a simplified analysis of plate structures using trefftz functions this paper presents a method for a quick evaluation of stresses and displacements in a plate structure for elastostatic problems first an approximation is built from the mathematical structure of the solutions for starshaped domains which is representative of long wavelength effects second a variational formulation consistent with this approximation is proposed finally two alternative procedures for coupling adjacent domains are demonstrated

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

cubic curves and totally geodesic subvarieties of moduli space in this paper we present the rst example of a primitive totally geodesic subvariety f m g n with dim f 1 the variety we consider is a surfacef m 1 3 dened using the projective geometry of

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

finiteness of teichmuller curves in non arithmetic rank 1 orbit closures we show that in any non arithmetic rank 1 orbit closure of translation surfaces there are only finitely many teichm uller curves we also show that in any non arithmetic rank 1 orbit closure any completely parabolic surface is veech

on the amplitude decay of strongly non linear damped oscillators the problem considered is that of the amplitude behavior of the strongly non linear damped oscillator u 2 u u f u 0 where is small u and f u are o 1 may be arbitrarily large and f u is an odd function a simple approximation to the amplitude decay is obtained by first linearizing the static terms and then using the wkb approximation of particular interest is the influence of the non linearity on the amplitude decay several examples which illustrate this influence are provided

two scale analysis of heterogeneous elastic plastic materials with asymptotic homogenization and voronoi cell finite element model in this paper a multiple scale finite element model vcfem homo has been developed for elastic plastic analysis of heterogeneous porous and composite materials by combining asymptotic homogenization theory with the voronoi cell finite element model vcfem vcfem for microstructural modeling originates from dirichlet tessellation of representative material elements at sampling points in the structure structural modeling is done by the general purpose finite element code abaqus and interfacing with the microscale vcfem analysis is done through the user subroutine in abaqus for material constitutive relation umat asymptotic homogenization in umat generates macroscopic material parameters for abaqus following the macroscopic analysis a local vcfem analysis is invoked to depict the true evolution of microstructural state variables various numerical examples are executed for validating the effectiveness of vcfem homo and the effect of size shape and distribution of heterogeneities on local and global response is examined

non linear free vibrations of a rotating flexible arm abstract the non linear moderately large amplitude flexural free vibrations of an arm clamped with a setting angle to a rigid rotating hub are studied the shear deformation and rotary inertia effects are assumed to be negligible but account is taken of axial inertia non linear curvature and the inextensibility condition the lagrangian approach in conjunction with the assumed modes method assuming constant hub rotation speed is used in a consistent manner to obtain the third order non linear uni modal temporal problem because of the strength of the non linearities in the temporal problem which includes elastic and inertial geometric stiffening as well as inertial softening terms a time transformation method is employed to obtain an approximate solution to the frequency amplitude relation of arm free oscillation results in non dimensional form are presented graphically for the effect of hub rotation speed blade setting angle and hub radius on the variation of the natural frequency with vibration amplitude

on the primary frequency response of strongly non linear oscillators a linearization approach abstract the problem considered is the primary frequency response of the class of strongly non linear forced oscillators u 2 u mu eg u p cos t whee g u is an odd non linear function of the displacement u t e may be arbitrarily large and m 1 0 or 1 a simple approximation to the fundamental harmonic of the response is obtained by first linearizing the static terms using the frequency relations developed in reference 1 for the autonomous conservative oscillator and then using the averaging method to solve the linearized forced problem a comparison with the numerical and other approximate analytic methods results is made which shows the advantages of the present technique in terms of computational effort and accuracy

large amplitude primary and superharmonic resonances in the duffing oscillator second order perturbation analyses are presented of the order three superharmonic resonance in a duffing oscillator u u u3 p cos t and of the primary resonance in a duffing oscillator with softening non linearity u u u3 p cos t it is found in the former case that it is necessary to go to the second order to obtain realistic steady state stability results in the latter problem however the second order solution gives little or no improvement on the first order result also presented for the latter problem is what is thought to be the first example of a double jump phenomenon for single degree of freedom harmonically excited oscillators

