discontinuous galerkin finite element methods for second order hyperbolic problems abstract we prove a priori and a posteriori error estimates for a finite element method for linear second order hyperbolic equations based on a space time finite element discretization with the basis functions being continuous in space and discontinuous in time

time discontinuous stabilized space time finite elements for timoshenko beams stabilized space time e nite element methods for the transient computational analysis of the elastodynamics of timoshenko beams have been developed the underlying time discontinuous galerkin formulation is implicit unconditionally stable higher order accurate and robust the employed interpolations are continuous in space and time inside time slabs but discontinuous in time between adjacent time slabs to suppress spurious numerical oscillations near discontinuities or high gradients galerkin least squares stabilization has been applied further improvement of the numerical representation of the transient elastic wave propagation phenomena has been achieved by specially designed galerkin gradient least squares operators because of the reduced phase and amplitude errors of these e nite elements much coarser spatial meshes may be used without loss of accuracy the resulting reduction of the number of unknowns leads to a signie cant decrease of computer time furthermore a globaladaptivetime stepping strategy has beenemployed basedon thetemporal jump residual of thetimee niteelement method as error estimator numerical examples of transientelastic wave propagation in timoshenko beams involving a wide spectrum of wave numbers and frequencies demonstrate the good performance of the developed methods

a space time finite element method for the wave equation a numerical method is introduced which uses finite elements in time and space simultaneously to solve the wave equation an error analysis for this scheme is presented and the results of several computations this scheme is accurate for time slabs of arbitrary thickness without introducing extra least squares or stabilization terms

enriched space time finite element method a new paradigm for multiscaling from elastodynamics to molecular dynamics summary the main objective of this paper is to present an enriched version of the space time fem method to incorporate multiple temporal scale features with a focus on dynamics problems the method is established by integrating the basic framework of the space time discontinuous galerkin method with the extended finite element method two versions of the method have been developed one at the continuum scale elastodynamics and the other focuses on the dynamics at the molecular level after an initial outline of the formulation we explore the incorporation of different types of enrichments based on the length scale of interest the effects of both continuous and discontinuous enrichments are demonstrated through numerical examples involving wave propagations and dynamic fracture in harmonic lattice the robustness of the method is evaluated in terms of convergence and the ability to capture the fine scale features it is shown that the enriched space time fem leads to an improvement in the convergence properties over the traditional space time fem for problems with multiple temporal features it is also highly effective in integrating atomistic with continuum representations with a coupled framework copyright 2012 john wiley sons ltd

application of the complex variable boundary element method to solving potential problems in doubly connected domains the complex variable boundary element method cvbem developed by hromadka for the solution of potential problems in simply connected domains is extended to the solution of heat conduction problems in doubly connected domains a cut is made in the doubly connected domain and it was found that the complex potentials along the cut do not cancel out but result in a complex stream function that plays the role of perturbation in the nodal equations cauchy riemann conditions are used to derive additional equations which relate the stream functions and the boundary heat fluxes and potentials when neumann and robin conditions are imposed on the boundaries the resulting nodal equations are expressed in matrix form and coding rules and methods for checking the matrix elements are developed three solution methods implicit explicit and hybrid are described and by means of examples the efficacy of these methods is discussed and compared

spurious resonances in numerical time integration methods for linear dynamics this paper deals with the accuracy of time integration methods for linear dynamics when applied near the resonance condition an approach for the analysis is considered which allows spurious resonance conditions to be detected the analysis of newmark methods shows the existence of such conditions which can adversely affect the quality of numerical computations as an alternative a higher order algorithm which can be viewed as a generalization of the trapezoidal rule is investigated the analysis reveals that the spurious disturbance near the resonance condition is greatly reduced the reported numerical tests confirm the theoretical predictions and demonstrate that high quality simulations can be obtained by means of higher order algorithms

