a new algorithm for contact detection between spherical particle and triangulated mesh boundary in discrete element method simulations summary in discrete element method dem simulations of real scale the spherical particles are commonly employed for increasing the computation speed and the complex boundary models are represented by triangle meshes with controllable accuracy a new contact detection algorithm has been developed to resolve the contacts between the spheres and the triangle mesh boundaries the application of the barycentric coordinates makes this algorithm more efficient to identify contacts in the intersection test as a particle probably collides with several triangles at the same time the multiple contacts would be reported as face contacts edge contacts or vertex contacts moreover the particle embedding in a triangle can be also contact with the edges or vertices of the next triangles these contacts should be considered as invalid for updating contact forces in the dem to exclude invalid records from the multiple contacts the algorithm gives attention to the mesh structure nearby contacts and analyzes all possible collision situations numerical experiments have been conducted to verify this algorithm by using the algorithm in the dem simulation framework the numerical results suggest that the algorithm can resolve all contacts precisely and stably when the spherical particles collide on the complex boundary circumstances copyright 2013 john wiley sons ltd

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

damage analysis and dynamic response of elasto plastic laminated composite shallow spherical shell under low velocity impact based on the elasto plastic mechanics the damage analysis and dynamic response of an elasto plastic laminated composite shallow spherical shell under low velocity impact are carried out in this paper firstly a yielding criterion related to spherical tensor of stress is proposed to model the mixed hardening orthotropic material and accordingly an incremental elasto plastic damage constitutive relation for the laminated shallow spherical shell is founded when a strain based hashin failure criterion is applied to assess the damage initiation and propagation secondly using the presented constitutive relations and the classical nonlinear shell theory a series of incremental nonlinear motion equations of orthotropic moderately thick laminated shallow spherical shell are obtained the questions are solved by using the orthogonal collocation point method newmark method and iterative method synthetically finally a modified elasto plastic contact law is developed to determine the normal contact force and the effect of damage geometrical parameters elasto plastic contact and boundary conditions on the contact force and the dynamic response of the structure under low velocity impact are investigated

lie point symmetry and some new soliton like solutions of the konopelchenko dubrovsky equations abstract in this paper the infinite dimensional symmetry groups of the 2 1 dimensional konopelchenko dubrovsky kd equation is found by the classical lie group method the symmetry groups are used to perform symmetry reduction and together with tanh function method we obtain soliton like solutions moreover a characterization of the corresponding lie algebra is given

on the inverse scattering transform of the 2 1 toda equation abstract the method of solution to the 2 1 dimensional toda equation is described in some detail this equation reduces directly to the well know toda lattice in 1 1 dimension and by an appropriate asymptotic reduction to the kadomtsev petviashvili equation in a continuous limit the solution exhibits a number of interesting aspects depending on certain choices of signs of which there are four in the equation for two choices of sign the equation is well posed and linearly stable unstable for the other choices of sign the equation is linearly illposed in these cases we can relate the solution to a boundary value problem and give a formal construction of the solution for one choice of signs in the illposed case an analogue of the sommerfeld radiation condition is developed in order to identify a unique solution in general the method of solution of the toda molecule equation requires an implementation of the dbar technique to cases where the associated eigenfunctions possess both smooth regions of nonholomorphicity and a discontinuity across a curve which in this problem is the unit circle special lump type solutions and solutions depending on suitable arbitrary functions are presented

the intrinsicality of lie symmetries ofu k n t fn t un a un b abstract discrete dynamical systems ddss of the formu k n t fn t un a un b withk 2 are studied for their lie symmetries we show that while there are ddss admitting nonintrinsic lie symmetries locally analytic lie symmetries of the ddss in the above form must be intrinsic unless the ddss are linear or weakly linear these will thus provide great impetus for symmetry practitioners to concentrate on finding mainly the intrinsic lie symmetries for practical ddss