on the critical exponent of infinitely generated veech groups we prove the existence of veech groups having a critical exponent strictly greater than any elementary fuchsian group i e frac 1 2 but strictly smaller than any lattice i e 1 more precisely every affine covering y of a primitive l shaped veech surface x ramified over the singularity and a non periodic connection point p in x has such a veech group mathrm sl y hubert and schmidt duke math j 123 49 69 2004 showed that these veech groups are infinitely generated and of the first kind we use a result of roblin and tapie monogr enseign math 43 61 92 2013 which connects the critical exponent of mathrm sl y with the cheeger constant of the schreier graph of mathrm sl x mathrm stab mathrm sl x p the main task is to show that the cheeger constant is strictly positive i e the graph is non amenable in this context we introduce a measure of the complexity of connection points that helps to simplify the graph to a forest for which non amenability can be seen easily

a multi level wave based numerical modelling framework for the steady state dynamic analysis of bounded helmholtz problems with multiple inclusions the wave based method wbm is an alternative numerical prediction method for both interior and exterior steady state dynamic problems which is based on an indirect trefftz approach it applies wave functions which are exact solutions of the governing differential equation to describe the dynamic field variables the smaller system of equations and the absence of pollution errors make the wbm very suitable for the treatment of helmholtz problems in the mid frequency range where element based methods are no longer feasible due to the associated computational costs a sufficient condition for convergence of the method is the convexity of the considered problem domain as a result only problems of moderate geometrical complexity can be considered and some geometrical features cannot be handled at all in this paper these limitations are alleviated through the development of a general modelling framework based on existing wbm methodologies which allows for the efficient introduction of inclusion configurations in bounded wbm models for problems governed by one or more helmholtz equations the feasibility and efficiency of the method is illustrated by means of numerical verification studies in which the methodology is applied to two types of dynamic problems on the one hand a single helmholtz equation associated with the steady state dynamic behaviour of acoustic cavities is studied on the other hand the framework is applied to the solution of the navier system of partial differential equations that describe the elastodynamic response of two dimensional perforated solids

variational formulations for tfem of piezoelectricity abstract the paper presents a family of variational formulations of trefftz finite elements wherein the assumed internal displacement and electric potential fields a priori fulfil the governing differential equations of the problem over the element sub domain while the inter element continuity and the boundary conditions are enforced using a modified variational principle together with an independent frame field defined on each element boundary it is based on four free energy densities each with two kinds of independent variables as basic independent variables i e d e e e d and e based on the assumed intra element and frame fields an element stiffness matrix equation is obtained which is implemented into computer programs for numerical analysis some numerical examples are considered to show the application of the proposed formulation

completely periodic directions and orbit closures of many pseudo anosov teichmueller discs in q 1 1 1 1 in this paper we investigate the closure of a large class of teichmuller discs in the stratum mathcal q 1 1 1 1 or equivalently in a rm gl 2 mathbb r invariant locus mathcal l of translation surfaces of genus three we describe a systematic way to prove that the rm gl 2 mathbb r orbit closure of a translation surface in mathcal l is the whole locus mathcal l the strategy of the proof is an analysis of completely periodic directions on such a surface and an iterated application of ratner s theorem to unipotent subgroups acting on an adequate splitting this analysis applies for example to all teichmuller discs obtained by the thurston veech s construction with a trace field of degree three which are moreover obviously not veech we produce an infinite series of such examples and show moreover that the favourable splitting situation does not arise everywhere on mathcal l contrary to the situation in genus two we also study completely periodic directions on translation surfaces in mathcal l for instance we prove that completely periodic directions are dense on surfaces obtained by the thurston veech s construction

analysis of non linear autonomous conservative oscillators by a time transformation method the problem considered is that of the free vibration of the class of strongly non linear oscillators u mu f u 0 where m 1 0 or 1 f u is a non linear function of the displacement u t and is not small through a continuous stretching of the time t a new time t is found in whose domain the response is simple harmonic this time transformation method allows the response u t and period to be calculated to any desired degree of accuracy however the primary objective is to develop reasonably simple accurate approximations for the oscillators considered

dynamics of sl2 ℝ over moduli space in genus two this paper classifies orbit closures and invariant measures for the natural action of sl2 r on um2 the bundle of holomorphic 1 forms over the moduli space of riemann surfaces of genus two

