stability analysis of particle methods with corrected derivatives abstract the stability of discretizations by particle methods with corrected derivatives is analyzed it is shown that the standard particle method which is equivalent to the element free galerkin method with an eulerian kernel and nodal quadrature has two sources of instability 1 rank deficiency of the discrete equations and 2 distortion of the material instability the latter leads to the so called tensile instability it is shown that a lagrangian kernel with the addition of stress points eliminates both instabilities examples that verify the stability of the new formulation are given

pi fuzzy controllers for integral plants to ensure robust stability new pi fuzzy controllers comprising takagi sugeno and mamdani fuzzy systems to control a class of integral plants specific to servo systems are proposed in this paper linear pi controllers are designed in the first phase they are tuned using the extended symmetrical optimum method to ensure the desired overshoot and settling time with respect to step setpoint modifications and three types of load disturbance inputs this type of pi controller design guarantees robust stability of the closed loop system in response to parametric variations in a controlled plant following this based on the results from the linear case and the modal equivalence principle an original development method for pi fuzzy controllers is proposed some experimental results are included to illustrate the effectiveness of the design process

moving least squares particle hydrodynamics i consistency and stability the smooth particle hydrodynamics sph method is derived in a novel manner by means of a galerkin approximation applied to the lagrangian equations of continuum mechanics as in the finite element method this derivation is modified to replace the sph interpolant with the moving least squares mls interpolant of lancaster and saulkaskas and define a new particle volume which ensures thermodynamic compatibility a variable rank modification of the mls interpolants which retains their desirable summation properties is introduced to remove the singularities that occur when divergent flow reduces the number of neighbours of a particle to less than the minimum required a surprise benefit of the galerkin sph derivation is a theoretical justification of a common ad hoc technique for variable h sph the new mlsph method is conservative if an anti symmetric quadrature rule for the stiffness matrix elements can be supplied in this paper a simple one point collocation rule is used to retain similarity with sph leading to a non conservative method several examples document how mlsph renders dramatic improvements due to the linear consistency of its gradients on three canonical difficulties of the sph method spurious boundary effects erroneous rates of strain and rotation and tension instability two of these examples are non linear lagrangian patch tests with analytic solutions with which mlsph agrees almost exactly the examples also show that mlsph is not absolutely stable if the problems are run to very long times a linear stability analysis explains both why it is more stable than sph and not yet absolutely stable and an argument is made that for realistic dynamic problems mlsph is stable enough the notion of coherent particles for which the numerical stability is identical to the physical stability is introduced the new method is easily retrofitted into a generic sph code and some observations on performance are made copyright 1999 john wiley sons ltd

smoothed particle hydrodynamics stability analysis abstract sph smoothed particle hydrodynamics is a gridless lagrangian technique which is appealing as a possible alternative to numerical techniques currently used to analyze large deformation events recent tests of the standard sph method using the cubic b spline kernel indicated the possibility of an instability in the tensile regime even though no such difficulties were observed in compression a von neumann stability analysis of the sph algorithm has been carried out which identifies the criterion for stability or instability in terms of the stress state and the second derivative of the kernel function the analysis explains the observation that the method is unstable in tension while apparently stable in compression but shows that it is possible to construct kernel functions which are stable in tension and unstable in compression the instability is shown to result from an effective stress with a negative modulus imaginary sound speed being produced by the interaction between the constitutive relation and the kernel function and is not caused by the numerical time integration algorithm that is changes in the effective stress act to amplify rather than reduce perturbations in the strain the analysis and the stability criterion provide insight into possible methods for removing the instability

a novel fuzzy framework for nonlinear system control nonlinear pid and gain scheduling controls have attracted much research interests in recent years these control strategies can accommodate some nonlinear characteristics by allowing the gains varied or rescheduled as a function of system states in this paper a novel fuzzy framework is developed to transfer this type of nonlinear controller to its fuzzy domain representation it is proved that the resulting fuzzy controller is functionally exactly identical to the original control system one of the benefits of the suggested approach is that it provides a well defined prototype for the design of fuzzy control system the resulting linguistic representation can facilitate investigation in linguistic terms into how the controller operates whereas expert knowledge can be effectively implemented to improve control performance the viability of the proposed mapping technique is demonstrated by using simulations corresponding to a flexible link robot