formulation and analysis of conserving algorithms for frictionless dynamic contact impact problems this paper presents the formulation of conserving time stepping algorithms for frictionless dynamic contact of solids a new class of finite element methods is proposed for the solution of these problems that exhibit the same conservation laws as the underlying continuum dynamical system the proposed methods are based on a penalty regularization of the constrained contact problem and lead to full conservation of the total energy of the system including the regularization penalty potential during persistent contact and restoration of the original energy upon release both linear and angular momenta are conserved by the scheme furthermore the newly developed methods have the ability to enforce the associated constraints in the velocity besides the impenetrability constraint in the displacements while preserving the conservation restoration properties of the final numerical scheme a modification of these schemes is described that assures positive energy dissipation if desired even in the highly nonlinear setting of contact impact problems leading to contact schemes with high frequency energy dissipation representative numerical simulations are presented illustrating the performance of the proposed numerical schemes

guaranteed quality triangular mesh generation for domains with curved boundaries guaranteed quality unstructured meshing algorithms facilitate the development of automatic meshing tools however these algorithms require domains discretized using a set of linear segments leading to numerical errors in domains with curved boundaries we introduce an extension of ruppert s delaunay refinement algorithm to two dimensional domains with curved boundaries and prove that the same quality bounds apply with curved boundaries as with straight boundaries we provide implementation details for two dimensional boundary patches such as lines circular arcs cubic parametric curves and interpolated splines we present guaranteed quality triangular meshes generated with curved boundaries and propose solutions to some problems associated with the use of curved boundaries copyright 2002 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

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

multidimensional nonlinear evolution equations and inverse scattering abstract in this paper we will review some recent work done in the field of integrable nonlinear evolution equations and inverse scattering we will concentrate on the basic underlying areas and refer interested readers to suitable references for complete details specifically background material can be found in various texts on this subject e g 1 by ablowitz and segur more recent references will be given as necessary the outline of the paper is as follows 1 1 introductory remarks 2 2 a discussion of two separate but related issues namely a solving certain nonlinear evolutions equations in infinite space and b inverse scattering these are important problems having many physical applications moreover they are related to each other by what we refer to as the inverse scattering transform ist 3 3 at the end of the paper we will make some remarks on the possibility of solving nonlinear evolution equations in high dimensions i e equations with more than two spatial and one time variable by using the ist method as we now understand it

a method for representing boundaries in discrete element modelling part ii kinematics the application of the dem to engineering problems involving the dynamic behaviour of discontinuous media has necessitated the introduction of moving boundary surfaces in this paper a method is presented for modelling three dimensional moving boundary surfaces within the discrete element framework the surfaces of boundary objects are discretized into triangular planar surfaces using the finite wall method wall elements are grouped and each group is associated with a single discrete boundary object which may move independently movement comprises any combination of translation and rotation of wall element groups subject to a given acceleration and velocity during a calculation cycle the scheme is explicit due to rigidity of the wall elements which are stationary fixed in position and orientation over a time step any in plane velocity is handled as a contact point velocity within a calculation cycle the kinematic conditions at each calculation cycle may be pre defined or returned from a separate calculation of rigid body motion of the boundary object the method provides a means for coupling sphere based particle dynamics with rigid body dynamics and structural analysis of boundary components copyright 2001 john wiley sons ltd

high performance computing of discrete nonsmooth contact dynamics with domain decomposition we investigate two algorithms for solving large scale granular problems using domain decomposition methods these numerical schemes can be connected to classical domain decompositions with and without overlapping developed in continuum mechanics the two algorithms are compared in terms of implementation and parallel performance we focus the numerical study on communication procedures between processors load balancing and scalability topics particularly crucial in nonlinear evolutive problems

