formulation of elastostatic hybrid trefftz stress elements abstract the hybrid trefftz stress hts element is derived from the fundamental conditions of linear elastostatics the stress and boundary displacement fields are directly approximated consistent finite element variables are so defined as to obtain boundary integral expressions for the finite element equilibrium and compatibility conditions encoded by dual transformations independent of the constitutive relations reciprocity is preserved in the finite element elasticity relations which are also found to be described by boundary integral arrays when the trefftz constraint is enforced consequent upon duality and reciprocity the resulting boundary integral solving system is symmetric and sparse the energy statements associated with the hybrid trefftz stress element are established and the conditions for the existence uniqueness multiplicity and static and kinematic admissibility of the finite element solutions are presented the hts clement is compared with the displacement frame based hybrid trefftz ht d element of jirousek it is shown that the ht d element is in fact an hybrid stress element the numerical tests performed to assess the relative performances of the hts and ht d elements show that better accuracy levels are obtained using discontinuous boundary approximation bases

experimental modal analysis of non linear systems a feasibility study experimental modal analysis techniques are based on the theory of linear systems in this paper the feasibility of their application to non linear systems is examined a three degree of freedom non linear mechanical system was modeled on an analog computer and system responses due to band limited random excitation were examined by using a two channel fft analyzer frequency response functions natural frequencies and model responses were studied experimentally for a number of example cases this study shows that the measured transfer function plots can alert one to the fact that the structure is non linear measured modal response data base can still give a rough idea about the system behavior in addition measured coherence function estimates can be used as the warning singls for inherent non linearities

dual hybrid trefftz element formulation based on independent boundary traction frame reference epfl article 102727view record in web of science record created on 2007 04 23 modified on 2016 08 08

forced harmonic response analysis of nonlinear structures using describing functions a semianalytical quasilinear method based on the describing function formulation is proposed for the harmonic response analysis of structures with symmetrical nonlinearities the equations of motion are converted to a set of nonlinear algebraic equations the linear and nonlinear parts of the structure are dealt with separately the former being represented by the constant linear receptance matrix and the latter by the generalized quasilinear matrix which is updated at each iteration several examples dealing with cubic stiffness piecewise linear stiffness and coulomb friction type of nonlinearities are presented

approachability and fixed points for non convex set valued maps this paper studies the approachability of upper semicontinuous nonconvex set valued maps by single valued continuous functions and its applications to fixed point theory the use of approximate selections was initiated by j von neumann 41 in the proof of his well known minimax principle this remarkable property was extended to the normed space setting by cellina s and cellina and lasota 9 in the context of a degree theory for upper semicontinuous convex compact valued maps it also holds for maps with compact contractible values defined on finite polyhedra of iw ma cole11 40 and more generally defined on compact anrs mclennan 39 it was recently taken up by gbrniewicz granas and kryszewski 22 241 in the context of an index theory for non convex maps defined on compact anrs the content of this paper is divided into three parts the first part is devoted to background material concerning the types of spaces and set valued maps studied herein in the second part we define the abstract class d of approachable set valued maps that is the class of maps a x y

elastic wave propagation in unsaturated porous media using hybrid trefftz stress elements summary the stress model of the hybrid trefftz finite element is formulated for the analysis of elastodynamic problems defined on unsaturated porous media the supporting mathematical model is the theory of mixtures with interfaces and considers the full coupling between the solid fluid and gas phases including the effect of seepage acceleration hybrid trefftz stress elements use the free field regular solutions of the homogeneous navier or beltrami equation to construct the approximation of the generalized stresses in the domain of the element the influence of non homogeneous terms in the navier equation is modelled using solutions of the corresponding static problem the resulting elements are highly convergent under p refinement and robust to both low and high excitation frequencies as the trial functions embody relevant physical information on the modelled phenomenon copyright 2013 john wiley sons ltd