use of post processing to increase the order of accuracy of the trapezoidal rule at time integration of linear elastodynamics problems in this paper we suggest a very simple and effective post processing procedure to increase the order of accuracy in time for numerical results obtained by the trapezoidal rule we first derive a new exact closed form a priori error estimator for time integration of linear elastodynamics equations by the trapezoidal rule with non uniform time increments based on this error estimator we suggest a new post processing procedure containing additional time integration of elastodynamics equations by the trapezoidal rule with few time increments that systematically improves the order of accuracy of numerical results with the increase in the number of additional time increments used for post processing for example the use of just one additional time increment for post processing after time integration with any number of uniform time increments renders the order of accuracy of numerical results equal to 10 3 numerical examples of the application of the new techniques to a system with a single degree of freedom and to a multi degree system confirm the corresponding increase in the order of convergence of numerical results after post processing because the same trapezoidal rule is used for basic computations and post processing the new technique retains all of the properties of the trapezoidal rule requires no writing of a new computer program for its implementation and can be easily used with any existing commercial and research codes for elastodynamics

boundary element method analysis of thermoelastic deformation in nonhomogeneous media abstract this paper presents a boundary element method bem formulation and numerical implementation of thermoelasticity problems in nonhomogeneous media the formulation uses the known kernels of the displacement equations for elasticity problems in homogeneous media this formulation leads to a domain integral containing the unknown displacement field in addition to the usual boundary integrals with displacements and tractions an iterative scheme is used to determine the displacement fields numerical results are presented for some illustrative plane strain problems the iterative scheme is shown to converge rapidly for these problems with moderate temperature gradients the bem results are compared with results from the finite element method fem for these problems and also with exact solutions whenever possible

a discontinuous galerkin finite element method for dynamic and wave propagation problems in non linear solids and saturated porous media a time discontinuous galerkin finite element method dgfem for dynamics and wave propagation in non linear solids and saturated porous media is presented the main distinct characteristic of the proposed dgfem is that the specific p3 p1 interpolation approximation which uses piecewise cubic hermite s polynomial and linear interpolations for both displacements and velocities in the time domain is particularly proposed consequently continuity of the displacement vector at each discrete time instant is exactly ensured whereas discontinuity of the velocity vector at the discrete time levels still remains the computational cost is then obviously saved particularly in the materially non linear problems as compared with that required for the existing dgfem both the implicit and explicit algorithms are developed to solve the derived formulations for linear and materially non linear problems numerical results illustrate good performance of the present method in eliminating spurious numerical oscillations and in providing much more accurate solutions over the traditional galerkin finite element method using the newmark algorithm in the time domain copyright 2003 john wiley sons ltd

accuracy of one step integration schemes for damped forced linear structural dynamics summary this paper proposes an energy based measure for the evaluation of the local truncation error of two level one step integration schemes the measure applies to multiple degree of freedom systems and does not necessarily require modal reduction to a scalar model it naturally handles the structural damping and external forcing terms that are generally and mistakenly neglected in error analyses and it segregates the error associated with the free and forced response components of the problem to illustrate the approach two examples associated with the application of the trapezoidal scheme and of a high order scheme proposed in the literature are analyzed the latter reveals the shortcomings of the standard approach that is based on the undamped unforced linear oscillator and therefore highlights the need for the proposed framework indeed the scheme order of accuracy is below expectation when structural damping or external forcing is considered in the numerically dissipative setting developments on the basis of the time discontinuous galerkin tdg method are then proposed to recover the scheme high order accuracy additionally they show the similarity that exists between schemes related to the tdg method and the ones obtained by integration by parts of the equation of motion copyright 2014 john wiley sons ltd

implementation and adaptivity of a space time finite element method for structural dynamics abstract in this paper we study the implementation and adaptivity of a space time finite element method for the analysis of two dimensional problems in structural dynamics the method also known as the time discontinuous galerkin method or the dg method employs finite elements discretizations in space and time simultaneously with bilinear basis functions that are continuous in space and discontinuous in time based on using the zienkiewicz zhu error estimate in space and the jumps discontinuities of displacements and velocities in the total energy norm as a local error estimate in time an h adaptive procedure which updates the spatial mesh and the time step size automatically so as to control the estimated errors within specified tolerances is proposed numerical examples are presented showing that the considered dg method is of second order accuracy in space in l 2 and third order accuracy in time and the adaptive procedure is capable of updating the spatial meshes and the time steps when necessary making the solutions reliable and the computation efficient