a method for representing boundaries in discrete element modelling part i geometry and contact detection the discrete element method for analysis of the dynamic behaviour of discontinuous media is well established however its application to engineering problems is still limited to simplified representations of structural boundaries and their kinematics in this paper a method is developed for representing three dimensional boundaries of arbitrary geometry and for modelling the interaction between boundary objects and particles within the discrete element modelling framework the approach which we term the finite wall method uses planar triangular elements to approximate the boundary surface topology any number of wall elements can be used to model the shape of the structure a contact detection scheme is presented for boundary surfaces and spheres based on a series of vector projections to reduce the problem dimensionally the algorithm employs spatial sporting to obtain the set of potential contacts between spheres and wall elements prior to contact resolution in a further stage all possible contact conditions including contact with surfaces edges and corners are explicitly determined part i of this two part series of papers describes the finite wall method for representation of surface geometry and fully elaborates the method for detecting and resolving contact between boundary wall elements and spheres in part ii the finite wall method is extended to apply kinematics to linearly independent boundary objects using combinations of translational and rotational motion an approach is developed for coupling the dem with the fem for the purpose of optimising the design of structures which are dynamically interacting with particulate media copyright 2001 john wiley sons ltd

automatic design of wing body nacelle configurations for minimum drag a computational fluid dynamics driven robust and accurate method for aerodynamic shape optimization previously developed by the authors is further enhanced by extending it to automatic multipoint design of wing body nacelle configurations the shape is optimized for minimum drag at fixed lift subject to numerous geometrical and aerodynamical constraints the method which is driven by genetic algorithms and full navier stokes computations combined with reduced order models approach is supported by massive multilevel parallelization the applications include single and multipoint aerodynamic designs for a transport type aircraft configuration for the considered class of shape optimizations significant drag reduction in on and off design conditions has been achieved it was also shown that the optimizations which start from markedly different initial shapes ultimately converge to optimum shapes very close one to one another the paper demonstrates how automated techniques based on the developed met

an energy conserved solitonic cellular automaton an energy conserved soliton cellular automaton is proposed it is a generalization of the park steiglitz and thurston model 1986 and is shown to contain richer solitonic phenomena a systematic comparison of their collision statistics is also given

accurate multiblock navier stokes solver for complex aerodynamic configurations a computational fluid dynamics tool capable to simulate accurately viscous flows around complex aerodynamic configurations is described the method combines a multiblock technique with a low dissipation numerical method incorporated into a multigrid framework structured subdomains blocks are united in multigrid multiblock structures and the blocks are treated independently at each stage of the numerical procedure maintaining a regular information exchange between the neighboring blocks in the numerical procedure the convection part of the equations is approximated by a low order upwind biased scheme employed for multigrid relaxation in combination with a higher order essentially nonoscillatory scheme used to supply a defect to the right hand side of the discrete equations on the finest multigrid level in a way ensuring the overall high accuracy of the scheme computational examples demonstrate the ability of the resulting method to perform accurate large scale computations of complex three dimensional turbulent flows around realistic aerodynamic configurations

nbs contact detection algorithm for bodies of similar size large scale discrete element simulations as well as a whole range of related problems involve contact of a large number of separate bodies in this context an efficient and robust contact detection algorithm is necessary there has been a number of contact detection algorithms with total detection time cpu time needed to detect all couples close to each other proportional to nln n where n is the total number of separate bodies reported in recent years in this work a contact detection algorithm with total detection time proportional to n is reported the algorithm is termed nbs which stands for no binary search in other words the proposed algorithm involves no binary search at any stage in addition the performance of the algorithm in terms of total detection time is not influenced by packing density while memory requirements are insignificant the only limitation of the algorithm is its applicability to the systems comprising bodies of similar size 1998 john wiley sons ltd

multiobjective aerodynamic optimization by variable fidelity models and response surface surrogates a computationally efficient procedure for multiobjective design optimization with variable fidelity models and response surface surrogates is presented the proposed approach uses the multiobjective evolutionary algorithm that works with a fast surrogate model obtained with kriging interpolation of the low fidelity model data enhanced by space mapping correction exploiting a few high fidelity training points the initial pareto front generated by multiobjective optimization of the surrogate using the multiobjective evolutionary algorithm can be iteratively refined by local enhancements of the surrogate model the latter are realized with a space mapping response correction based on a limited number of high fidelity training points allocated along the initial pareto front the proposed method allows us to obtain at a low computational cost a set of designs representing tradeoffs between the conflicting objectives the current approach is illustrated using examples of airfoil design one in transonic flo

a matrix spectral problem in one complex space dimension the inverse spectral method for an n n spectral problem is studied via the delta problem for a one dimensional complex space the complex mkdv equations are explicitly solved as an example