on the orthogonalised reverse path method for nonlinear system identification abstract the problem of obtaining the underlying linear dynamic compliance matrix in the presence of nonlinearities in a general multi degree of freedom mdof system can be solved using the conditioned reverse path crp method introduced by richards and singh 1998 journal of sound and vibration 213 4 pp 673 708 the crp method also provides a means of identifying the coefficients of any nonlinear terms which can be specified a priori in the candidate equations of motion although the crp has proved extremely useful in the context of nonlinear system identification it has a number of small issues associated with it one of these issues is the fact that the nonlinear coefficients are actually returned in the form of spectra which need to be averaged over frequency in order to generate parameter estimates the parameter spectra are typically polluted by artefacts from the identification of the underlying linear system which manifest themselves at the resonance and anti resonance frequencies a further problem is associated with the fact that the parameter estimates are extracted in a recursive fashion which leads to an accumulation of errors the first minor objective of this paper is to suggest ways to alleviate these problems without major modification to the algorithm the results are demonstrated on numerically simulated responses from mdof systems in the second part of the paper a more radical suggestion is made to replace the conditioned spectral analysis which is the basis of the crp method with an alternative time domain decorrelation method the suggested approach the orthogonalised reverse path orp method is illustrated here using data from simulated single degree of freedom sdof and mdof systems

mixed finite element formulation for the solution of parabolic problems a mixed formulation of the finite element method is used to establish a higher order incremental method for the solution of parabolic equations the displacement and velocity fields in the terminology of solid mechanics are approximated independently in time using a hierarchical adaptive basis three time bases are tested namely polynomial radial and wavelet bases the time approximation criterion ensures stability and preserves parabolicity the resulting discretization in the time domain leads to an uncoupled governing system in the space dimension this system can be subsequently solved using the alternative formulations for the finite element and boundary element methods the application of the conventional conform displacement formulation of the finite element method is illustrated particular attention is given to the extension of pian and trefftz type hybrid stress finite elements for transient analysis in the time domain the performance of the coupled time space integration method is assessed and the results obtained are compared with the results reported in the literature for alternative time integration procedures

hybrid trefftz stress and displacement elements for axisymmetric incompressible biphasic media abstract the stress and displacement models of the hybrid trefftz finite element formulation are applied to the solution of incompressible axisymmetric saturated porous media the use of a trefftz approximation basis ensures that all domain conditions of the problem are satisfied in a strong form namely the equilibrium the constitutive and the strain displacement relations and the mixture incompressibility condition the alternative stress and displacement models are fully complementary in terms of approximation criteria the stress displacement model is derived from the direct approximation of the stress and pressure fields the displacements in the solid and fluid phases in the domain of the element the displacements of the solid phase and the normal displacement of the fluid phase are approximated independently on the boundary of the stress element and used to enforce in a weak form the inter element and boundary equilibrium conditions on the forces in the solid phase and on the fluid pressure the boundary approximation used in the displacement element is on the solid surface forces and the fluid pressure and is used to enforce on average the inter element and boundary displacement continuity conditions the resulting finite element governing systems are sparse well suited to adaptive refinement and parallel processing and their coefficients are defined by boundary integral expressions the energy statements associated with the formulation are recovered and sufficient conditions for the uniqueness of the finite element solutions are stated benchmark tests on hydrated soft tissue modelling are used to assess the performance of the alternative stress and displacement models of the hybrid trefftz formulation

wavelets in hybrid mixed stress elements the objective of this paper is to present the application of wavelets in the implementation of the stress model of the hybrid mixed finite element formulation independent wavelet bases are used to approximate the stresses in the domain and the displacements both in the domain and on the boundary of elastostatic finite elements except for the kinematic boundary conditions which are enforced directly all the remaining equations of elastostatics are enforced in a weighted residual form so designed as to ensure that the discrete model embodies the relevant properties of the continuum fields they represent namely static kinematic duality and elastic reciprocity numerical examples are used to illustrate the characteristics of the numerical model being presented and to assess its accuracy and efficiency

fixed point theorems for multifunctions having kkm property on almost convex sets in this paper for two nonempty subsets x and y of a linear space e we define the class kkm x y and investigate the fixed point problem for t kkm x x with x an almost convex subset of a locally convex space our fixed point theorem contains lassonde fixed point theorem for kakutani factorizable multifunctions as special case

ekeland s variational principle minimax theorems and existence of nonconvex equilibria in complete metric spaces abstract in this paper we introduce the concept of function which generalizes the concept of w distance studied in the literature we establish a generalized ekeland s variational principle in the setting of lower semicontinuous from above and functions as applications of our ekeland s variational principle we derive generalized caristi s common fixed point theorems a generalized takahashi s nonconvex minimization theorem a nonconvex minimax theorem a nonconvex equilibrium theorem and a generalized flower petal theorem for lower semicontinuous from above functions or lower semicontinuous functions in the complete metric spaces we also prove that these theorems also imply our ekeland s variational principle

