on stability and reflection transmission analysis of the bipenalty method in contact impact problems a one dimensional homogeneous case study summary the stability and reflection transmission properties of the bipenalty method are studied in application to explicit finite element analysis of one dimensional contact impact problems it is known that the standard penalty method where an additional stiffness term corresponding to contact boundary conditions is applied attacks the stability limit of finite element model generally the critical time step size rapidly decreases with increasing penalty stiffness recent comprehensive studies have shown that the so called bipenalty technique using mass penalty together with standard stiffness penalty preserves the critical time step size associated to contact free bodies in this paper the influence of the penalty ratio ratio of stiffness and mass penalty parameters on stability and reflection transmission properties in one dimensional contact impact problems using the same material and mesh size for both domains is studied the paper closes with numerical examples which demonstrate the stability and reflection transmission behaviour of the bipenalty method in one dimensional contact impact and wave propagation problems of homogeneous materials this article is protected by copyright all rights reserved

isophoric arrays massively thinned phased arrays with well controlled sidelobes traditional filled phased arrays have an element placed in every location of a uniform lattice with half wavelength spacing between the lattice points massively thinned arrays have fewer than half the elements of their filled counterparts such drastic thinning is normally accompanied by loss of sidelobe control this paper describes a class of massively thinned linear and planar arrays that show well behaved sidelobes in spite of the thinning the term isophoric is derived from greek roots to denote uniform weight in isophoric arrays element placement based on difference sets forces uniformly weighted spatial coverage this constraint forces the array power pattern to pass through v uniformly spaced equal and constant values that are less than 1 k times the main beam peak where v is the aperture size in half wavelengths and k is the number of elements in the array the net result is reduced peak sidelobes especially when compared to cut and try random placement approaches an isophoric array will exhibit this sidelobe control even when the array has been thinned to the extent that k is approximately the square root of v where more than one beam must be generated at a time isophoric array designs may be used to advantage even within a traditional filled array by interweaving two isophoric subarrays within a filled array and by appropriate cyclic shifting of the element assignments over time two independent antenna power patterns can be generated each with a sidelobe region that is approximately a constant value of 1 2k relative to the main beam where k is the number of elements in the subarray

binary spatial partitioning of the central difference time integration scheme for explicit fast transient dynamics this paper proposes a generalization of the explicit central difference time integration scheme using a time step variable not only in time but also in space the solution at each element node is advanced in time following local rather than global stability limitations this allows substantial saving of computer time in realistic applications with non uniform meshes especially in multi field problems like fluid structure interactions a binary scheme in space is used time steps are not completely arbitrary but stay in a constant ratio of two when passing from one partition level to the next one this choice greatly facilitates implementation via an integer based logic ensures inherent synchronization and avoids any interpolations necessary in other partitioning schemes in the literature but which may reduce numerical stability the mesh partition is automatically built up and continuously updated by simple spatial adjacency considerations the resulting algorithm deals automatically with large variations in time of stability limits the paper introduces the core spatial partitioning technique in the lagrangian formulation some academic numerical examples allow a detailed comparison with the standard spatially uniform algorithm a final more realistic example shows the application of partitioning in simulations with arbitrary lagrangian eulerian formulation and fully coupled boundary conditions fluid structure interaction copyright 2008 john wiley sons ltd

an explicit dynamics extended finite element method part 2 element by element stable explicit explicit dynamic scheme abstract this paper presents a general explicit time integration scheme for dynamics simulations using the extended finite element method with standard critical time step we use the generalized mass lumping technique proposed in part i of this paper this technique allows us to consider arbitrary enrichment functions in the x fem for explicit dynamics simulations in this second part the proposed approach allows the use of standard finite elements critical time step estimates for that purpose we develop a classical element by element strategy that couples the standard central difference scheme with the unconditionally stable explicit scheme proposed by chang s y chang an explicit method with improved stability property int j numer methods engrg 77 8 2008 1100 1120 this scheme coupled with x fem allows us to recover fe critical time steps independently of the enrichment functions considered furthermore a study of the stability property of this new explicit scheme is proposed in the x fem framework both with fixed enrichments and evolving enrichments with time some examples illustrate the good properties of the new explicit numerical time scheme and some applications to dynamics crack growth are given

optimization of sparse linear arrays using harmony search algorithms a sparse linear array composed of a uniformly spaced core subarray and an extended sparse subarray is synthesized using a harmony search hs and an exploratory harmony search ehs algorithms the optimal solution is searched by changing the amplitudes of all the elements and the positions of the extended elements under a set of practical constraints performance of the ehs the hs a genetic algorithm ga and a particle swarm optimization pso algorithm has also been compared in synthesizing these sparse linear arrays

dynamic lagrangian computations for solids with variable nodal connectivity for severe distortions this paper presents an algorithm for dynamic lagrangian computations for solids in plane strain geometry with variable nodal connectivity to allow for severe distortions the nodes are somewhat analogous to flexible circular disks when they move closer together than their equilibrium distance they generate compressive repulsive forces conversely when they move apart they generate tensile attractive forces material strength effects are also included because a node can only be affected by its neighbour nodes the approach has been designated the nabor approach the key to this approach is that it is possible to have variable nodal connectivity a node can acquire new neighbours thus allowing all forms of distortion the nabor algorithm has been incorporated as an option into the explicit finite element code epic 2 by using both the nabor grid and the epic 2 finite element grid together it is possible to perform lagrangian computations for a wide range of problems

a hybrid approach based on pso and hadamard difference sets for the synthesis of square thinned arrays a hybrid approach for the synthesis of planar thinned antenna arrays is presented the proposed solution exploits and combines the most attractive features of a particle swarm algorithm and those of a combinatorial method based on the noncyclic difference sets of hadamard type numerical experiments validate the proposed solution showing improvements with respect to previous results