postbuckling analysis of thin plates by a hybrid trefftz finite element method abstract a hybrid trefftz finite element ht fe model for postbuckling analysis of thin plates is presented based on a modified variational principle with the aid of incremental form of equilibrium equations all non linear terms may be viewed as pseudo loads and then the in plane and out of plane equations can be uncoupled as a consequence the solution procedure for the postbuckling plate becomes very simple two numerical examples are considered to illustrate the correctness and accuracy of the proposed formulation

on a problem of modified lindstedt poincare for certain strongly non linear oscillators in the present paper concerns the modified lindstedt poincare method is presented for extending the rang of the validity of perturbation expansion to strongly non linear oscillation it is an effective method for dealing with strongly non linear vibration of single degree of freedom system which cannot be treated by the standard l p method therefore a strongly non linear system with large parameter m is transformed into a small parameter system with respect to a this method is suitable for the system with even non linearities as well as with odd non linearities all numerical results computed are in pretty good and displayed graphysically this method is suitable for the system with even non linearities as well as with odd non linearities all numerical results computed are in pretty good and displayed graphysically

comments on development of two dimensional elements with a central circular hole a k soh z f long comput methods appl mech engrg 188 2000 431 440

hodge teichmuller planes and finiteness results for teichmuller curves we prove that there are only finitely many algebraically primitive teichmuller curves in the minimal stratum in each prime genus at least 3 the proof is based on the study of certain special planes in the first cohomology of a translation surface which we call hodge teichmuller planes we also show that algebraically primitive teichmuller curves are not dense in any connected component of any stratum in genus at least 3 the closure of the union of all such curves in a fixed stratum is equal to a finite union of affine invariant submanifolds with unlikely properties results of this type hold even without the assumption of algebraic primitivity combined with work of nguyen and the second author a corollary of our results is that there are at most finitely many nonarithmetic teichmuller curves in h 4

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

the fast solution of poisson s and the biharmonic equations on irregular regions we present fast methods for solving laplace s and the biharmonic equations on irregular regions with smooth boundaries the methods used for solving both equations make use of fast poisson solvers on a rectangular region in which the irregular region is embedded they also both use an integral equation formulation of the problem where the integral equations are fredholm integral equations of the second kind the main idea is to use the integral equation formulation to define a discontinuous extension of the solution to the rest of the rectangular region fast solvers are then used to compute the extended solution aside from solving the equations we have also been able to compute derivatives of the solutions with little loss of accuracy when the data was sufficiently smooth

geodesic planes in hyperbolic 3 manifolds this paper initiates the study of rigidity for immersed totally geodesic planes in hyperbolic 3 manifolds m of infinite volume in the case of an acylindrical 3 manifold whose convex core has totally geodesic boundary we show that the closure of any immersed geodesic plane is a properly immersed submanifold of m on the other hand we show that rigidity fails for quasifuchsian manifolds

trefftz indirect methods for plane piezoelectricity in this paper a unified theory for the general solutions of three dimensional elasticity is employed to transform the governing equations of plane piezoelectricity into three generalized laplace equations the latter equations are uncoupled and can be pursued separately by introducing three generalized complex variables the complete solution sets for plane piezoelectricity are constructed by adopting the constituents in the solution sets as the trial functions the trefftz collocation and the trefftz galerkin methods are formulated both methods fall into the category of trefftz indirect methods as the coefficients of their trial functions are non physical numerical examples are presented to illustrate the efficacy of the formulations copyright 2005 john wiley sons ltd

teichmuller curves in moduli space eisenstein series and an application to triangular billiards there exists a teichmuller disc n containing the riemann surface ofy2 x n 1 in the genus n 1 2 teichmuller space such that the stabilizer of n in the mapping class group has a fundamental domain of finite poincare volume in n application is given to an asymptotic formula for the length spectrum of the billiard in isosceles triangles with angles n n n 2 n and to the uniform distribution of infinite billiard trajectories in the same triangles