transient fokker planck kolmogorov equation solved with smoothed particle hydrodynamics method summary probabilistic theories aim at describing the properties of systems subjected to random excitations by means of statistical characteristics such as the probability density function pdf the time evolution of the pdf of the response of a randomly excited deterministic system is commonly described with the transient fokker planck kolmogorov fpk equation the fpk equation is a conservation equation of a hypothetical or abstract fluid which models the transport of probability this paper presents a generalized formalism for the resolution of the transient fpk equation by using the well known mesh free lagrangian method smoothed particle hydrodynamics numerical implementation shows notable advantages of this method in an unbounded state space 1 the conservation of total probability in the state space is explicitly written 2 no artifact is required to manage far field boundary conditions 3 the positivity of the pdf is ensured and 4 the extension to higher dimensions is straightforward furthermore thanks to the moving particles this method is adapted for a large kind of initial conditions even slightly dispersed distributions the fpk equation is solved without any a priori knowledge of the stationary distribution just a precise representation of the initial distribution is required copyright 2013 john wiley sons ltd

constructing smoothing functions in smoothed particle hydrodynamics with applications this paper presents a general approach to construct analytical smoothing functions for the meshfree lagrangian and particle method of smoothed particle hydrodynamics the approach uses integral form of function representation and applies taylor series expansion to the sph function and derivative approximations the constructing conditions are derived systematically which not only interpret the consistency condition of the method but also describe the compact supportness requirement of the smoothing function examples of sph smoothing function are constructed including some existing ones with this approach a new quartic smoothing function with some advantages is constructed and is applied to the one dimensional shock problem and a one dimensional tnt detonation problem the good agreement between the sph results and those from other sources shows the effectiveness of the approach and the newly constructed smoothing function in numerical simulations

adaptive kernel estimation and sph tensile instability we propose an alternative method to remove the tensile instability in standard sph simulations of a fluid the method relies on an adaptive density kernel estimation adke algorithm which allows the width of the kernel interpolant to vary locally in such a way that only the minimum necessary smoothing is applied to the data by means of a linear perturbation analysis of the sph equations for a heat conducting viscous van der waals fluid we derive the corresponding dispersion relation solution of the dispersion relation in the short wavelength limit shows that the tensile instability is effectively removed for a wide range of the adke parameters application of the method to the formation of equilibrium liquid drops confirms the analytical results of the linear stability analysis examples of the resolving power of the method are also given for the nonlinear oscillations of an excited drop and the sedov blast wave problem

enhancement of stability and accuracy of the moving particle semi implicit method as a lagrangian gridless particle method the mps moving particle semi implicit method has been proven useful in a wide range of engineering applications up to now most of mps applications have been limited to problems with compressive stress states this paper investigates the performance and stability of mps method in simulation of more general hydrodynamic problems including those characterized by tensile stresses or by changes in the stress states it is shown that mps based simulations are prone to become destabilized in presence of attractive interparticle forces this instability appears to be similar to the so called tensile instability in sph method two new modifications namely a modified poisson pressure equation and a corrective matrix for pressure gradient model are proposed to resolve this shortcoming these two new modifications together with two previously proposed improvements are shown to stabilize and enhance the performance of mps method

enhanced local maximum entropy approximation for stable meshfree simulations abstract we introduce an improved meshfree approximation scheme which is based on the local maximum entropy strategy as a compromise between shape function locality and entropy in an information theoretical sense the improved version is specifically designed for severe finite deformation and offers significantly enhanced stability as opposed to the original formulation this is achieved by i formulating the quasistatic mechanical boundary value problem in a suitable updated lagrangian setting ii introducing anisotropy in the shape function support to accommodate directional variations in nodal spacing with increasing deformation and eliminate tensile instability iii spatially bounding and evolving shape function support to restrict the domain of influence and increase efficiency iv truncating shape functions at interfaces in order to stably represent multi component systems like composites or polycrystals the new scheme is applied to benchmark problems of severe elastic and elastoplastic deformation that demonstrate its performance both in terms of accuracy as compared to exact solutions and where applicable finite element simulations and efficiency importantly the presented formulation overcomes the classical tensile instability found in most meshfree interpolation schemes as shown for stable simulations of e g the inhomogeneous extension of a hyperelastic block up to 100 or the torsion of a hyperelastic cube by 200 both in an updated lagrangian setting and without the need for remeshing

lanczos generalized derivative insights and applications generalizations of the lanczos derivative provide a basis for certain grid free finite interpolation methods fims which appear to have advantages over alternatives such as the standard finite difference methods fdms or finite element methods fems for certain problems e g hypervelocity impact problems in computational material dynamics