the inside outside contact search algorithm for finite element analysis a new contact search algorithm inside outside algorithm for the sheet forming simulation has been developed and implemented in the dynamic explicit fe code dynamic the inside outside algorithm is derived based on the feature of the inside outside status of a nodal mesh normal vector in respect to a surface segment for the judgment of the contact of fe nodes with the tool surface this new algorithm includes local search local track and penetration calculation processes almost no additional cpu time is required for the local search process because the calculations for both global and local search are combined moreover the problems of conventional contact searching algorithms such as iterations for local search and the deadzone problem are resolved therefore the quick robust contact searching and accurate evaluation of penetration have been achieved the numerical results show that the new contact searching algorithm is more cost effective and robust than conventional ones 1997 john wiley sons ltd

a family of higher order mixed finite element methods for plane elasticity the dirichler problem for the equations of plane elasticity is approximated by a mixed finite element method using a new family of composite finite elements having properties analogous to those possessed by the raviart thomas mixed finite elements for a scalar second order elliptic equation estimates of optimal order and minimal regularity are derived for the errors in the displacement vector and the stress tensor inl 2 and optimal order negative norm estimates are obtained inh s for a range ofs depending on the index of the finite element space an optimal order estimate inl for the displacement error is given also a quasioptimal estimate is derived in an appropriate space all estimates are valid uniformly with respect to the compressibility and apply in the incompressible case the formulation of the elements is presented in detail

integrable dynamical systems with quadratic and cubic nonlinearities related to graded lie algebras practical implementation of two important methods of constructing integrable dynamical systems the lax pair method and the adler konstant symes theorem is studied general considerations are illustrated by several examples that contain multiwave interaction systems and interacting garnier systems as particular cases

a 3 d discrete element method for dry granular flows of ellipsoidal particles abstract we use 3 d discrete element method dem to simulate dry granular flows of non spherical particles in our simulation code non spherical particles are represented by clusters of spheres for contact detection and for contact force calculation for particles in contact the normal force displacement nfd model is simulated by a partially latching spring system whereas the tangential force displacement tfd model is simulated by an incremental relation that corresponds to a simplification of the mindlin and deresiewicz r d mindlin h deresiewicz asme j appl mech 20 1953 327 344 contact mechanics theory to establish the validity of the simulation procedure benchmark tests such as superball and superbean simulations were carried out we present various results obtained from the simulation of ellipsoidal particles flowing down a chute having a bumpy bottom these ellipsoidal particles had their physical properties obtained from experiments

a new integrable davey stewartson type equation a new integrable nonlinear partial differential equation pde in 2 1 dimensions is derived starting from the konopelchenko dubrovsky equation we use an asymptotically exact reduction method based on fourier expansion and spatio temporal rescaling and obtain a new integrable davey stewartson type equation in order to demonstrate the integrability of the new equation by the inverse scattering method we apply the reduction technique to the lax pair of the konopelchenko dubrovsky equation and find the corresponding lax pair of the new equation the new equation reduces to the davey stewartson or the nonlinear schrodinger equation by appropriate limits

algebraic grid generation on trimmed parametric surface using non self overlapping planar coons patch using a coons patch mapping to generate a structured grid in the parametric region of a trimmed surface can avoid the singularity of elliptic pde methods when only c1 continuous boundary is given the error of converting generic parametric c1 boundary curves into a specified representation form is also avoided however overlap may happen on some portions of the algebraically generated grid when a linear or naive cubic blending function is used in the mapping this severely limits its usage in most of engineering and scientific applications where a grid system of non self overlapping is strictly required to solve the problem non trivial blending functions in a coons patch mapping should be determined adaptively by the given boundary so that self overlapping can be averted we address the adaptive determination problem by a functional optimization method the governing equation of the optimization is derived by adding a virtual dimension in the parametric space of the given trimmed surface both one and two parameter blending functions are studied to resolve the difficulty of guessing good initial blending functions for the conjugate gradient method used a progressive optimization algorithm is then proposed which has been shown to be very effective in a variety of practical examples also an extension is added to the objective function to control the element shape finally experiment results are shown to illustrate the usefulness and effectiveness of the presented method copyright 2004 john wiley sons ltd