vectorial and parallel processing in stress analysis with the boundary element method the purpose of this short paper is to describe an experience at converting a scalar serial elastic axisymmetric bem code to a vector parallel environment on an ibm this is a single zone bem computer program

an efficient implementation of bem for two and three dimensional multi region elastoplastic analyses abstract boundary element methods bem have been implemented for solving multi region elastoplastic problems with the maximum efficiency a new form of newton raphson algorithm in nonlinear bem is established in which the formation of the right hand side terms in each iteration is accurately represented in this new algorithm only the equations related to the yielded nodes need gaussian elimination at each load step this advantage combined with the sub region technique now makes bem a viable tool for multi region elastoplastic analyses a combined analytical and numerical integration of boundary and volume integrals have been performed for both two and three dimensional analyses whenever the geometry of the volume cells meets the straight line or flat surface requirements the analytical integration is faster and more accurate than numerical integration the numerical results using the above formulation have been presented for some two and three dimensional practical problems commonly encountered in structural and geotechnical engineering and compared with other available solutions

structural dynamic analysis by a time discontinuous galerkin finite element method this paper studies a time discontinuous galerkin finite element method for structural dynamic problems by which both displacements and velocities are approximated as piecewise linear functions in the time domain and may be discontinuous at the discrete time levels a new iterative solution algorithm which involves only one factorization for each fixed time step size and a few iterations at each step is presented for solving the resulted system of coupled equations by using the jumps of the displacements and the velocities in the total energy norm as error indicators an adaptive time stepping procedure for selecting the proper time step size is described numerical examples including both single dof and multi dof problems are used to illustrate the performance of these algorithms comparisons with the exact results and or the results by the newmark integration scheme are given it is shown that the time discontinuous galerkin finite element method discussed in this study possesses good accuracy third order and stability properties its numerical implementation is not difficult and the higher computational cost needed in each time step is compensated by use of a larger time step size

explicit predictor multicorrector time discontinuous galerkin methods for non linear dynamics abstract explicit predictor multicorrector time discontinuous galerkin tdg methods developed for linear structural dynamics are formulated and implemented in a form suitable for arbitrary non linear analysis of structural dynamics problems the formulation is intended to inherit the accuracy properties of the exact parent implicit tdg methods to this end suitable predictors and correctors are designed to achieve third order accuracy large stability limits and controllable numerical dissipation by means of an algorithmic parameter as the study of a general non linear case is rather complex the analysis of the convergence properties of the resulting algorithms are restricted to conservative duffing oscillators for which closed form solutions are available it is shown that the main properties of the underlying parent scheme can be retained finally results of representative numerical simulations relevant to duffing oscillators and to a stiff spring pendulum discretized with finite elements illustrate the performance of the numerical schemes and confirm the analytical estimates

an efficient time discontinuous galerkin procedure for non linear structural dynamics this paper presents an effective time discontinuous galerkin procedure for non linear dynamics the procedure is based on a cheap iterative algorithm which is rather different from previous efforts in fact the algorithm is designed so that the corrected solutions inherit the desired stability and dissipative properties and the iterations serve only to improve accuracy some numerical tests illustrate the good performance of the present procedure which appears to be competitive with the available implementations of time discontinuous galerkin methods

time discontinuous galerkin methods with energy decaying correction for non linear elastodynamics in this paper a new time discontinuous galerkin tdg formulation for non linear elastodynamics is presented the new formulation embeds an energy correction which ensures truly energy decaying thus allowing to achieve unconditional stability that as shown in the paper is not guaranteed by the classical tdg formulation the resulting method is simple and easily implementable into existing finite element codes moreover it inherits the desirable higher order accuracy and high frequency dissipation properties of the classical formulation numerical results illustrate the very good performance of the proposed formulation copyright 2010 john wiley sons ltd

lines on the fermat quintic threefold and the infinitesimal generalized hodge conjecture we study the deformation theory of lines on the fermat quintic threefold we formulate an infinitesimal version of the generalized hodge conjecture and use our analysis of lines to prove it in a special case