an accurate and robust contact detection algorithm for particle solid interaction in combined finite discrete element analysis when applying the combined finite discrete element method for analysis of dynamic problems contact is often encountered between the finite elements and discrete elements and thus an effective contact treatment is essential in this paper an accurate and robust contact detection algorithm is proposed to resolve contact problems between spherical particles which represent rigid discrete elements and convex quadrilateral mesh facets which represent finite element boundaries of structural components different contact scenarios between particles and mesh facets or edges or vertices have been taken into account for each potential contact pair the contact search is performed in an hierarchical way starting from mesh facets possibly going to edges and even further to vertices the invalid contact pairs can be removed by means of two reasonable priorities defined in terms of geometric primitives and facet identifications this hierarchical contact searching scheme is effective and its implementation is straightforward numerical examples demonstrated the accuracy and robustness of the proposed algorithm copyright 2015 john wiley sons ltd

an algorithm for the matrix free solution of quasistatic frictional contact problems a contact enforcement algorithm has been developed for matrix free quasistatic finite element techniques matrix free iterative solution algorithms such as non linear conjugate gradients cg and dynamic relaxation dr are desirable for large solid mechanics applications where direct linear equation solving is prohibitively expensive but in contrast to more traditional newton raphson and quasi newton iteration strategies the number of iterations required for convergence is typically of the same order as the number of degrees of freedom of the model it is therefore crucial that each of these iterations be inexpensive to per form which is of course the essence of a matrix free method in applying such methods to contact problems we emphasize here two requirements first that the treatment of the contact should not make an average equilibrium iteration considerably more expensive and second that the contact constraints should be imposed in such a way that they do not introduce spurious energy that acts against the iterative solver these practical concerns are utilized to develop an iterative technique for accurate constraint enforcement that is suitable for non linear conjugate gradient and dynamic relaxation iterative schemes copyright 1999 john wiley sons ltd

contact between spheres and general surfaces abstract this work presents a mathematical model to establish the weak form and tangent operator contributions due to contact between spherical surfaces and general surfaces normal and friction components are included such as dissipative actions the main concern herein is the proper consideration of the kinematics of the spherical surface and its influence on contact forces including the appropriate description of the spherical motion by gap functions in normal and tangential directions this leads to the possibility of dealing with complex kinematics of rolling or alternating rolling sliding of the spherical surface mapping its motion on another general surface to achieve that the model is based on rotational and translational degrees of freedom used to map the motion of contacting surfaces one may employ such strategy for interactions between spheres and rigid or flexible bodies modeled using finite element meshes as examples parameterizations of rigid and flexible surfaces are proposed and used practical applications are shown with usage of beam and shell finite elements experiencing contact interactions

free vibration analysis of a cylindrical shell circular plate system with general coupling and various boundary conditions abstract the free vibration of a structure consisting of a finite circular cylindrical shell closed at one end by a circular plate is analyzed in this paper emphasis is given to the characterization of structural coupling and boundary conditions these are incorporated into the model by means of continuous distributions of springs along the shell and the plate interface a general formulation based on a variational principle is used this formulation allows a wide spectrum of boundary conditions and coupling conditions between the shell and the plate an issue the importance of which is clearly shown by a literature review very good accuracy of the method is demonstrated by solving test problems for lower order modes of the plate and of the shell for which some results are available in the literature comparisons are also made using finite element analysis on a plate ended shell showing that the proposed approach is a convenient effecient and accurate one for determining the modal behavior of such a complex structural system other numerical results are then presented for a shell rigidly attached to a plate to illustrate the coupling phenomena between the shell and the plate it is shown that there exist three different types of modes for this combined structure they are termed plate controlled modes shell controlled modes and strongly coupled modes respectively it is also shown that each type is closely related to the modal character of each of uncoupled elements

rectangular thinned arrays based on mcfarland difference sets a new class of analytical rectangular thinned arrays with low peak sidelobe level psl is introduced the proposed synthesis technique exploits binary sequences derived from mcfarland difference sets to design thinned layouts on a lattice of p p p 2 positions for any prime p the pattern features of the arising massively thinned arrangements characterized by only p p 1 active elements are discussed and the results of an extensive numerical analysis are presented to assess advantages and limitations of the mcfarland based arrays

on a multiscale computational strategy with time and space homogenization for structural mechanics a new multiscale computational strategy was recently proposed for the analysis of structures described both on a fine space scale and a fine time scale this strategy which involves homogenization in space as well as in time could replace in several domains of application the standard homogenization techniques which are generally limited to the space domain it is an iterative strategy which calls for the resolution of problems on both a micro fine scale and a macro homogenized scale in this paper we review the bases of this approach and present improved approximation techniques to solve the micro and macro problems

stability of explicit subcycling time integration with linear interpolation for first order finite element semidiscretizations an explicit subcycling time integration algorithm based on an element partition is presented for first order finite element systems this method uses linear interpolation to compute intermediate values at nodes in the subdomains integrated with the larger time steps stability of the algorithm for the two partition cases is analyzed by showing that the eigenvalues of the amplification matrix for the total integration cycle are not greater than one in absolute value using this stability criterion critical time steps for the element subdomains are derived in terms of element eigenvalues several numerical examples are considered to compare the accuracy of the method with previously developed subcycling algorithms to numerically verify the stability analysis

polygon based contact resolution for superquadrics the representation of discrete objects in the discrete element modelling is a fundamental issue which has a direct impact on the efficiency of discrete element implementation and the dynamic behaviour of particulate systems disks and spheres are the most commonly used geometric shapes due to their geometric simplicity and computational efficiency but they are unable to provide resistance to rolling motion for this reason some non circular spherical objects such as polygons polyhedrons superquadrics or the clustering of disks spheres to form irregular shapes are introduced when superquadrics are used as discrete elements the bottleneck of contact resolution is associated with the searching for intersections of two non linear functions which is a very expensive operation and may sometimes fail in finding the solution in this work an efficient and robust algorithm is proposed for contact resolution of 2d superquadrics in which any superquadric is approximated with a convex polygon through adaptive sampling then by clipping two polygons an efficient linear algorithm is performed to search for intersections and overlap area of the polygons the contact forces and directions are determined by employing a newly established corner corner contact model it is important to highlight that the proposed methodology can also be extended to general non circular discrete object cases the performance of the algorithm is demonstrated via numerical examples copyright 2005 john wiley sons ltd