duality and symmetry in mixed integral methods of elastostatics mixed formulations for integral methods of elastostatic analysis of structures are presented both finite and boundary element approaches are considered a governing system exhibiting symmetry is obtained in both cases by preserving duality in the descriptions of equilibrium and compatibility and reciprocity in the elastic constitutive relations the theorems of virtual forces and displacements are interpreted as the energetic representation of static kinematic duality the quadratic programs associated with the governing system are identified as the theorems of minimum potential energy and co energy mathematical programming theory is used to establish conditions for the existence and uniqueness of solutions

use of the hilbert transform in modal analysis of linear and non linear structures abstract an initial study into the application of the hilbert transform in modal analysis procedures is presented it is shown that typical structural non linearities such as non linear damping and stiffness can be detected and identified directly without the need to generate explicit models no assumptions regarding the degree of non linearity are made which is a restriction in the classical methods for dealing with non linearities the properties of the hilbert transform are discussed with respect to linear and non linear dynamical systems and a discrete transform developed from the continuous functions is derived in the frequency domain and adapted to modal analysis data in the form of mobility transfer functions truncation effects arising from limited frequency ranges of the mobility transfer functions are accounted for by employing correction terms in the frequency domain several examples are studied of single and multi mode systems with non linearities such as friction clearance and non linear stiffness these examples indicate that the hilbert transform offers a new method for extending modal analysis to the domains of non linear systems

three dimensional hybrid trefftz stress elements the stress model of the hybrid trefftz finite element formulation is applied to the linear elastostatic analysis of solids the stresses are approximated in the domain of the element and displacements on its boundary complete linearly independent hierarchical polynomial approximation functions are used in both domain and boundary approximations the displacement basis is defined independently on each inter element surface continuity at the edges and on the corners of the elements is not enforced a priori the stress basis is constrained to solve locally the beltrami governing differential equation it is derived from the associated papkovitch neuber elastic displacement solution generalized variables are used to ensure that the approximations are independent of the geometric description of the elements the solving system is derived directly from the fundamental relations of elastostatics the solving system is symmetric when the same property applies to the local elasticity condition sparse described by boundary integral arrays and well suited to p refinement and parallel processing the numerical implementation of these equations is discussed and numerical tests are presented to illustrate the performance of the finite element formulation copyright 2000 john wiley sons ltd

hybrid trefftz stress elements for incompressible biphasic media summary a wavelet based high order time integration method is applied to replace the parabolic problem governing the response of incompressible biphasic media by a set of uncoupled helmholtz problems their formal solutions are used to formulate the stress model of the hybrid trefftz finite element formulation the stress pressure and displacement fields are directly approximated and designed to satisfy locally the equilibrium condition in each phase of the mixture this basis is used to enforce on average the compatibility conditions and the constitutive relations of the mixture the displacements in the solid and the normal displacement in the fluid are approximated independently on the boundary of the element and the basis is used to enforce in weak form the boundary equilibrium conditions the resulting solving system is sparse well suited to adaptive refinement and parallel processing the energy statements associated with the formulation are recovered and sufficient conditions for the uniqueness of the finite element solutions are stated testing problems reported in the literature are used to illustrate the quality of the pressure stress displacement and velocity estimates obtained with the hybrid trefftz stress element copyright q 2009 john wiley sons ltd

generalized finite differences using fundamental solutions summary it is well known that solutions for linear partial differential equations may be given in terms of fundamental solutions the fundamental solutions solve the homogeneous equation exactly and are obtained from the solution of the inhomogeneous equation where the inhomogeneous term is described by a dirac delta distribution fundamental solutions are the building blocks of the boundary element method and of the method of fundamental solutions and are traditionally used to build boundary only global approximations in the domain of interest in this work the same characteristic of the fundamental solutions that of solving the homogeneous equation exactly is used but not to build a global approximation on the contrary local approximations are built in such a manner that it is possible to construct finite difference operators that are free from any form of structured grid copyright q 2009 john wiley sons ltd

some results for the family kkm x y and the φ mapping abstract in this paper we first establish a fixed point theorem for a k set contraction map on the family kkm x x which not needs to be a compact map next we establish the matching theorems coincidence theorems and minimax theorems on the family kkm x y and the mapping

