literature for instance the effect of mean operating point is examined for 0 and 0 18 0 25 cases where is the stiffness ratio of the piecewise linear elastic function in addition the number of harmonic terms that must be included in the hbm response calculations given sinusoidal excitation has been investigated finally some simple analytical predictions for super and sub harmonic resonances are presented

computational method for optimization of structural shapes in the direct method of shape optimum design mesh regridding is a necessary step in avoiding the distortion of finite element grids the effect of internal nodal movements on the shape design sensitivity associated with the regridding process has been carefully examined in this paper it shows that to maintain computational accuracy the effects of internal nodal movement should be considered in shape design sensitivity analysis to take the internal nodal movement into account the numerical accuracy of the speed method is investigated a new approach which constructs the velocity field over the element domain is presented although it takes more computational time the new approach does improve the accuracy of shape design sensitivity

stability and dynamics of a harmonically excited elastic perfectly plastic oscillator this paper deals with the stability and the dynamics of a harmonically excited elastic perfectly plastic oscillator the hysteretical system is written as a non smooth forced autonomous system it is shown that the dimension of the phase space can be reduced using adapted variables free vibrations of such a system are then considered for the damped system the extended direct method of liapounov is applied to this non smooth mechanical system and the asymptotic stability of the origin is proven in the new phase space the forced vibration of such an oscillator is treated by numerical approach by using the time locating techniques the stability of the limit cycles is analytically investigated with a perturbation approach the boundary between elastoplastic shakedown and alternating plasticity is given in closed form it is shown that this boundary corresponds to a bifurcation boundary for the undamped system period doubling bifurcation finally the equivalent damping of this hysteretic system is characterized from dynamical properties

a systematic approach to shape sensitivity analysis abstract a fully detailed development of the domain parameterization method is presented for shape sensitivity analysis it is shown that equivalent results are obtained from the material derivative method in fact the material derivative method may be viewed as a special case of the domain parameterization method which occurs when the reference configuration coincides with the body configuration the method is illustrated for the laplace problem in which explicit shape sensitivities are derived by the adjoint and direct differentiation methods both finite element and boundary element applications are discussed the similarities between this approach and the isoparametric finite boundary element method are transparent in the finite element approach it is shown that the sensitivity integrals may be transformed to the boundary as is commonly done in the material derivative method for the adjoint method however this does not seem possible for the direct differentiation method finally in the boundary element approach the sensitivities do not require the differentiation of the fundamental solutions

stability and bifurcation analysis for oscillators with motion limiting constraints abstract the stability and bifurcation analysis is presented for a class of non linear single degree of freedom vibrating systems excited by harmonic forcing the common characteristic of these systems is that their damping and stiffness parameters can change abruptly at certain displacement values the most general n periodic steady state solutions with an arbitrary number of contacts per response cycle are analyzed it is shown that when the damping is positive the change of stability of the steady state response cannot happen through a hopf bifurcation

an exposition of the material derivative approach for structural shape sensitivity analysis abstract the material derivative approach for structural shape design sensitivity analysis is described in a unified manner using the continuum formulation both the direct differentiation and adjoint methods are derived and computer implementation aspects are discussed the basic purpose of the paper is to present the shape design sensitivity analysis as an application of the material derivative concept of continuum mechanics and the calculus of variation procedures for taking variations of integrals over the variable domains it is also shown that the use of a recently developed variational principle for design sensitivity analysis greatly simplifies derivation of the adjoint method the indicial notation is used and expressions derived by different authors are related to each other a basic understanding of the material derivative approach of shape sensitivity analysis has been gained which can lead to insights for computer implementations of the method