contact impact by the pinball algorithm with penalty and lagrangian methods contact impact algorithms which are sometimes called slideline algorithms are a computationally time consuming part of many explicit simulations of non linear problems because they involve many branches so they are not amenable to vectorization which is essential for speed on supercomputers the pinball algorithm is a simplified slideline algorithm which is readily vectorized its major idea is to embed pinballs in surface elements and to enforce the impenetrability condition only to pinballs it can be implemented in either a lagrange multiplier or penalty method it is shown that in any lagrange multiplier method no iterations are needed to define the contact surface examples of solutions and running times are given

linear array thinning exploiting almost difference sets this paper describes a class of linear thinned arrays with predictable and well behaved sidelobes the element placement is based on almost difference sets and the array power pattern is forced to pass through n uniformly spaced values that although neither equal nor constant as for difference sets are a priori known from the knowledge of the aperture size the number of active array elements k and the features of the correlation function such a property allows one to predict the bounds of the confidence range of the peak sidelobe of the admissible arrays obtainable through simple shift operations on a binary sequence the expected peak sidelobe performances turn out to be comparable with those from difference sets even though obtainable in a wider set of array configurations and improved in comparison with cut and try random placements

an effective two dimensional frictional contact model for arbitrary curved geometry a finite element model is developed on the basis of a variational formulation of the perturbed lagrange type and the classical coulomb law of friction for the analysis of frictional contact problems in two dimensions the model accounts for all geometric kinematic non linearities associated with large sliding motions as well as arbitrary contact surface curvatures explicit forms for the contact force and tangent stiffness operators and a penalty type format is utilized in the implementation an extensive number of numerical simulations are used to demonstrate the effectiveness and practical usefulness of the model

design of energy conserving algorithms for frictionless dynamic contact problems this paper proposes a formulation of dynamic contact problems which enables exact algorithmic conservation of linear momentum angular momentum and energy in finite element simulations it is seen that a lagrange multiplier enforcement of an appropriate contact rate constraint produces these conservation properties a related method is presented in which a penalty regularization of the aforementioned rate constraint is utilized this penalty method sacrifices the energy conservation property but is dissipative under all conditions of changing contact so that the global algorithm remains stable notably it is also shown that augmented lagrangian iteration utilizing this penalty kernel reproduces the energy conserving i e lagrange multiplier solution to any desired degree of accuracy the result is a robust stable method even in the context of large deformations as is shown by some representative numerical examples in particular the ability of the formulation to produce accurate results where more traditional integration schemes fail is emphasized by the numerical simulations 1997 by john wiley sons ltd

on proper holomorphic mappings between rigid polynomial domains in cn 1 abstract we study the behavior of the branch locus of proper holomorphic mappings between nondegenerate rigid polynomial domains in c n 1 nonnecessary pseudoconvex in particular we show that it depends only on the first domain this paper generalizes publ mat 45 2001 69 77 in the nonpseudoconvex case

selective mass scaling for distorted solid shell elements in explicit dynamics optimal scaling factor and stable time step estimate summary the use of solid shell elements in explicit dynamics has been so far limited by the small critical time step resulting from the small thickness of these elements in comparison with the in plane dimensions to reduce the element highest eigenfrequency in inertia dominated problems the selective mass scaling approach previously proposed in g cocchetti m pagani and u perego comp struct 2013 127 39 52 for parallelepiped elements is here reformulated for distorted solid shell elements the two following objectives are achieved the critical time step is governed by the smallest element in plane dimension and not anymore by the thickness the mass matrix remains diagonal after the selective mass scaling the proposed approach makes reference to one gauss point trilinear brick element for which the maximum eigenfrequency can be computed analytically for this element it is shown that the proposed mass scaling can be interpreted as a geometric thickness scaling obtaining in this way a simple criterion for the definition of the optimal mass scaling factor a strategy for the effective computation of the element maximum eigenfrequency is also proposed the considered mass scaling preserves the element translational inertia while it modifies the rotational one leading to errors in the kinetic energy when the motion rotational component is dominant the error has been rigorously assessed for an individual element and a simple formula for its estimate has been derived numerical tests both in small and large displacements and rotations using a state of the art solid shell element taken from the literature confirm the effectiveness and accuracy of the proposed approach copyright 2014 john wiley sons ltd

on the central difference algorithm in discrete element modelling of impact the paper provides a comprehensive analysis of the accuracy and stability of the central difference scheme when applied to simulate a simple impact problem in the context of the discrete element approach it is revealed that the algorithm exhibits some different behaviour due to the inherent nonlinearity discontinuity of the impact system particularly for an elastic or slightly inelastic impact the stable unstable region governing the selection of a maximum time step size is essentially different from that defined by the conventional linear stability criterion and thus a smaller time step should be employed in order to reduce the possible occurrence of an unexpected numerical instability

existence of natural frequencies of systems with artificial restraints and their convergence in asymptotic modelling a major limitation of the rayleigh ritz method for determining the natural frequencies of a system is the need to choose admissible functions that do not violate the geometric constraints of that system courant 1943 bulletin of the american mathematical society49 1 23 several researchers have attempted to overcome this problem by asymptotically modelling the rigid constraints with artificial imaginary restraints of very large stiffness courant 1943bulletin of the american mathematical society49 1 23 warburton and edney 1984 journal of sound and vibration95 537 552 gorman 1989 journal of applied mechanics56 893 899 kim et al 1990 journal of sound and vibration143 379 394 yuan and dickinson 1992 journal of sound and vibration153 203 216 yuan and dickinson 1992 journal of sound and vibration159 39 55 cheng and nicolas 1992 journal of sound and vibration155 231 247 yuan and dickinson 1994computers and structures53 327 334 lee and ng 1994 applied acoustics42 151 163 amabili and garziera 1999 journal of sound and vibration224 519 539 amabili and garziera 2000 journal of fluids and structures14 669 690 while the numerical results thus obtained for the systems considered in the literature were in close agreement with exact values for the natural frequencies corresponding to the first few modes sample calculations show that the error introduced by the asymptotic modelling increases with mode number and therefore to obtain accurate results for higher modes the magnitude of stiffness should also be increased in any event the error due to the asymptotic modelling would remain uncertain except when the correct frequency values are known however the use of artificial restraints with negative stiffness a new concept which was introduced in a recent publication ilanko and dickinson 1999 journal of sound and vibration219 370 378 paves the way for estimating the error due to asymptotic modelling this is possible since in this work the rayleigh ritz frequencies of the constrained system were found to be bracketed by the frequencies of the asymptotic models with positive and negative restraints however the use of artificial restraints with negative stiffness has raised some important questions would a system with a large negative restraint become unstable and if so what is the guarantee that the frequencies of the asymptotic model would converge to that of the constrained system this paper is the result of the author s attempt to answer these questions and gives a proof of existence of natural frequencies for systems with artificial restraints springs having positive or negative stiffness coefficients and their convergence towards constrained systems based on rayleigh s theorem of separation it has been shown that a vibratory system obtained by the addition of h restraints to an n degree of freedom d o f system where h n will have at least n h natural frequencies and modes and that as the magnitude of the stiffness of the added restraints becomes very large these n h natural frequencies will converge to the n h natural frequencies of a constrained system in which the displacements restrained by the springs are effectively constrained