time continuous galerkin methods for linear heat conduction problems abstract a petrov galerkin formulation of the semidiscrete linear transient heat conduction problem is given from which a unified set of a stable higher order time integration methods is derived accuracy and stability properties can be controlled by an algorithmic parameter introduced in the definition of the test functions in this manner a stable algorithms of order 2p and l stable algorithms of order 2p 1 are derived from a unique formulation in addition algorithms with intermediate accuracy and stability properties are made available the effects of varying the algorithmic parameter are investigated numerical tests are included to support the theoretical analysis

time discontinuous material point method for transient problems abstract this paper presents a time discontinuous material point method tdmpm for transient problems such as the wave propagation and impact responses in solids by dividing the continuous time domain into discrete time intervals the weak form of the tdmpm is established by considering the discrete grid based governing equations constraint and discontinuity conditions the displacement and velocity fields in a time interval are interpolated with the piecewise cubic and linear functions respectively by substituting the assumed displacement and velocity fields into the weak form a novel computational framework for the grid displacements and velocities at the discrete time instants is constructed in the new formulations the displacement field at each time instant remains to be continuous whereas the velocity field at the time instant becomes discontinuous these unique features ensure the tdmpm could properly capture the discontinuous characteristics and control the spurious numerical oscillations two numerical examples under the impact loading are used to verify the proposed method two representative impact problems are then presented for further verification and demonstration besides the corresponding contact algorithm adopted in the tdmpm is shown to be capable of capturing the correct contact behavior with higher fidelity and less computational cost than the mpm the presented results illustrate that the tdmpm could successfully control the spurious numerical oscillations associated with transient simulations

axisymmetric viscoplastic deformation by the boundary element method abstract this paper presents a boundary element formulation and numerical implementation of the problem of small axisymmetric deformation of viscoplastic bodies while the extension from planar to axisymmetric problems can be carried out fairly simply for the finite element method fem this is far from true for the boundary element method bem the primary reason for this fact is that the axisymmetric kernels in the integral equations of the bem contain elliptic functions which cannot be integrated analytically even over boundary elements and internal cells of simple shape thus special methods have to be developed for the efficient and accurate numerical integration of these singular and sensitive kernels over discrete elements the accurate determination of stress rates by differentiation of the displacement rates presents another formidable challenge a successful numerical implementation of the boundary element method with elementwise called the mixed approach or pointwise called the pure bem or bem approach determination of stress rates has been carried out a computer program has been developed for the solution of general axisymmetric viscoplasticity problems comparisons of numerical results from the bem and fem for several illustrative problems are presented and discussed in the paper it is possible to get direct solutions for the simpler class of problems for cylinders of uniform cross section and these solutions are also compared with the bem and fem results for such cases

direct computation of cauchy principal value integrals in advanced boundary elements this paper presents a new method for the direct computation of strongly singular integrals existing in the cauchy principal value sense it can be usefully applied in the solution by the direct boundary element method of many different problems initially some considerations are provided in order to summarize the state of the art on this issue then the features of the proposed method are reported the procedure allows the direct calculation of cauchy principal value integrals with first order singularity and it is applicable even in advanced boundary element methods employing high order elements it requires only the use of standard gaussian quadrature formulae plus the computation of a logarithmic term some examples show the effectiveness and efficiency of the procedure

adaptive finite element procedures for linear and non linear dynamics this paper discusses implementation and adaptivity of the discontinuous galerkin dg finite element method as applied to linear and non linear structural dynamic problems by the dg method both displacements and velocities are approximated as piecewise bilinear functions in space and time and may be discontinuous at the discrete time levels both implicit and explicit iterative algorithms for solving the resulted system of coupled equations are derived they are third order accurate and while the implicit procedure is unconditionally stable the explicit one is conditionally stable an h adaptive procedure based on the zienkiewicz zhu error estimate using the spr technique is applied numerical examples are presented to show the suitability of the dg method for both linear and non linear structural dynamic analysis copyright 1999 john wiley sons ltd