the meshless standard and hypersingular boundary node methods applications to error estimation and adaptivity in three dimensional problems the standard singular boundary node method bnm and the novel hypersingular boundary node method hbnm are employed for the usual and adaptive solutions of three dimensional potential and elasticity problems these methods couple boundary integral equations with moving least squares interpolants while retaining the dimensionality advantage of the former and the meshless attribute of the latter the hypersingular residuals developed for error estimation in the mesh based collocation boundary element method bem and symmetric galerkin bem by paulino et al are extended to the meshless bnm setting a simple a posteriori error estimation and an effective adaptive refinement procedure are presented the implementation of all the techniques involved in this work are discussed which includes aspects regarding parallel implementation of the bnm and hbnm codes several numerical examples are given and discussed in detail conclusions are inferred and relevant extensions of the methodology introduced in this work are provided copyright 2001 john wiley sons ltd

a semi analytic meshfree method for almansi michell problems of piezoelectric cylinders abstract saint venant s problem almansi michell problems meshfree methods piezoelectricity we present a semi analytical method for analyzing prismatic nonhomogeneous piezoelectric cylinders with arbitrary cross sectional geometry the prescribed loads considered in this study include axial forces torques moments and voltage resultants prescribed at the cylinder s ends as well as body forces lateral surface shears voltages and pressures as long as they can be represented by a power series in the axial coordinate this problem can be considered as an extension of saint venant and almansi michell problems for elastic bodies to piezoelectric bodies in this computationally efficient method the cross sectional plane is discretized with a meshfree approach and the solution is obtained analytically with respect to the axial coordinate a number of examples are provided to demonstrate the veracity and utility of the proposed method

a polytree based adaptive polygonal finite element method for multi material topology optimization abstract this study presents a polytree based adaptive methodology for multi material topology optimization mmtop polytree data structure is introduced as a general recursive multi level mesh that is automatically refined in processing based on error analysis in order to resolve hanging nodes in element edges the wachspress coordinate is employed on a reference element before using a mapping scheme to obtain shape functions and their derivatives for any polygons a new definition of filter radius is also proposed to improve the efficiency of filters and optimized results the combination of polytree meshes and adaptive filters not only clarifies the interfaces between material phases including void phase but also decreases the computing time of the overall process in comparison to using the regular fine meshes several benchmark and practical problems are considered to show distinct features of the proposed method

implementation of regularized isogeometric boundary element methods for gradient based shape optimization in two dimensional linear elasticity the present work addresses shape sensitivity analysis and optimization in two dimensional elasticity with a regularized isogeometric boundary element method igabem non uniform rational b splines are used both for the geometry and the basis functions to discretize the regularized boundary integral equations with the advantage of tight integration of design and analysis the application of igabem in shape optimization reduces the mesh generation regeneration burden greatly the work is distinct from the previous literatures in igabem shape optimization mainly in two aspects 1 the structural and sensitivity analysis takes advantage of the regularized form of the boundary integral equations eliminating completely the need of evaluating strongly singular integrals and jump terms and their shape derivatives which were the main implementation difficulty in igabem and 2 although based on the same computer aided design cad model the mesh for structural and shape sensitivity analysis is separated from the geometrical design mesh thus achieving a balance between less design variables for efficiency and refined mesh for accuracy this technique was initially used in isogeometric finite element method and was incorporated into the present igabem implementation

smoothing and accelerated computations in the element free galerkin method two topics in the formulation and implementation of meshless methods are considered the smoothing of the approximating functions at concave boundaries and the speedup of the calculation of the approximating functions and their derivatives these techniques are described in the context of the element free galerkin method but they are applicable to other meshless methods results are presented for some elastostatic problems which show a moderate improvement in the accuracy of the smoothed interpolant the speedup in calculating the shape functions is about a factor of two