asymptotic modelling theorems for the static analysis of linear elastic structures the work presented here justifies the use of restraints with large positive and negative stiffness values to asymptotically model geometric constraints of a structure in linear structural analysis replacing constraints by very stiff restraints improves the versatility of variational methods such as the rayleigh ritz method as the limitation on the choice of functions is removed based on recently published theorems on the existence of natural frequencies of systems with artificial restraints of positive and negative stiffness and their convergence towards the frequencies of the corresponding constrained systems a proof is given to show that the displacement of a constrained structure caused by any action along its direction is approached and bracketed by the displacement of systems with artificial restraints of positive and negative stiffness positive and negative penalty functions as the magnitude of stiffness is increased a procedure for the practical use of positive and negative penalty functions in static analysis of linear structures is also proposed

a global local synthesis approach for large non regular arrays a method is proposed for the synthesis of large planar non regular arrays assuming constant magnitude for the excitation of the elements the approach which combines global and local optimization is based on distinguishing aperture type and non coherent parts of the array factor the following constraints are considered minimal separation of the antennas maximum size of the array and fixed mainbeam width the level of the sidelobes is reduced via the minimization of a new type of flexible averaging cost function based on an lp norm possible applications of this model lie in the field of radio astronomy satellite communications and radar systems the proposed optimization strategy consists of three successive steps designed to be independent of each other starting with an equivalent continuous aperture the first two steps act as global transformations of the radial and azimuthal positions of the elements in the initial array while the third step performs a local optimization of individual elements of the array this last step heavily relies on computations of the gradient of the cost function which can be done quickly using an fft based procedure the method is illustrated for several large scale examples by considering as inputs four different types of non regular arrays

ads based guidelines for thinned planar arrays we propose an analytical technique based on almost difference sets adss for thinning planar arrays with well controlled sidelobes the method allows one to synthesize bidimensional arrangements with peak sidelobe levels psls predictable and deducible from the knowledge of the array aperture the filling factor and the autocorrelation function of the ads at hand the numerical validation concerned with both small and very large apertures points out that the expected psl values are significantly below those of random arrays and comparable with those from different sets dss although obtainable in a wider range of configurations

square array antennas based on hadamard difference sets a regular method for synthesizing a planar aperiodic thinned array antenna aa with a low peak sidelobe level is suggested it is based on using specific combinatorial constructions noncyclic difference sets dss the method uses the fact that when the elements of an equiamplitude aa are arranged according to a ds law its power pattern takes constant value in the net of uniformly located space points in the sidelobe region and this value is less than where is the element number in distinction to the method using cyclic dss see leeper 1999 which enables one to build planar aas only on rectangular grids with co prime sidelengths the represented method omits such a constraint the most important class of the noncyclic 2 d dss is represented by the sets of hadamard type sets based on such sets rectangular and square aperiodic roughly half filled aas can be built here the numerical results obtained for the square aas with the element number in the array up to 300 are presented

a time staggered partitioned coupling algorithm for transient heat conduction we present a time staggered partitioned coupling algorithm for transient heat conduction finite element simulations this algorithm divides a large structural mesh into a number of smaller subdomains solves the individual subdomains separately and couples the solutions to obtain the response to the original problem the proposed algorithm is a mixed multi timestep algorithm and enables arbitrary time integration schemes and meshes to be coupled with different timesteps in the various subdomains in this procedure the solution of each partition is separately evaluated over a system timestep after which the interfacial conditions are enforced making this a staggered algorithm that facilitates parallel computation we present examples showing the feasibility of the coupling algorithm and discuss the merits in terms of convergence and stability

lagrange constraints for transient finite element surface contact a new approach to enforce surface contact conditions in transient non linear finite element problems is developed in this paper the method is based on the lagrange multiplier concept and is compatible with explicit time integration operators compatibility with explicit operators is established by referencing lagrange multipliers one time increment ahead of associated surface contact displacement constraints however the method is not purely explicit because a coupled system of equations must be solved to obtain the lagrange multipliers an important development herein is the formulation of a highly efficient method to solve the lagrange multiplier equations the equation solving strategy is a modified gauss seidel method in which non linear surface contact force conditions are enforced during iteration the new surface contact method presented has two significant advantages over the widely accepted penalty function method surface contact conditions are satisfied more precisely and the method does not adversely affect the numerical stability of explicit integration transient finite element analysis results are presented for problems involving impact and sliding with friction a brief review of the classical lagrange multiplier method with implicit integration is also included

a general 3d contact smoothing method based on radial point interpolation this paper presents a general 3d contact smoothing method based on the meshfree radial point interpolation method to improve the numerical simulation of contact problems in particular a locally smooth contact surface is constructed from the scattered surface nodes by point interpolation using the combination of polynomial and radial bases with such bases this method reproduces smooth surfaces even for coarse meshes and the constructed surface passes exactly through the surface nodes results for contact problems involving deformable bodies are included to demonstrate its advantages

united elements method for general contact impact problems abstract this work presents the details of a finite element based numerical method to analyse general contact impact problems called united elements method uem in contrast to usual methods that is lagrange multipliers and penalty function this method is conceptual suitable for computer programming and free from inherent deficiencies of those methods the key points of this procedure are elimination of the normal degree of freedom of the contactor node from the system energy potential functional in terms of target surface motion and proper calculation of target element unbalanced forces to incorporate the contact constraints after a review on classic formulations the mathematical and matrix presentation of the united element stiffness matrix are discussed solution of some examples adopting a newton raphson based solution together with a normal return scheme support the capability and accuracy of the procedure in static and dynamic problems