the simplest fuzzy controllers using different inference methods are different nonlinear proportional integral controllers with variable gains abstract the author analytically proves that the simplest fuzzy controllers using different inference methods are different nonlinear proportional integral pi controllers with proportional gains and integral gains changing with inputs of the controllers the inference methods involved are mamdani s minimum inference method larsen s product inference method the drastic product inference method and the bounded product inference method configuration of the fuzzy controllers is minimal which includes two input fuzzy sets three output fuzzy sets four control rules zadeh fuzzy logic and lukasiewicz fuzzy logic or and a center of gravity defuzzification algorithm after analytically investigating properties of the nonlinear pi controllers the author reveals that the bounded product inference method is inappropriate for the control purpose while the other three inference methods are appropriate dynamic and static control behaviors of the fuzzy controllers with the appropriate inference methods are analytically compared with each other and are also compared with those of the linear pi controller finally it is analytically proven that the fuzzy control systems have the same local stability at the equilibrium point as the corresponding linear pi control system does

theory and application of a novel fuzzy pid controller using a simplifier takagi sugeno rule scheme we first present a novel general purpose nonlinear pid controller realized via fuzzy pid control that uses our newly introduced simplified takagi sugeno ts rule scheme analytical structure of the fuzzy pid controller is derived and its structure is analyzed in relation to the linear pid controller the unique features of the fuzzy controller are as follows first the proportional integral and derivative gains constantly vary with the output of the system under control the gain variation leads to a shorter rise time a less overshoot and a smaller settling time as compared to a comparable linear pid controller second the characteristics of the gain variation are determined by the fuzzy rules and can intuitively be designed we have also investigated the local stability of the fuzzy pid control systems as an application demonstration we have developed a fuzzy pid control system to regulate in computer simulation blood pressure in postsurgical patients we have chosen this particular control problem because the studies in the literature have established that in order to achieve satisfactory control results using a nonlinear controller with variable gains is necessary the simulation results show that the fuzzy pid controller significantly outperforms its linear counterpart and is safer and more robust over a wide range of patient condition 2000 published by elsevier

an sph projection method for simulating fluid hypoelastic structure interaction abstract in this paper an incompressible smoothed particle hydrodynamics sph method is proposed for simulation of fluid structure interaction problems deploying the pressure poisson equation to satisfy incompressibility constraints viscous fluid flow past rigid and hypoelastic solid surfaces is studied the fluid is fully coupled with the solid structure that can undergo large structural deformations a key feature of the proposed scheme is that the no slip and coupling conditions on the contact surface are satisfied automatically to alleviate the numerical difficulties encountered when a hypoelastic solid structure is highly stretched an artificial stress term is incorporated into the momentum equation which reduces the risk of unrealistic fractures in the material to demonstrate the ability of the proposed method in dealing with large deformation of free surface the well known pure dam breaking problem is solved and then the oscillations of an cantilever beam is simulated to show the capability of the method in capturing the large deformations of an elastic solid eventually three challenging test cases deformation of an elastic plate subjected to time dependent water pressure collapse of a water column with an obstacle and breaking dam on a hypoelastic wall are solved to demonstrate the capability of the proposed scheme the simulated results are in very good agreement with available experimental and numerical results

a level set enhanced natural kernel contact algorithm for impact and penetration modeling summary a natural kernel contact nkc algorithm under the framework of the semi lagrangian reproducing kernel particle method semi lagrangian rkpm is proposed to model multi body contact with specific consideration for impact and penetration modeling the nkc algorithm utilizes the interaction of the semi lagrangian kernel functions associated with contacting bodies to serve as the non penetration condition the effects of friction are represented by introducing a layer of the friction like elasto plasticity material between contacting bodies this approach allows the frictional contact conditions and the associated kinematics to be naturally embedded in the semi lagrangian rkpm inter particle force calculation the equivalence in the karush kuhn tucker conditions between the proposed nkc algorithm and the conventional contact kinematic constraints as well as the associated state variable relationships are identified a level set method is further introduced in the nkc algorithm to represent the contact surfaces without pre defined potential contact surfaces the stability analysis performed in this work shows that temporal stability in the semi lagrangian rkpm with nkc algorithms is related to the velocity gradient between contacting bodies the proposed methods have been verified by several benchmark problems and applied to the simulation of impact and penetration processes copyright 2014 john wiley sons ltd