generalized finite element analysis with t complete boundary solution functions the use of a complete and nonsingular set of trefftz functions in the solution of quasi harmonic equations is demonstrated and shown to be often superior to the more conventional singularity distribution in boundary type approximation procedures for coupling separate domains of such solution and indeed of deriving equivalent finite elements are demonstrated

a quadrilateral mixed finite element with two enhanced strain modes summary an improved plane strain stress element is derived using a hu washizu variational formulation with bilinear displacement interpolation seven strain and stress terms and two enhanced strain modes the number of unknowns of the four node element is increased from eight to ten degrees of freedom for linear and non linear applications the two unknowns associated with the enhanced strain terms can be eliminated by static condensation so that eight displacement degrees of freedom remain for the proposed element which is denoted by qe2 the excellent performance of the proposed element is demonstrated using several linear and non linear examples

analysis of stress concentrations in plates with rectangular openings by a combined conformal mapping finite element approach plates with rectangular openings develop stress concentrations under bending while these stresses can be determined using finite elements in many problems this would be difficult because a high density mesh would be needed in the neighborhood of every opening corner in this paper it is shown how a complex variable conformal mapping approach can be numerically coupled with the finite element method to analyze these corner stresses this approach can be used even with relatively coarse meshes where the finite element results by themselves do not resolve the stress concentrations in essence the method relies on finite element analysis to obtain information on the stress field in a region surrounding the plate opening this information is subsequently used to set up the parameters of the conformal mapping approach to obtain the near field stresses at the opening corners

hybrid trefftz plane elasticity elements with p method capabilities a family of p method plane elasticity elements is derived based on the hybrid trefftz formulation 1 exact solutions of the lame navier equations are used for the intra element displacement field together with an independent displacement frame function field along the element boundary the final unknowns are the parameters of the frame function field consisting of the usual degrees of freedom at corner nodes and an optional number of hierarchic degrees of freedom associated with the mid side nodes since the element matrices do not involve integration over the element area the elements have a polygonal contour with an optional number of curved sides the quadrilateral element has the same external appearance as the conventional p method plane elasticity element 2 3 but unlike in the conventional p method approach suitable special purpose trefftz functions are generally used to handle the singularity and or stress concentration problems rather than a local mesh refinement the practical efficiency of the new elements is assessed through a series of examples

analysis of forced non linear undamped oscillators by a time transformation method the recently developed time transformation method 1 3 is extended to the analysis of forced vibration of the strongly non linear undamped oscillator u u ef u p t where f u is a non linear function of the displacement u t and e is not necessarily small two types of external loading p t are considered a step input and a simple harmonic input the frequency amplitude relation is obtained through a slight modification of the results developed in reference 2 for the unforced oscillator a comparison with the results of numerical and other analytic methods is made it can be deduced that the time transformation approach offers simple and accurate approximations for the oscillators considered

variations of hodge structures of a teichmuller curve teichmuller curves are geodesic discs in teichmuller space that project to an algebraic curve in the moduli space mg we show that for all g 2 teichmuller curves map to the locus of real multiplication in the moduli space of abelian varieties observe that mcmullen has shown that precisely for g 2 the locus of real multiplication is stable under the sl2 r action on the tautological bundle mg we also show that teichmuller curves are defined over number fields and we provide a completely algebraic description of teichmuller curves in terms of higgs bundles as a consequence we show that the absolute galois group acts on the set of teichmuller curves

finite element analysis of nonlinear oscillators presented in this paper is a finite element method for the analysis of nonlinear oscillations which exhibit periodic response the basic idea of the method is to recast the initial value problem as a boundary value problem in which the domain that is period may be unknown we apply the method to study the free response of the conservative oscillator u mu f u 0 where m is either 1 0 or 1 f u is an odd nonlinear function and need not be small the harmonically forced case u mu f u psin t is also considered and it is shown that the superharmonic response can be efficiently calculated using this technique

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

billiards and teichmuller curves on hilbert modular surfaces this paper exhibits an infinite collection of algebraic curves isometrically embedded in the moduli space of riemann surfaces of genus two these teichmuller curves lie on hilbert modular surfaces parameterizing abelian varieties with real multiplication explicit examples constructed from l shaped polygons give billiard tables with optimal dynamical properties