a monolithic energy conserving method to couple heterogeneous time integrators with incompatible time steps in structural dynamics a new hybrid multi time method for multi time scales structural dynamics simulations is described a monolithic method in a schur dual domain decomposition framework is proposed and allows to consider heterogeneous time integrators with their own time discretization and possible large ratio between the time steps for each subdomain in the proposed method zero numerical dissipation is ensured at the interface this implies that the global stability of the coupling method is governed by the stability of each time integrator without influence of the interface for that purpose velocity continuity is ensured in a weak sense at the interfaces and time integrators newmark hht simo krenk verlet are introduced in a unified framework incremental velocity formulation furthermore dynamics governing equations are introduced from a weak formulation in time in other words equilibrium equation is no more ensured in a strong sense at a given time step but rather on average on a time interval some numerical examples illustrate the efficiency and the robustness of the proposed method for ratio of time scales close to 1000 without any numerical dissipation at the interfaces

a new bipenalty formulation for ensuring time step stability in time domain computational dynamics summary it is well known that use of standard penalty methods can decrease the critical time step of time domain dynamic finite element analyses the bipenalty method utilises both stiffness and mass penalties to impose constraints that have a minimal effect on the eigenfrequencies of the finite element system one way of achieving this goal is to find a ratio of stiffness and mass penalty parameters the critical penalty ratio cpr that does not affect the maximum eigenfrequency and therefore for conditionally stable solution schemes the critical time step of a system in this contribution we develop a new method of calculating the cpr associated with a finite element formulation by examining the eigenvalue problem in detail advantages of the method compared with previous solutions include increased simplicity and generality and the ability to consider multiple constraints the method is demonstrated by deriving cprs for a few finite element formulations which are then verified using simple numerical examples the superiority of the bipenalty method over standard mass penalty methods is also demonstrated copyright 2011 john wiley sons ltd

geometrically nonlinear vibrations of rectangular plates carrying a concentrated mass abstract nonlinear forced vibrations of rectangular plates carrying a central concentrated mass are studied the plate is assumed to have immovable edges and rotational springs numerical results are presented for clamped plates the von karman nonlinear plate theory is used but in plane inertia in both the plate and the mass is retrained the problem is discretized into a multi degree of freedom dof system by using an energy approach and lagrange equations taking damping into account a pseudo arclength continuation method is used in order to obtain numerical solutions results are presented as both i frequency amplitude curves and ii time domain responses the effect of gravity and the effect of the consequent initial plate deflection are also investigated

stability of multi time step partitioned integrators for first order finite element systems abstract mixed time integration procedures are those in which different time steps and different integrators are used in different parts of the mesh a rigorous stability analysis is provided for the first time for this type of time integration for first order semidiscretizations such as arise in diffusion problems the stability analysis is verified by some numerical examples

partitioned procedures for the transient solution of coupled aroelastic problems part i model problem theory and two dimensional application abstract in order to predict the dynamic response of a flexible structure in a fluid flow the equations of motion of the structure and the fluid must be solved simultaneously in this paper we present several partitioned procedures for time integrating this focus coupled problem and discuss their merits in terms of accuracy stability heterogeneous computing i o transfers subcycling and parallel processing all theoretical results are derived for a one dimensional piston model problem with a compressible flow because the complete three dimensional aeroelastic problem is difficult to analyze mathematically however the insight gained from the analysis of the coupled piston problem and the conclusions drawn from its numerical investigation are confirmed with the numerical simulation of the two dimensional transient aeroelastic response of a flexible panel in a transonic non linear euler flow regime

analytic continuation of holomorphic correspondences and equivalence of domains in ℂ n the following result is proved let d and d be bounded domains in n d is smooth real analytic simply connected and d is connected smooth real algebraic then there exists a proper holomorphic correspondence f d d if and only if there exist points p d and p d such that d and d are locally cr equivalent near p and p this leads to a characterization of the equivalence relationship between bounded domains in n modulo proper holomorphic correspondences in terms of local cr equivalence of their boundaries

on the flexural vibration of rectangular plates approached by using simple polynomials in the rayleigh ritz method abstract sets of simple polynomials are proposed for use as admissible functions in the rayleigh ritz method for the study of the flexural vibration of rectangular plates the plates may be subject to a number of different complicating factors including the presence of in plane forces concentrated masses point and line spring supports and special orthotropy of the plate material the sets of polynomials are shown to be equivalent to the orthogonally generated polynomials used very successfully in earlier studies but are more easily generated and the subsequent evaluation of the integrals in the resulting eigenvalue problem are more simply performed numerical results are presented for several problems illustrating the applicability of the method and its accuracy

a uniform strain hexahedron and quadrilateral with orthogonal hourglass control the treatment of zero energy modes which arise due to one point integration of first order isoparametric finite elements is addressed a method for precisely isolating these modes for arbitrary geometry is developed two hourglass control schemes viscous and elastic are presented and examined in addition a convenient one point integration scheme which analytically integrates the element volume and uniform strain modes is presented

the effects of element shape on the critical time step in explicit time integrators for elasto dynamics summary in this paper the effects of element shape on the critical time step are investigated the common rule of thumb used in practice is that the critical time step is set by the shortest distance within an element divided by the dilatational compressive wave speed with a modest safety factor for regularly shaped elements many analytical solutions for the critical time step are available but this paper focusses on distorted element shapes the main purpose is to verify whether element distortion adversely affects the critical time step or not two types of element distortion will be considered namely aspect ratio distortion and angular distortion and two particular elements will be studied four noded bilinear quadrilaterals and three noded linear triangles the maximum eigenfrequencies of the distorted elements are determined and compared to those of the corresponding undistorted elements the critical time steps obtained from single element calculations are also compared to those from calculations based on finite element patches with multiple elements copyright 2014 john wiley sons ltd