prime fuzzy ideals in rings abstract in this paper give a characterization of prime fuzzy ideals we introduce weakly completely prime fuzzy ideals and establish a relation between completely prime fuzzy ideals and weakly completely prime fuzzy ideals

normalized sph with stress points smoothed particle hydrodynamics is extended to a normalized staggered particle formulation with boundary conditions a companion set of interpolation points is introduced that carry the stress velocity gradient and other derived field variables the method is stable linearly consistent and has an explicit treatment of boundary conditions also a new method for finding neighbours is introduced which selects a minimal and robust set and is insensitive to anisotropy in the particle arrangement test problems show that these improvements lead to increased accuracy and stability published in 2000 by john wiley sons ltd

sph hydrocodes can be stabilized with shape shifting grid free methods such as sph smoothed particle hydrodynamics may eventually be more efficacious in their representations of material dynamics than the standard fixed grid methods however standard sph with stress and interpolation weight w has instabilities when w 0 and in tension 0 conservative smoothing can control the sph instabilities but it may smooth out more of the short wave length structure than desired sph can also be stabilized by shifting the shape of w to change the sign of w

a peridynamic model for plasticity micro inertia based flow rule entropy equivalence and localization residuals this article presents a non ordinary state based peridynamic pd model for thermo visco plasticity that incorporates a microinertia driven dynamic flow rule in addition to the three displacement degrees of freedom the model assigns to each particle an internal degree of freedom namely the equivalent plastic strain the flow rule itself is in the form of an integro differential micro force balance written in terms of appropriate pd states associated with micro stresses corresponding to the internal degree of freedom an equation for entropy balance adapted to the pd setup is also proposed along with the internal energy equivalence we exploit a notion of equivalence of the local entropy production for the constitutive modelling of the force states as we also demonstrate the pd model naturally accounts for the localization residual terms in the local balances for internal energy and entropy originally conceived of by edelen and co workers nearly half a century ago as a source of nonlocal interaction the model is numerically implemented for the problem of impact between two 4340 steel plates and the results show that the model provides information on nontrivial effects of micro inertia on the plastic flow and temperature generation by incorporating a classical damage model in the pd set up we also discuss an extension of the approach for ductile failure and report on the numerical results against tension test on an a440 steel plate with holes c 2017 elsevier b v all rights reserved

clustered generalized finite element methods for mesh unrefinement non matching and invalid meshes in spite of significant advancements in automatic mesh generation during the past decade the construction of quality finite element discretizations on complex three dimensional domains is still a difficult and time demanding task in this paper the partition of unity framework used in the generalized finite element method gfem is exploited to create a very robust and flexible method capable of using meshes that are unacceptable for the finite element method while retaining its accuracy and computational efficiency this is accomplished not by changing the mesh but instead by clustering groups of nodes and elements the clusters define a modified finite element partition of unity that is constant over part of the clusters this so called clustered partition of unity is then enriched to the desired order using the framework of the gfem the proposed generalized finite element method can correctly and efficiently deal with i elements with negative jacobian ii excessively fine meshes created by automatic mesh generators iii meshes consisting of several sub domains with non matching interfaces under such relaxed requirements for an acceptable mesh and for correctly defined geometries today s automated tetrahedral mesh generators can practically guarantee successful volume meshing that can be entirely hidden from the user a detailed technical discussion of the proposed generalized finite element method with clustering along with numerical experiments and some implementation details are presented copyright 2006 john wiley sons ltd

tl subrings and tl ideals part 1 basic concepts abstract in 25 27 we put forward a rudimentary frame of the theory of tl subalgebras in 26 we established a theory of tl subgroups and tl subgroups in this paper we will continue our work in concern with basic ideas provided in 25 27 introduce the notions of tl subrings and tl ideals of a ring and study some of their properties where t is an arbitrary infinitely distributive t norm on a given complete brouwerian lattice l

arbitrarily smooth generalized finite element approximations this paper presents a procedure to build ck k arbitrarily large generalized finite element fe shape functions defined on non structured finite element meshes the functions have the same support as corresponding global fe lagrangian shape functions meshes with both convex and non convex clouds set of elements sharing a vertex node can be used the so called r functions are used to build ck fe based partition of unity functions with non convex support a technique to combine c0 lagrangian fe shape functions with the proposed ck partition of unity is presented the technique allows the use of ck generalized fe shape functions in parts of the computational domain where their high smoothness is required as in the case of problems with distributional boundary conditions and the less computationally demanding c0 generalized fe shape functions elsewhere in the domain a linear elasticity problem with a concentrated moment is solved using the proposed ck generalized fe method higher order distributional boundary conditions can also be handled by the method a detailed convergence analysis is presented for this class of problems as well as for problems in energy space the integrability of the functions using standard gauss legendre rules is also investigated