explicit exact solutions for the 2 1 dimensional konopelchenko dubrovsky equation in this paper we construct new explicit exact solutions for the coupled the 2 1 dimensional konopelchenko dubrovsky equation kd equation by using a improved mapping approach and variable separation method by means of the method new types of variable separation solutions including solitary wave solutions periodic wave solutions and rational function solutions for the kd system are successfully obtained the improved mapping approach and variable separation method can be applied to other higher dimensional coupled nonlinear evolution equations

restricted multiple three wave interactions integrable cases of this system and other related systems restricted multiple three wave interactions in which a set of wave triads interact through one shared wave are discussed it is shown that this system is integrable when all triads have equal coupling coefficients regardless of the frequency mismatches this system is then used as a starting point from which to determine integrable cases of a more general class of three wave interactions

integrable non isospectral flows associated with the kadomtsev petviashvili equations in 2 1 dimensions the symmetries of the kadomtsev petviashvili kp equations in 2 1 dimensions yield two hierarchies of integrable non linear evolution equations nee one is the familiar family of isospectral flows the kp hierarchy the other is non isospectral and its flows have coefficients which depend linearly on x and y the spectral methods used to solve kp can be used to solve all these nee an underlying infinite dimensional lie algebra is used to determine all the lax pairs for both families and it also determines their symplectic structures constants of the motion are constructed for the non isospectral cases

symmetry reductions of the lax pair for the 2 1 dimensional konopelchenko dubrovsky equation based on the symbolic computational system maple the similarity reduction arising from the classical lie point symmetries of the lax pair for the 2 1 dimensional konopelchenko dubrovsky kd equation is carried out we obtain several interesting reductions by analyzing not only the reduced lax pair but also the kd equation reduced under the same symmetry group we find that the reduced lax pairs do not always lead to the reduced kd equation

new analytical and numerical results for two dimensional contact profiles recently a generalized coulomb law for elastic bodies in contact has been developed by the author which assumes that the tangential traction is the difference of the slip stress of the contact and the stick area whereby each stick area corresponds to a smaller contact area it holds for multiple contact regions also several applications for elastic half planes half spaces thin and thick layers and impact problems have been published for plane contact of equal bodies with friction it provides exact solutions and the interior stress field can be expressed with analytical results in closed form in this article a singular superposition of flat punch solutions is outlined in which the punches are aligned with an edge of the contact area it is shown that this superposition satisfies coulomb s inequalities directly and new results for the muskhelishvili potentials of several profiles are presented it is illustrated how problems of singularity and multi valuedness of complex functions can be solved in closed form and the chebyshev approximation used by earlier authors can be avoided for comparison some previous solutions for symmetric profiles are appended some results for the interior stress field the pressure the frictional traction and the surface displacements are compared with fem solutions of an equivalent problem the small differences between both methods show characteristic features of the fem model and the theoretical assumptions and are shortly explained further this example can be used as benchmark test for fem and bem programs

combined partial bar and riemann hilbert inverse methods for integrable non linear evolution equations in 2 1 dimensions the authors give a natural combination of partial bar and riemann hilbert problem inverse methods for an n th order scalar spectral problem which solves a number of integrable non linear evolution equations in two space and one time 2 1 dimensions the theory embraces the two kadomtsev petviashvili equations 1970 and their lump solutions

the inverse problem for ordinary differential operators on the line on etudie le probleme inverse sur la ligne pour l operateur p d n q n 2 d n 2 q 0 d d idx pour tout ordre n 2 et sans hypothese de propriete d auto adjoint

an elastoplastic contact force displacement model in the normal direction displacement driven version we present an elastoplastic normal forcedisplacement nfd model for spheres in collision among several possible applications of this model are the granularflow simulations using a discreteelement