multi time step integration using nodal partitioning an algorithm is presented which integrates different groups of nodes of a finite element mesh with different time steps and different integrators since the nodal groups are updated independently no unsymmetric systems need be solved stability is demonstrated by showing that an energy norm of the solution decreases after every update if the time step is less than a given critical value the element eigenvalue inequality theorem is used to give the critical time step in terms of element eigenvalues

autocorrelation driven synthesis of antenna arrays the case of ds based planar isophoric thinned arrays a new methodology for the design of isophoric thinned arrays with a priori controlled pattern features is introduced a fully analytical and general i e valid for any lattice and set of weights relationship between the autocorrelation of the array excitations and the power pattern samples is first derived binary 2 d sequences with known autocorrelation properties namely the difference sets ds s are then chosen as a representative benchmark to prove that it is possible to deduce closed form synthesis formulas that a priori guarantee to fit requirements on the sidelobe level sll the directivity the half power beamwidth and the power pattern in user defined directions the selected results from a wide numerical assessment which also includes full wave simulations with realistic radiators are illustrated to validate the reliability and the accuracy of the proposed design equations and the associated performance bounds

introducing the use of positive and negative inertial functions in asymptotic modelling the work presented here shows that the natural frequencies of constrained systems may be obtained from asymptotic models of corresponding systems where the constraints are replaced by artificial mass or moment of inertia of very large positive and negative values this offers a convenient alternative to the current practice of using artificial elastic restraints of large stiffness a concept introduced by courant in 1943 to remove a limitation on the choice of admissible functions recent publications show that in order to control the error caused by approximating constraints with restraints of large stiffness it is necessary to use both positive and negative stiffness values however the negative stiffness introduces instability near the lower modes of vibration and the magnitude of negative stiffness parameter used must be greater than the highest critical stiffness to ensure bounded results are obtained the use of positive and negative artificial inertial parameters overcomes this problem as they do not introduce instability near the lower modes allowing the natural frequencies of constrained systems to be delimited to any desired accuracy

peak sidelobe level reduction with a hybrid approach based on gas and difference sets this paper presents an approach for the optimization of the beam pattern produced by massively thinned arrays the method which combines the most attractive features of a genetic algorithm and those of a combinatorial technique namely the difference sets method is aimed at synthesizing massively thinned antenna arrays in order to suitably reduce the peak sidelobe level selected numerical results are presented in order to assess the effectiveness and reliability of the proposed approach

mass lumping strategies for x fem explicit dynamics application to crack propagation this paper deals with the numerical modelling of cracks in the dynamic case using the extended finite element method more precisely we are interested in explicit algorithms we prove that by using a specific lumping technique the critical time step is exactly the same as if no crack were present this somewhat improves a previous result for which the critical time step was reduced by a factor of square root of 2 from the case with no crack the new lumping technique is obtained by using a lumping strategy initially developed to handle elements containing voids to be precise the results obtained are valid only when the crack is modelled by the heaviside enrichment note also that the resulting lumped matrix is block diagonal blocks of size 2 2 for constant strain elements linear simplex elements the critical time step is not modified when the element is cut thanks to the lumped mass matrix the critical time step never tends to zero moreover the lumping techniques conserve kinetic energy for rigid motions in addition tensile stress waves do not propagate through the discontinuity hence the lumping techniques create neither error on kinetic energy conservation for rigid motions nor wave propagation through the crack both these techniques will be used in a numerical experiment copyright 2007 john wiley sons ltd

the use of the reciprocals of positive and negative inertial functions in asymptotic modelling this paper shows how the recently introduced concept of positive and negative inertial functions in asymptotic modelling may be used effectively noting an almost linear variation of the natural frequency over a wide range of values of the reciprocal of the inertial parameter the results presented show that both the natural frequencies of constrained systems can be calculated accurately using only moderately large artificial inertial parameters e g which are only about 10 times that of the system mass and also that values about a million times more than this do not precipitate ill conditioning when using 16 figure computer accuracy this helps to minimize the chances of numerical problems occurring due to the limitation of machine precision

the bipenalty method for arbitrary multipoint constraints summary in finite element fe analysis traditional penalty methods impose constraints by adding virtual stiffness to the fe system in dynamics this can decrease the critical time step of the system when conditionally stable time integration schemes are used by introducing spurious modes with high eigenfrequencies recent studies have shown that using mass penalties alongside traditional stiffness penalties can mitigate this effect for systems with a one single point constraint in the present work we extend this finding to include systems with an arbitrary set of multipoint constraints by analysing the generalised eigenvalue problem we show that the values of spurious eigenfrequencies may be controlled by the choice of stiffness and mass penalty parameters the method is demonstrated using numerical examples including a one dimensional contact impact formulation and a two dimensional crack propagation analysis the results show that constraint imposition using the bipenalty method can be employed such that the critical time step of an analysis is unaffected whereas also displaying superiority over the mass penalty method in terms of accuracy and versatility copyright 2012 john wiley sons ltd

wittrick williams algorithm proof of bracketing and convergence theorems for eigenvalues of constrained structures with positive and negative penalty parameters the well established wittrick williams algorithm is used to derive novel and general proofs that show that the eigenvalues of systems with constraints can be bracketed by replacing the constraints by positive and negative pairs of either ordinary or inertial penalty parameters it is also shown that convergence occurs from both above and below when the numerical values of these parameters are increased towards infinity the proofs are applicable in many contexts but are derived in that of structural systems for which the eigenvalues are either buckling load factors or the squares of natural frequencies of vibration ordinary penalty parameters are stiffnesses of translational and rotational springs and inertial penalty parameters are either masses or rotary inertias the penalty parameters can be used to constrain a system or to impose constraints between systems it is shown that the use of inertial penalty parameters has several advantages compared with using ordinary ones then the pth eigenvalue of a system with n constraints is bounded closely from above by the p n th eigenvalue of the system with very large positive inertial penalty parameters and from below by the pth eigenvalue when large negative values are used instead this work is expected to enhance the versatility of numerical eigenproblem methods e g the rayleigh ritz method copyright 2007 john wiley sons ltd