structural shape sensitivity analysis relationship between material derivative and control volume approaches the material derivative and control volume approaches for structural shape design sensitivity analysis are presented analyzed and compared starting with a continuum formulation and a general response functional needing sensitivity analysis the two approaches are derived it is shown that the final design sensitivity expression for one approach can be obtained from the final expression for the other thus the two approaches are theoretically equivalent discretizations of the continuum expressions are presented and it is shown that the two approaches can lead to different implementations for numerical calculations a unified interpretation is developed in which the explicit design variations partial derivatives with respect to the design variables of the internal and external forces are the major calculations needed to implement the design sensitivity analysis the discretized forms of the continuum sensitivity expressions are also compared with the ones obtained by starting with the discretized model ab initio this comparison shows that these two approaches lead to similar expressions for numerical calculations therefore the exact same procedures can be used for computer implementations for both of the approaches the presented analyses give insights for implementation of the design sensitivity analysis theory with the finite element analysis programs

on a direct method of analyzing impacting mechanical systems the paper presents an analytic method of investigating impacting mechanical systems the method is based on presentation of impact forces as sequences of dirac delta functions periodic vibrations are described by particular solutions of the equations of motion resulting from trigonometric expansions of sequences of dirac distributions the fourier form of the solution is avoided by establishing the initial state vector which ensures the occurrence of periodic motion and allows one to determine the solution in a compact form the infinite series describing elements of the initial state vector are convergent and their sums have been determined forced vibrations of the impacting systems are considered for dissipative and conservative systems the method is illustrated by an example of an impacting system with three degrees of freedom

continuous and discontinuous grazing bifurcations in impacting oscillators this paper seeks to formulate conditions for the persistence of a local attractor in the immediate vicinity of periodic and quasiperiodic grazing trajectories in an impacting mechanical system a local analysis based on the discontinuity mapping approach is employed to derive a normal form description of the dynamics near the grazing trajectory in agreement with previous studies of grazing periodic trajectories it is found that the catastrophic loss of a local attractor and strong instability characteristic of grazing bifurcations is directly associated with the repeated application of a square root term that appears to lowest order in the normal form expansion specifically it is found that the square root term is absent in the description of the dynamics normal to a quasiperiodic trajectory covering a co dimension one invariant torus resulting in a piecewise linear description of the normal dynamics and at most a weak instability in contrast for co dimension two or higher the square root term is generically present in the normal dynamics here however the quasiperiodicity of the grazing motion implies that there is no upper limit to the time between impacts on nearby trajectories suggesting the persistence of a local attractor for some interval about the parameter value corresponding to grazing the results of the analysis are illustrated through a series of model examples

a meshless compositional approach to shape optimal design meshless computational strategies for shape optimal design through the composition of behavioral fields are developed in this paper the composition of behavioral fields is carried out in a manner that is procedurally similar to composition of primitive geometrical entities through set theoretic boolean operations in constructive solid geometry the methodology is shown to lead to a tighter integration between design and analysis and is termed constructive solid analysis a meshless approximation using non uniform rational b spline basis functions is used to discretize the behavioral fields defined over the geometrical primitives remeshing which is a critical bottleneck in shape optimization using conventional finite element analysis is either eliminated or limited to those primitives that are modified further it is demonstrated that the reconstruction of stiffness matrices is required only for those geometrical primitives that are affected by the design changes design sensitivity analysis techniques are developed for the discretized solution system arising out of the compositional analysis an adaptive numerical integration scheme is developed and shown to be necessary to accurately compute the effect of small domain perturbations on the problem functions some of the common challenges in conventional shape optimization problems such as difficulty in creating and merging multiple holes are naturally resolved using the developed compositional approach several representative problems are solved to validate and to demonstrate the methodology

non linear frequency response characteristics of an impact pair abstract the method of harmonic balance is used to develop approximate analytical solutions to the equations of motion of a single impact pair including a general discussion of the existence and stability of these solutions non linear frequency response characteristics are obtained for a single frequency excitation and primary resonance no subharmonic or superharmonic response and the results are validated using an analog computer simulation it has been found that the use of digital simulation numerical integration may lead to inaccurate results over certain frequency ranges it is also shown that although the shapes of the force displacement relationship for clearance non linearity and the classic cubic non linearity are similar the resulting non linear frequency response curves can be quite different various issues related to the clearance non linearity problem are discussed