nonlinear schrodinger equations and simple lie algebras we associate a system of integrable generalised nonlinear schrodinger nls equations with each hermitian symmetric space these nls equations are considered as reductions of more general systems this time associated with a reductive homogeneous space the nonlinear terms are related to the curvature and torsion tensors of the appropriate geometrical space the hamiltonian structure is investigated using r matrix techniques and shown to be canonical for all these equations throughout the reduction procedure this hamiltonian structure does not degenerate each of the above systems of equations is gauge equivalent to a generalised ferromagnet reductions of the latter are discussed in terms of the corresponding nls type equations

normal and tangential force displacement relations for frictional elasto plastic contact of spheres abstract in this paper we present the data obtained from numerical experiments that are at the foundation of our successful elasto plastic force displacement fd models in both the normal direction and tangential direction of spheres in collision we also present in detail how these data were obtained our numerical experiments are in the form of frictional elasto plastic finite element analysis of spherical particles in contact we use the numerical experiments to observe the behavior of various quantities involved in the contact e g contact area radius contact curvature stresses fd relations etc this observation has helped us to devise an accurate and consistent model for frictional elasto plastic contact of spherical particles that are used in granular flow simulations that may involve tens of thousands of these particles

a contact algorithm for smoothed particle hydrodynamics abstract this paper describes the development and testing of a contact algorithm for smoothed particle hydrodynamics sph the treatment of contact boundary conditions in sph has not been adequately addressed and the development of the normalised smoothing function approach has highlighted the need for correct treatment of boundary conditions a particle to particle contact algorithm was developed for 2d the penalty formulation was used to enforce the contact condition and several equations for the penalty force calculation were considered the contact algorithm was tested for 1 and 2d problems for the velocity range between 0 2 and 4 0 km s to determine the best penalty force equation and the best approach for applying the contact force the tests showed that the zero energy mode problem in the sph method had to be addressed as contact excited a zero energy mode that caused non physical motion of particles the test results were compared to the dyna3d results for the same problems

mr linear contact detection algorithm large scale discrete element simulations as well as a whole range of related problems involve contact of a large number of separate bodies and an efficient and robust contact detection algorithm is necessary there has been a number of contact detection algorithms with total detection time proportional to n ln n where n is the total number of separate bodies reported in the past in more recent years algorithms with total cpu time proportional to n have been developed in this work a novel contact detection algorithm with total detection time proportional to n is proposed the performance of the algorithm is not influenced by packing density while memory requirements are insignificant the algorithm is applicable to systems comprising bodies of a similar size the algorithm is named mr munjiza rougier munjiza devised the algorithm rougier implemented it in the second part of the paper the algorithm is extended to particles of different sizes the new algorithm is called mmr multi step mr algorithm copyright 2005 john wiley sons ltd

an accurate elasto plastic frictional tangential force displacement model for granular flow simulations displacement driven formulation we present in this paper the displacement driven version of a tangential force displacement tfd model that accounts for both elastic and plastic deformations together with interfacial friction occurring in collisions of spherical particles this elasto plastic frictional tfd model with its force driven version presented in l vu quoc l lesburg x zhang an accurate tangential force displacement model for granular flow simulations contacting spheres with plastic deformation force driven formulation journal of computational physics 196 1 2004 298 326 is consistent with the elasto plastic frictional normal force displacement nfd model presented in l vu quoc x zhang an elasto plastic contact force displacement model in the normal direction displacement driven version proceedings of the royal society of london series a 455 1991 4013 4044 both the nfd model and the present tfd model are based on the concept of additive decomposition of the radius of contact area into an elastic part and a plastic part the effect of permanent indentation after impact is represented by a correction to the radius of curvature the effect of material softening due to plastic flow is represented by a correction to the elastic moduli the proposed tfd model is accurate and is validated against nonlinear finite element analyses involving plastic flows in both the loading and unloading conditions the proposed consistent displacement driven elasto plastic nfd and tfd models are designed for implementation in computer codes using the discrete element method dem for granular flow simulations the model is shown to be accurate and is validated against nonlinear elasto plastic finite element analysis