multi time step explicit implicit method for non linear structural dynamics we present a method with domain decomposition to solve time dependent non linear problems this method enables arbitrary numeric schemes of the newmark family to be coupled with different time steps in each subdomain this coupling is achieved by prescribing continuity of velocities at the interface we are more specifically interested in the coupling of implicit explicit numeric schemes taking into account material and geometric non linearities the interfaces are modelled using a dual schur formulation where the lagrange multipliers represent the interfacial forces unlike the continuous formulation the discretized formulation of the dynamic problem is unable to verify simultaneously the continuity of displacements velocities and accelerations at the interfaces we show that within the framework of the newmark family of numeric schemes continuity of velocities at the interfaces enables the definition of an algorithm which is stable for all cases envisaged to prove this stability we use an energy method i e a global method over the whole time interval in order to verify the algorithms properties then we propose to extend this to non linear situations in the following cases implicit linear explicit non linear explicit non linear explicit non linear and implicit non linear explicit non linear finally we present some examples showing the feasibility of the method copyright 2001 john wiley sons ltd

vibrations of rectangular plates with elastically restrained edges abstract the rayleigh ritz method is used to determined natural frequencies in transverse vibration of rectangular plates with elastically restrained edges by treating an elastically restrained edge as intermediate between an appropriate pair of classical boundary conditions and using the corresponding vibration mode shapes of beams with classical boundary conditions as assumed functions a relatively small number of functions is required consequently only a modest quantity of computation is necessary the good accuracy of the method is demonstrated by solving test problems the method can be applied to a wide range of elastic restraint conditions any aspect ratio and for higher modes in addition to the fundamental the usefulness and accuracy of existing simplified approaches to the problem are assessed the effect of in plane forces on the natural frequencies and the determination of critical loads for plates with these restraint conditions are considered also

a new method to introduce constraints in cell centered lagrangian schemes we describe a new method to introduce constraints in cell centered lagrangian schemes in the framework of compressible hydrodynamics in this paper we apply it to the modeling of contact and sliding on solid wall boundaries we illustrate our method which is based on the minimization of a specific objective function by several basic problems

subcycling first and second order generalizations of the trapezoidal rule subcycling algorithms which employ multiple timesteps have been previously proposed for explicit direct integration of first and second order systems of equations arising in finite element analysis as well as for integration using explicit implicit partitions of a model the author has recently extended this work to implicit implicit multi timestep partitions of both first and second order systems in this paper improved algorithms for multi timestep implicit integration are introduced that overcome some weaknesses of those proposed previously in particular in the second order case improved stability is obtained some of the energy conservation properties of the newmark family of algorithms are shown to be preserved in the new multi timestep extensions of the newmark method in the first order case the generalized trapezoidal rule is extended to multiple timesteps in a simple way that permits an implicit implicit partition explicit special cases of the present algorithms exist these are compared to algorithms proposed previously c 1998 john wiley sons ltd

explicit multi time stepping methods for convection dominated flow problems abstract in this paper we introduce a multi time stepping method for convection dominated flow problems the idea behind this method and its applications will be explained and the stability and accuracy of the method will be studied by using a one dimensional model problem the convection diffusion equation here the method is applied to a uniform two block grid we will prove that local stability conditions in the blocks are sufficient for global stability of the multi time stepping scheme under certain conditions some numerical experiments are performed to investigate cases beyond the theory we will show that in case of rung kutta 3 time integration extremely large ratios between mesh widths and time steps may be used without affecting the stability of the multi time stepping method conditions for time accurate behaviour are also investigated by means of numerical experiments

on asymptotic modelling of constraints that do not change the degrees of freedom this paper shows that the asymptotic modelling method using positive and negative restraints may be applied to systems where the constraints do not affect the number of degrees of freedom this applies in cases where the constraints are not associated with mass or inertia the existence and convergence theorems have been refined to cover this type of systems

explicit algorithms for the nonlinear dynamics of shells abstract a finite element formulation and algorithm for the nonlinear analysis of the large deflection materially nonlinear response of impulsively loaded shells is presented a unique feature of this algorithm is the use of a bilinear four node quadrilateral element with single point quadrature and a simple hourglass control which is orthogonal to rigid body modes on an element level and does not compromise the consistency of the equations the geometric nonlinearities are treated by using a corotational description wherein a coordinate system that rotates with the material is embedded at the integration point thus the algorithm is directly applicable to anisotropic materials without any corrections for frame invariance of material property tensors this algorithm can treat about 200 element time steps per cpu second on a cyber 170 730 computer in the explicit time integration mode numerous results are presented for both elastic and elastic plastic problems with large strains that show that the method in most cases is comparable in accuracy with an earlier version of this algorithm employing a cubic triangular plate shell element but substantially faster

the use of asymptotic modelling in vibration and stability analysis of structures abstract the use of springs with very large stiffness to model constraints in vibratory systems has been a popular approach to overcome the limitations on the choice of admissible functions in the rayleigh ritz method the maximum possible error resulting from this asymptotic modelling can be determined by using positive and negative stiffness values or in general terms using positive and negative penalty functions this paper illustrates how this method could be used to determine the critical loads of structures

a perturbed lagrangian formulation for the finite element solution of contact problems making use of a perturbed lagrangian formulation a finite element procedure for contact problems is developed for the general case in which node to node contact no longer holds the proposed procedure leads naturally to a discretization of the contact interface into contact segments within the context of a bilinear interpolation for the displacement field a mixed finite element approximation is introduced by assuming discont naous contact pressure constant on the contact segment because of this piece wise constant approximation the gap function enters into the formulation in an average sense instead of through a point wise definition numerical examples are presented that illustrate the performance of the proposed procedure current finite element formulations for contact problems based on either the classical lagrange parameter procedure l 3 12 203 or the penalty function method 4 6 11 are characterized by a point wise enforcement of the contact constraint condition in the sense that penetration of the bodies is established on a nodal basis moreover in this methods the recovery of the contact pressure over the element from the contact nodal forces generally requires an additional procedure within the framework of classical lagrange multiplier methods the contact condition is exactly satisfied by transforming the constrained problem into an unconstrained one with the introduction of additional variables lagrange multipliers these extra variables add computational effort to the solution process which often requires special procedures to handle the presence of zero diagonal terms penalty methods on the other hand enable one to transform the constrained problem into an unconstrained one without introducing additional variables the constraint condition is now satisfied only approximately for finite values of the penalty parameter the main difhculty associated with these methods however lies in the poor conditioning of the problem as the penalty is increased to more accurately enforce the constraint condition this is a well understood phenomenon particularly in the context of the incompressible and nearly incompressible problem in solid and fluid mechanics e g see l 22 25 for a review recently augmented lagrangian procedures have been proposed as a promising way to partially overcome these difficulties and regularize the penalty formulation e g see the survey in 7 8 within the framework of zinearited e u c it is possible to restrict the finite element formulation of contact problems by assuming that node to node contact occurs this is in fact the case often considered in the literature l 2 4 6 12 20 211 in the general context of fully