a general formulation of equilibrium macro elements with control of spurious kinematic modes the exorcism of an old curse this paper illustrates a method whereby a family of robust equilibrium elements can be formulated in a general manner the effects of spurious kinematic modes present to some extent in all primitive equilibrium elements are eliminated by judicious assembly into macro equilibrium elements these macroelements are formulated with sufficient generality so as to retain the polynomial degree of the stress field as a variable such a family of macro elements is a new development and results for polynomials of degree greater than two have not been seen before the quality of results for macro equilibrium elements with varying degrees of polynomial is demonstrated by numerical examples

hybrid finite element formulations for elastodynamic analysis in the frequency domain abstract three alternative sets of hybrid formulations to solve linear elastodynamic problems by the finite element method are presented they are termed hybrid mixed hybrid and hybrid trefftz and differ essentially on the field conditions that the approximation functions are constrained to satisfy locally two models namely the displacement and the stress models are obtained for each formulation depending on whether the tractions or the boundary displacements are the field chosen to implement interelement continuity a fourier time discretization is used to uncouple the solving system in the frequency domain the basic space discretization criterion is implemented directly on the fundamental relations of elastodynamics and used to derive the stress and displacement models of the hybrid mixed formulation the hybrid and hybrid trefftz formulations are presented in sequence as the variants of the hybrid mixed formulation obtained by progressively increasing the constraints on the approximation bases numerical implementation aspects are briefly discussed and the performance of the finite element models is illustrated with numerical applications

existence of solutions for quasi equilibrium problems in noncompact topological spaces abstract in this paper a new fan browder type fixed point theorem is proved under noncompact setting of general topological spaces by applying the fixed point theorem several new existence theorems of solutions for quasi equilibrium problems are proved under noncompact setting of topological spaces these theorems improve and generalize a number of important known results in literature

on the generalized quasi variational inequality problems the purpose of this paper is to study the existence problem of solutions for some kinds of abstract generalized quasi variational inequality problems by using a new kind of fixed point approach

continuous selection and fixed point theorems in this paper we obtain continuous selection theorems with range in a g convex space or in a space related to a g convex space and noncompact domain some applications to fixed point theorems and coincidence theorems are given we obtain some new results as well as generalizations of many known results

a further generalization of yannelis prabhakar s continuous selection theorem and its applications abstract in this article we first prove one improved version of the yannelis prabhakar continuous selection theorem and next as its applications a fixed point theorem in noncompact product spaces a nonempty intersection theorem some existence theorems of solutions for the generalized quasi variational inequalities and some equilibrium existence theorems for the abstract economies are given

system of coincidence theorems with applications in this paper we establish systems of coincidence theorems from which solution of system of inequalities and system of minimax theorems was established in this paper

a mixed hybrid finite element model based on orthogonal functions a mixed hybrid formulation for stress finite elements is presented the stresses and the displacements in the domain of the element and the displacements on the boundary are simultaneously and independently approximated using orthogonal functions the stress approximation functions are used as weighting functions in the weighted residual enforcement of the local compatibility and constitutive equations similarly the displacement approximation functions in the domain and on the boundary are used as weighting functions in the weighting residual enforcement of the local equilibrium equation and of the static boundary conditions respectively legendre polynomials and fourier series are used to illustrate the performance of the finite element formulation when applied to elastostatic problems

a hybrid mixed finite element model based on legendre polynomials for reissner mindlin plates abstract a hybrid mixed formulation for reissner mindlin plates is presented the finite element formulation is derived from first principles of mechanics the stress resultants and the displacements in the domain of the element and the displacements on the boundary are simultaneously and independently approximated using legendre polynomials numerical applications are presented to illustrate the performance of the suggested reissner mindlin plate element

a set of hybrid equilibrium finite element models for the analysis of three dimensional solids in this paper an approach to the formulation of equilibrium elements for the analysis of three dimensional elasticity problems is presented this formulation is an extension of the approach previously proposed for the analysis of two dimensional elasticity problems the general aspects of the formulation remain unchanged when applied to the new problem but new points are considered namely the way to perform volume integrations for general elements and the techniques used to obtain the self equilibrated three dimensional stress approximation functions the numerical behaviour of such elements is presented and discussed