an optimal order process for solving finite element equations a k level iterative procedure for solving the algebraic equations which arise from the finite element approximation of elliptic boundary value problems is presented and analyzed the work estimate for this procedure is proportional to the number of unknowns an optimal order result general geometry is permitted for the underlying domain but the shape plays a role in the rate of convergence through elliptic regularity finally a short discussion of the use of this method for parabolic problems is presented

mesh independent analysis of shell like structures summary mesh independent analysis is motivated by the desire to use accurate geometric models represented as equations rather than approximated by a mesh the trial and test functions are approximated or interpolated on a background mesh that is independent of the geometry this background mesh is easy to generate because it does not have to conform to the geometry essential boundary conditions can be applied using the implicit boundary method where the trial and test functions are constructed utilizing approximate step functions such that the boundary conditions are guaranteed to be satisfied this approach has been demonstrated for two dimensional 2d and three dimensional 3d structural analysis and is extended in this paper to model shell like structures the background mesh consists of 3d elements that use uniform b spline approximations and the shell geometry is assumed to be defined as parametric surfaces to allow arbitrarily complex shell like structures to be modeled several benchmark problems are used to study the validity of these 3d b spline shell elements copyright 2012 john wiley sons ltd

a class of integrable davey stewartson type systems a new integrable davey stewartson type class of systems of partial differential equations in 2 1 dimensions is derived from a previously known integrable equation by means of an asymptotically exact nonlinear reduction method based on fourier expansion and spatio temporal rescaling the integrability by the inverse scattering method is explicitly demonstrated because the reduction technique is applied to the lax pair of the starting equation and the corresponding lax pair of the class of systems of equations is found the particular characteristics of the reduction method imply that the new systems are likely to be of applicative relevance

geometrical representation and integration in bie analysis boundary representation by straight lines and circular arcs is described and the error introduced through the common representation of circular arc boundaries by quadratic geometrical shape functions is investigated this error is shown to be in some cases the major contributor to the total error an even more significant advantage of exact boundary representation is that it permits many of the required integrations to be performed analytically rather than by using gaussian quadrature for example all integrations in any rectilinear domain can then be evaluated analytically this generally produces an increase in accuracy and a saving in the computing time required to assemble the coefficient matrices in slender domains both this increase in accuracy and saving in computing time are very marked as analytical integrations permit the use of very much coarser discretization than would be required for numerical quadrature

constrained aerodynamic optimization of three dimensional wings driven by navier stokes computations ar obust and efficient approach to the multiobjective constrained design previously developed by the authors is extended to optimization of three dimensional aerodynamic wings the objective is to minimize the total drag at fixed lift subject to various geometrical and aerodynamical constraints the approach employs genetic algorithms gas as an optimization tool in combination with a reduced order models rom method based on linked local databases obtained by full navier stokes computations the work focuses on the following issues geometrical representation of three dimensional shapes handling of sensitive nonlinear constraints such as pitching moment and the influence of flight conditions on the results of optimization the method implemented in the computer code optimas optimization of aerodynamic shapes was applied to the problem of multipoint transonic threedimensional wing optimization with nonlinear constraints the results include a variety of optimization cases for two wings a classical test case of onera m6 wing and a generic cranked transport type wing for the investigated class of problems significant aerodynamic gains have been obtained nomenclature c d total drag coefficient cl total lift coefficient c m total pitching moment coefficient c p pressure coefficient m freestream mach number n d dimension of the search space nws number of sectional airfoils q objective function r c relative radius of the airfoil leading edge re freestream reynolds number t c relative thickness of airfoil angle of attack trailing edge angle of airfoil

robust hybrid approach to multiobjective constrained optimization in aerodynamics a new approach to the multiobjective constrained design of aerodynamic shapes is suggested the approach employs genetic algorithms ga as an optimization tool in combination with a reduced order models method based on linked local databases obtained by full navier stokes computations the method was applied to the problem of multiobjective transonic profile optimization with nonlinear constraints the results demonstrated that the method retains high robustness of conventional gas while keeping computational fluid dynamics computational volume to an acceptable level as a result of a limited use of full navier stokes computations a significant computational time saving in comparison with optimization tools fully based on navier stokes computations allowed the algorithm to be used in a demanding engineering environment