a methodology for the generation of low cost higher order methods for linear dynamics this work presents a methodology which generates efficient higher order methods for linear dynamics by improving the accuracy properties of norsett methods towards those of pade methods the methodology is based on a simple and low cost iterative procedure which is used to implement a set of higher order methods with controllable dissipation a sequence of improved solutions is obtained which correspond to algorithms offering an effective compromise between the efficiency of norsett methods and the accuracy of pade methods moreover a direct control over high frequency dissipation is possible by means of an algorithmic parameter numerical tests are reported which confirm that this set of algorithms is really attractive for linear dynamic analysis copyright 2003 john wiley sons ltd

multi field spacetime discontinuous galerkin methods for linearized elastodynamics we extend the single field spacetime discontinuous galerkin sdg method for linearized elastodynamics of abedi et al 1 to multi field versions a three field method in displacement velocity and strain is derived by invoking a bubnov galerkin weighted residuals procedure on the system of spacetime field equations and the corresponding jump conditions a two field formulation in displacement and velocity and the one field displacement formulation of 1 are obtained from the three field model through strong enforcement of kinematic compatibility relations all of these formulations balance linear and angular momentum at the element level and we prove that they are energy dissipative and unconditionally stable as in 1 we implement the sdg models using a causal advancing front meshing procedure that enables a patch by patch solution procedure with linear complexity in the number of spacetime elements numerical results show that the three field formulation is most efficient wherein all interpolated fields converge at the optimal o hp 1 rate for a given mesh size the three field model delivers error values that are more than an order of magnitude smaller than those of the one and two field models the three field formulation s efficiency is also superior independent of whether the comparison is based on matching polynomial orders or matching convergence rates

the complex variable boundary element method applications the complex variable boundary element method cvbem is used to approximate several potential problems where analytical solutions are known a modelling result produced from the cvbem is a measure of relative error in matching the known boundary condition values of the problem a cvbem error reduction algorithm is used to reduce the relative error of the approximation by adding nodal points in boundary regions where error is large from the test problems overall error is reduced significantly by utilizing the adaptive integration algorithm

a three dimensional bem solution for plasticity using regression interpolation within the plastic field this paper presents an improved solution of three dimensional plasticity problems using the boundary element method bem the bem formulation for plasticity requires volume as well as boundary discretizations an initial stress formulation is used to satisfy the material non linearity conventionally the plastic field in the volume element or cell is interpolated based on the value of plastic stress at the nodes of the cell in this paper the distribution of the plastic field in the cell is based on a number of points interior to the cell the plastic field is described using regression interpolation polynomials through these interior points the constitutive relation is satisfied at each interior point the number of points can be varied in each cell thus allowing for adaptive volume cells the plastic stresses are computed at the interior points only therefore the need for surface stress computation which uses numerical derivatives at the surface is completely eliminated three dimensional applications are used to compare the present regression interpolation procedure with the conventional method for elasto plasticity problems in all variations of the applications studied regression interpolation based on interior points provided superior results to those determined via the conventional nodal interpolation method

discontinuous galerkin finite element in time for solving periodic differential equations the dynamics of rotating systems can be modeled by ordinary differential equations with periodic time varying coefficients and forcing discontinuous galerkin dg methods which are known to be higher order accurate a stable and locally conservative are used to solve such equations in this work dg methods are shown to find the steady state periodic solution of a constant coefficient structural dynamics problem with periodic forcing and b helicopter rotor rigid blade flapping equation which is a parametric ordinary differential equation with periodic time varying coefficients and periodic forcing convergence of the numerical solution obtained is studied for both the above equations while h and p are refined separately it is found that the dg method works well for these problems and allows the development of an element level error estimate which can be used to monitor convergence and hence develop adaptive schemes it is clear from the results that even though higher order polynomials result in much faster convergence with reduced computational effort it also results in deterioration of the numerical performance for p 12 two adaptive strategies based on the element level displacement jump norm i e h and hp refinement are proposed and demonstrated on problems with higher harmonic forcing primary controls and parametric variations