bipenalty method for time domain computational dynamics penalty functions can be used to add constraints to systems of equations in computational mechanics stiffness type penalties are the common choice however in dynamic applications stiffness penalties have the disadvantage that they tend to decrease the critical time step in conditionally stable time integration schemes leading to increased cpu times for simulations in contrast inertia penalties increase the critical time step in this paper we suggest the simultaneous use of stiffness penalties and inertia penalties which is denoted as the bipenalty method we demonstrate that the accuracy of the bipenalty method is at least as good as and usually better than using either stiffness penalties or inertia penalties furthermore for a number of finite elements bar elements beam elements and square plane stress plane strain elements we have derived ratios of the two penalty parameters such that their combined effect on the critical time step is neutral the bipenalty method is thus superior to using stiffness penalties because the decrease in critical time step can be avoided the bipenalty method is also superior to using inertia penalties since the constraints are realized with higher accuracy

a mixed eulerian lagrangian displacement model for large deformation analysis in solid mechanics abstract a new mixed kinematic description for large deformation solid mechanics is presented the novel aspect of the new model is that both the initial and current configurations are treated as unknown large deformation statements of the principles of virtual work and stationary potential energy are formulated with the new description and presented in incremental form suitable for iterative finite element solutions the well known total lagrangian and updated lagrangian descriptions are shown to be special cases of the mixed formulation the new description is advantageous in situations where it is difficult to select an appropriate material discretization prior to analysis applications to large deformation frictional contact and fracture mechanics are presented to demonstrate the utility of the new kinematic description

synthesis of linear and planar arrays with minimum element selection a new method for the synthesis of linear and planar arrays having prescribed beamwidth and sidelobe levels and a minimum number of elements is proposed in the method the number of elements in an array is minimized while constraining the amplitude response error in the mainlobe region the attenuation in the sidelobe region and the array dimensions an iterative constrained optimization method is used where the amplituderesponse error is linearly approximated at each iteration while concurrently minimizing a re weighted l1 norm of the array coefficients to ensure robustness of the array we constrain a sensitivity parameter namely the white noise gain to be above a prescribed level furthermore the method also provides the additional flexibility of controlling the array dimensions symmetry properties and element positions of the array two variants have been developed in the first variant both the array coefficients and the positions of the elements are optimized in the second variant only the array coefficients are optimized while the elements are fixed at predefined positions experimental comparisons with several state of the art competing methods show that the proposed method provides greater flexibility of controlling the robustness beampattern response error array dimensions and element positions while at the same time the number of elements is less than or equal to that of the competing methods

the use of negative penalty functions in linear systems of equations contrary to what is commonly thought it is possible to obtain convergent results with negative rather than positive penalty functions this has been shown and proven on various occasions for vibration analysis but in this contribution it will also be shown and proven for systems of linear equations subjected to one or more constraints as a key ingredient in the developed arguments a pseudo force is identified as the derivative of the constrained degree of freedom with respect to the inverse of the penalty parameter since this pseudo force can be proven to be constant for large absolute values of the penalty parameter it follows that the exact solution is bounded by the results obtained with negative and positive penalty parameters the mathematical proofs are presented and two examples are shown to illustrate the principles

a technique for the systematic choice of admissible functions in the rayleigh ritz method abstract a simple and systematic choice of admissible functions which are the eigenfunctions of the closest simple problem extracted from the one considered is proposed the extracted problem must be less constrained than the original one in other words it must be a problem where some constraints or other complications e g added masses are eliminated elastic constraints replace the eliminated rigid ones the convergence is also analyzed this approach has practical applications when it is possible to extract a problem with eigenfunctions expressed in closed form it also allows a very simple calculation of the potential energy of the system solutions for several cases involving beams are given in order to show the power of the method application of the method to circular plates and shells is also addressed

explicit multi time step integration for first and second order finite element semidiscretizations abstract explicit multi time step subcycling integration algorithms based on nodal partitions for both first and second order systems are presented the algorithm is identical to an earlier algorithm of the senior author but some simplifications have been made in the actual algorithm which make it easier to implement in general purpose programs consistency convergence and stability analyses of this algorithm for first order systems are given interpolations on the interfaces between different time step domains are studied a general conjecture on the stability criterion for second order systems with subcycling and nodal partitions is also proposed and some unsolved theoretical difficulties are posed

an efficient approach for the assembly of mass and stiffness matrices of structures with modifications the finite element method is one of the most common tools for the comprehensive analysis of structures with applications reaching from static often nonlinear stress strain to transient dynamic analyses for single calculations the expense to generate an appropriate mesh is often insignificant compared to the analysis time even for complex geometries and therefore negligible however this is not the case for certain other applications most notably structural optimization procedures where the re meshing effort is very important with respect to the total runtime of the procedure thus it is desirable to find methods to efficiently generate mass and stiffness matrices allowing to reduce this effort especially for structures with modifications of minor complexity e g panels with cutouts therefore a modeling approach referred to as energy modification method is proposed in this paper the underlying idea is to model and discretize the basis structure e g a plate and the modifications e g holes separately the discretized energy expressions of the modifications are then subtracted from or added to the energy expressions of the basis structure and the coordinates are related to each other by kinematical constraints leading to the mass and stiffness matrices of the complete structure this approach will be demonstrated by two simple examples a rod with varying material properties and a rectangular plate with a rectangular or circular hole using a finite element discretization as basis convergence studies of the method based on the latter example follow demonstrating the rapid convergence and efficiency of the method finally the energy modification method is successfully used in the structural optimization of a circular plate with holes with the objective to split all its double eigenfrequencies