shape optimization with hybrid trefftz displacement elements the displacement model of the hybrid trefftz finite element formulation is applied to the shape optimization of linear elastostatic problems the model is based on the direct approximation of the displacements in the domain of the element and of the tractions on its boundary the independent description of the geometry is based on the parametric description of the shape of the element sides the finite element solving system is symmetric and sparse as the displacement approximation is extracted from the solution set of the governing differential equations all structural matrices are defined by boundary integral expressions the approximation bases are compact and naturally p hierarchical high order approximations are implemented to obtain accurate solutions using coarse meshes of macro elements the sensitivities are determined analytically and remeshing is not implemented during the optimization procedure because the elements are weakly sensitive to gross shape distortion numerical testing is based on a standard set of two dimensional linear elastostatic problems copyright 2001 john wiley sons ltd

hybrid trefftz displacement element for spectral analysis of bounded and unbounded media the hybrid trefftz displacement element is applied to the elastodynamic analysis of bounded and unbounded media in the frequency domain the displacements are approximated in the domain of the element using local solutions of the wave equation the neumann conditions are enforced directly and the surface forces are approximated on the dirichlet and inter element boundaries of the finite element mesh two alternative elements are developed to model unbounded media namely a finite element with absorbing boundaries and an unbounded element that satisfies explicitly the sommerfeld condition the finite element equations are derived from the fundamental relations of elastodynamics written in the frequency domain the numerical implementation of these equations is discussed and numerical tests are presented to assess the performance of the formulation

three dimensional hybrid trefftz stress finite elements for plates and shells three dimensional hybrid trefftz stress finite elements for plates and shells are proposed two independent fields are approximated stresses within the element and displacement on their boundary the required stress field derived from the papkovitch neuber solution of the navier equation which a priori satisfies the trefftz constraint is generated using homogeneous harmonic polynomials restriction on the polynomial degree in the coordinate measured along the thickness direction is imposed to reduce the number of independent terms explicit expressions of the corresponding independent polynomials are listed up to the fifth order illustrative applications to evaluate displacements and stresses are carried out by hexahedral hybrid trefftz stress element models the hierarchical p refinement and h refinement strategy are exploited in the numerical tests

fixed point theorems for better admissible multimaps on almost convex sets abstract we obtain new fixed point theorems on multimaps in the class b p defined on almost convex subsets of topological vector spaces our main results are applied to deduce various fixed point theorems coincidence theorems almost fixed point theorems intersection theorems and minimax theorems consequently our new results generalize well known works of kakutani fan browder himmelberg lassonde and others

fixed point theorems for the ψ set contraction mapping on almost convex sets abstract in this paper we first discuss the properties of the almost convex subsets of a hausdorff topological vector space then in the setting of the almost convex sets we establish some fixed point theorems for the two k k m and b d type set valued mappings with either set contraction or 1 set contraction next we also establish new cycle point theorems for three set valued mappings our results generalize the results of chang et al t h chang c l yen kkm property and fixed point theorems j math anal appl 203 1996 224 235 and park s park fixed point theorems for better admissible multimaps on almost convex sets j math anal appl 329 2007 690 702

a new particular solution strategy for hyperbolic boundary value problems using hybrid trefftz displacement elements summary a new indirect approach to the problem of approximating the particular solution of non homogeneous hyperbolic boundary value problems is presented unlike the dual reciprocity method which constructs approximate particular solutions using radial basis functions polynomials or trigonometric functions the method reported here uses the homogeneous solutions of the problem obtained by discarding all time derivative terms from the governing equation nevertheless what typifies the present approach from a conceptual standpoint is the option of not using these trial functions exclusively for the approximation of the particular solution but to fully integrate them with the trefftz compliant homogeneous solution basis the particular solution trial basis is capable of significantly improving the trefftz solution even when the original equation is genuinely homogeneous an advantage that is lost if the basis is used exclusively for the recovery of the source terms similarly a sufficiently refined trefftz compliant basis is able to compensate for possible weaknesses of the particular solution approximation the method is implemented using the displacement model of the hybrid trefftz finite element method the functions used in the particular solution basis reduce most terms of the matrix of coefficients to boundary integral expressions and preserve the hermitian sparse and localized structure of the solving system that typifies hybrid trefftz formulations even when domain integrals are present they are generally easy to handle because the integrand presents no singularity copyright 2015 john wiley sons ltd