the norsett time integration methodology for finite element transient analysis this paper presents a set of methods for time integration of problems arising from finite element semidiscretizations the purpose is to obtain computationally efficient methods which possess higher order accuracy and controllable dissipation in the spurious high modes the methods are developed and analysed by a general collocation methodology which leads to the class of norsett approximants an algorithmic parameter is used to achieve an effective control over numerical dissipation moreover a simple and efficient implementation scheme is presented at each time step algorithms based on p order collocation polynomials require the solution of p sets of linear algebraic equations with the same coefficient matrix in this way a single factorization is needed and no transformations are required to recover the approximate solution at the end or within the time interval to demonstrate the performance of the proposed algorithms a wide experimental evaluation is carried out on typical test problems in finite element transient analysis

extended framework of hamilton s principle for continuum dynamics abstract hamilton s principle is the variational principle for dynamical systems and it has been widely used in mathematical physics and engineering however it has a critical weakness termed end point constraints which means that in the weak form we cannot use the given initial conditions properly by utilizing a mixed formulation and sequentially assigning initial conditions this paper presents a novel extended framework of hamilton s principle for continuum dynamics to resolve such weakness the primary applications lie in an elastic and a j 2 viscoplastic continuum dynamics the framework is simple and initiates the development of a space time finite element method with the proper use of initial conditions non iterative numerical algorithms for both elasticity and j 2 viscoplasticity are presented

a method for direct evaluation of singular integral in direct boundary element method a new method is presented for evaluating the cauchy principal value integral and the free term in the three dimensional elastic boundary element method this method expresses the singular integral as the sum of a weakly singular integral and an integrable cauchy principal value integral the former can be computed by means of the usual standard gaussian quadrature after a transformation suggested by lachat and watson 10 who correctly limited its use only to weakly singular integral the latter can be calculated by direct integration in the cauchy principal value sense this paper also points out some limitations in the use of triangle polar co ordinate suggested by li et al 11 and later extended by zhang and xu 16 the general expression of the free term for a boundary point with arbitrary characteristic surface is also presented simple numerical examples which verify the efficiency and accuracy of the present method are given

comparison of boundary element and finite element methods in the inelastic torsion of prismatic shafts the accuracy and computational efficiency of the boundary element and the finite element methods are compared in this paper for problems of time dependent inelastic torsion of prismatic shafts several cross sections and two types of twisting history are considered in the numerical examples the shaft material is assumed to obey an elastic time hardening creep constitutive model

solution of linear elastodynamics problems with space time finite elements on structured and unstructured meshes abstract a new implicit approach for the solution of linear elastodynamics problems on structured and unstructured meshes with space time finite elements is suggested new weak formulations are based on time continuous tcg and discontinuous tdg galerkin methods it was shown that for structured meshes the new tcg method has a higher order of accuracy by a factor of two than that of the standard tcg method at the same number of degrees of freedom the accuracy of the new tcg method is one order higher than the accuracy of the standard tdg method the introduction of new weighting functions for the weak formulations of the tcg and tdg methods allows control of the high frequency behavior without degradation of accuracy of the methods a variable number of elements in the time direction as well as a variable order of polynomial time approximations of finite elements for time slabs allows the implementation of a coupled space time adaptive procedure using structured or unstructured meshes numerical examples for 1 d problems demonstrate the effectiveness of the technique

a complex variable boundary element method development a generalized boundary integral equation method for the solution of the laplace equation is developed based on the cauchy integral theorem for analytical complex variable functions although the approach is complicated by the utilization of complex variable theory the resulting model involves direct integration along straight line boundary segments elements rather than using quadrature formulae that are required in current real variable boundary element formulations previously published boundary integral equation methods based on the cauchy integral theorem are shown to be a subset of the generalized model theory developed in this paper

a space time discontinuous galerkin method for linearized elastodynamics with element wise momentum balance abstract we present a new space time discontinuous galerkin finite element method for linearized elastodynamics that delivers exact balance of linear and angular momentum over every space time element the method is formulated for use with fully unstructured space time grids and uses displacement basis functions that are discontinuous across all inter element boundaries we introduce a new space time formulation of continuum elastodynamics that uses differential forms and the exterior calculus on manifolds to generate a system of space time field equations and jump conditions then we invoke a bubnov galerkin weighted residuals procedure to formulate the finite element method we describe an implementation on patch wise causal meshes that features linear complexity in the number of elements and special per pixel accurate visualization numerical examples confirm an a priori error estimate and demonstrate the method s shock capturing capabilities

hypersingular boundary integral equation for axisymmetric elasticity an axisymmetric hypersingular boundary integral formulation for elasticity problems is presented in this paper the hypersingular and strong singular fundamental solutions are derived and their singular behaviour is discussed in detail for different locations of the source point several free terms arise from the limiting process when generating hypersingular boundary integral equations including an extra one specific to the axisymmetric formulation which does not appear in two and three dimensional cases the singularity subtraction technique is used to regularize all strong singular and hypersingular integrals and their evaluation procedure is explained finally the developed formulation is assessed through simple numerical tests copyright 2001 john wiley sons ltd

a variable stiffness type boundary element formulation for axisymmetric elastoplastic media a new direct elastoplastic boundary element formulation for axisymmetric bodies is developed the procedure exploits certain features of the constitutive relationship to express the unknwon non linear initial stress rate tensor as a scalar quantity which can then be eliminated from the boundary equation system though a back substitution of the modified stress rate equations this formulation is implemented in a multi region system that utilizes quadratic isoparametric shape functions to model the geometry and field variables of the boundary and domain of a body the kernel functions are presented in appendix i and the singularities associated with these kernels are discussed new techniques are described to calculate the coefficients associated with the singular nodes

a space time discontinuous galerkin method for the solution of the wave equation in the time domain in recent years the focus of research in the field of computational acoustics has shifted to the medium frequency regime and multiscale wave propagation this has led to the development of new concepts including the discontinuous enrichment method its basic principle is the incorporation of features of the governing partial differential equation in the approximation in this contribution this concept is adapted for the simulation of transient problems governed by the wave equation we present a space time discontinuous galerkin method with lagrange multipliers where the shape approximation in space and time is based on solutions of the homogeneous wave equation the use of hierarchical wave like basis functions is enabled by means of a variational formulation that allows for discontinuities in both the spatial and the temporal discretizations numerical examples in one space dimension demonstrate the outstanding performance of the proposed method compared with conventional space time finite element methods copyright 2008 john wiley sons ltd

a particular integral bem time discontinuous fem methodology for solving 2 d elastodynamic problems abstract this study proposes a time discontinuous galerkin finite element method fem for solving second order ordinary differential equations in the time domain the equations are formulated using a particular integral boundary element method bem in the space domain for elastodynamic problems the particular integral bem technique depends only on elastostatic displacement and traction fundamental solutions without resorting to commonly used complex fundamental solutions for elastodynamic problems based on the time discontinuous galerkin fem the unknown displacements and velocities are approximated as piecewise linear functions in the time domain and are permitted to be discontinuous at the discrete time levels this leads to stable and third order accurate solution algorithms for ordinary differential equations numerical results using the time discontinuous galerkin fem are compared with results using a conventional finite difference method the houbolt method both methods are employed for a particular integral bem analysis in elastodynamics this comparison reveals that the time discontinuous galerkin fem is more stable and more accurate than the traditional finite difference methods

hierarchical higher order dissipative methods for transient analysis this work focuses on devising an efficient hierarchy of higher order methods for linear transient analysis equipped with an effective dissipative action on the spurious high modes of the response the proposed strategy stems from the norsett idea and is based on a multi stage algorithm designed to hierarchically improve accuracy while retaining the desired dissipative behaviour computational efficiency is pursued by requiring that each stage should involve just one set of implicit equations of the size of the problem to be solved as standard time integration methods and in addition all the stages should share the same coefficient matrix this target is achieved by rationally formulating the methods based on the discontinuous collocation approach the resultant procedure is shown to be well suited for adaptive solution strategies in particular it embeds two natural tools to effectively control the error propagation one estimates the local error through the next stage solution which is one order more accurate the other through the solution discontinuity at the beginning of the current time step which is permitted by the present formulation the performance of the procedure and the quality of the two error estimators are experimentally verified on different classes of problems some typical numerical tests in transient heat conduction and elasto dynamics are presented copyright 2006 john wiley sons ltd

conservation properties of a time fe method part ii time stepping schemes for non linear elastodynamics in the present paper one step implicit integration algorithms for non linear elastodynamics are developed the discretization process rests on galerkin methods in space and time in particular the continuous galerkin method applied to the hamiltonian formulation of semidiscrete non linear elastodynamics lies at the heart of the time stepping schemes algorithmic conservation of energy and angular momentum are shown to be closely related to quadrature formulas that are required for the calculation of time integrals we newly introduce the assumed strain method in time which enables the design of energy momentum conserving schemes and which can be interpreted as temporal counterpart of the well established assumed strain method for finite elements in space the numerical examples deal with quasi rigid motion as well as large strain motion copyright 2001 john wiley sons ltd

time finite element methods for structural dynamics summary time finite element methods are developed for the equations of structural dynamics the approach employs the time discontinuous galerkin method and incorporates stabilizing terms having least squares form these enable a general convergence theorem to be proved in a norm stronger than the energy norm results are presented from finite difference analyses of the time discontinuous galerkin and least squares methods with various temporal interpolations and commonly used finite difference methods for structural dynamics these results show that for particular interpolations the time finite element method exhibits improved accuracy and stability

collocation methods with controllable dissipation for linear dynamics abstract this paper introduces a unified set of collocation methods for linear dynamics in which a parameter is used to control the position of the collocation points in this manner both a stable algorithms of order 2 p and l stable algorithms of order 2 p 1 are derived from collocation polynomials of degree p in addition algorithms with intermediate accuracy and stability properties are made available the effects of varying the algorithmic parameter are investigated with particular reference to the numerical dissipation of spurious high frequency modes numerical tests are reported which support the theoretical analysis and demonstrate the performance of the proposed algorithms

on the efficiency and accuracy of the boundary element method and the finite element method the efficiency and computational accuracy of the boundary element and finite element methods are compared in this paper this comparison is carried out by employing different degrees of mesh refinement to solve a specific illustrative problem by the two methods

locating a crack of arbitrary but known shape by the method of path independent integrals abstract the solution of a crack problem of an arbitrary but known shape inside an infinite plane isotropic elastic medium can be achieved in general by the method of complex singular integral equations and their numerical solution by using the gauss or the lobatto chebyshev methods in a few special cases like straight or circular arc shaped cracks this solution is available in closed form in this paper we will not contribute to the above methods of solution of crack problems but we will propose a method for the determination of the exact position of such a crack inside a closed contour in the elastic medium by gathering and using information along this contour only by experimental techniques and applying the method of complex path independent integrals for the location of the crack this paper constitutes a nontrivial generalization of relevant previous results by the author and it is of quite general applicability in fracture mechanics for nondestructive testing numerical results for the particular case of a straight crack are displayed for the illustration of the efficiency of the method the generalization of the present results to the determination of additional geometric and loading parameters of the crack is also suggested very briefly and related numerical results concerning the length of the crack and the pressure distribution on it in the aforementioned numerical application are also presented

multiscale methods for mechanical science of complex materials bridging from quantum to stochastic multiresolution continuum recent development in the multiscale method based on the bridging scale concept is presented with an emphasis on complex material systems the bridging scale method bsm was originally proposed by wagner and liu j comput phys 2003 190 249 274 as an effective way of treating the interface in coupled atomistic continuum simulation since its publication the bsm has become a very useful paradigm that has been applied to solve a host of problems in mechanical sciences of complex material systems in this paper we present a review on the recent developments we first describe the application of bsm to the coupled atomistic continuum simulation of dynamic fracture the important extensions within the framework of space time method and multiscale non equilibrium molecular dynamics are then presented we then focus on the multiresolution continuum theory that inherits the bsm concept in the analysis of heterogeneous material structures recent work of incorporating statistical factors into this model based on the concurrent nested homogenization of randomness of the material structures is highlighted finally we present the use of the bridging scale concept in resolving the electron mechanical coupling mechanism the robustness of the bsm is demonstrated through many benchmark problems and application examples copyright 2010 john wiley sons ltd