on fuzzy quotient rings induced by fuzzy ideals abstract in this paper we define fuzzy quotient rings induced by fuzzy ideals and study the relation between fuzzy quotient rings and fuzzy ideals

constructing nonlinear variable gain controllers via the takagi sugeno fuzzy control we investigated the analytical structure of the takagi sugeno ts type of fuzzy controllers which was unavailable in the literature the ts fuzzy controllers we studied employ a new and simplified ts control rule scheme in which all the rule consequent use a common function and are proportional to one another greatly reducing the number of parameters needed in the rules other components of the fuzzy controllers are general arbitrary input fuzzy sets any type of fuzzy logic and the generalized defuzzifier which contains the popular centroid defuzzifier as a special case we proved that all these ts fuzzy controllers were nonlinear variable gain controllers and characteristics of the gain variation were parametrized and governed by the rule proportionality we conducted an in depth analysis on a class of nonlinear variable gain proportional derivative pd controllers we present the results to show 1 how to analyze the characteristics of the variable gains in the context of control 2 why the nonlinear variable gain pd controllers can outperform their linear counterpart and 3 how to generate various gain variation characteristics through the manipulation of the rule proportionality

fuzzy factor rings in this paper the fuzzy factor ring is defined and the fundamental theorem of homomorphisms as well as the isomorphism theorem of fuzzy rings are also obtained

on fuzzy ideals of a ring 1 abstract the aim of this paper is to study fuzzy ideals of a ring to characterise regular rings and noetherian rings by fuzzy ideals and to determine all fuzzy prime ideals of the ring z of integers

a lagrangian particle method for the simulation of linear and nonlinear elastic models of soft tissue we present a novel lagrangian particle method for the simulation of linear and nonlinear elastic models of soft tissue linear solids are represented by the lagrangian formulation of the stress strain relationship that is extended to nonlinear solids by using the lagrangian evolution of the deformation gradient described in a moving framework the present method introduces a level set description along with the particles to capture the body deformations and to enforce the boundary conditions furthermore the accuracy of the method in cases of large deformations is ensured by implementing a particle remeshing procedure the method is validated in several benchmark problems in two and three dimensions and the results compare well with the results of respective finite elements simulations in simulations of large solid deformation under plane strain compression the finite element solver exhibits spurious structures that are not present in the lagrangian particle simulations the particle simulations are compared with experimental results in an aspiration test of liver tissue

structural analysis of fuzzy controllers with nonlinear input fuzzy sets in relation to nonlinear pid control with variable gains the popular linear pid controller is mostly effective for linear or nearly linear control problems nonlinear pid controllers however are needed in order to satisfactorily control highly nonlinear plants time varying plants or plants with significant time delay this paper extends our previous papers in which we show rigorously that some fuzzy controllers are actually nonlinear pi pd and pid controllers with variable gains that can outperform their linear counterparts in the present paper we study the analytical structure of an important class of two and three dimensional fuzzy controllers we link the entire class as opposed to one controller at a time to nonlinear pi pd and pid controllers with variable gains by establishing the conditions for the former to structurally become the latter unlike the results in the literature which are exclusively for the fuzzy controllers using linear fuzzy sets for the input variables this class of fuzzy controllers employs nonlinear input fuzzy sets of arbitrary types our structural results are thus more general and contain the existing ones as special cases two concrete examples are provided to illustrate the usefulness of the new results

a generalized smoothed particle hydrodynamics method for nonlinear dynamic problems abstract a generalized smoothed particle hydrodynamics sph method was developed for the numerical simulation of nonlinear dynamic problems the performance of the proposed method was demonstrated by solving burgers equations over a wide range of the viscosity parameters in one and two space dimensions it was shown that the present results agree very well with other existing solutions as compared to other meshless methods this algorithm is quite straightforward and simple and can be coded easily

three dimensional simulation of a solid liquid flow by the dem sph method abstract in this paper we describe a new lagrangian lagrangian algorithm which is referred to be the dem sph method for solid liquid flows involving free surfaces the dem solid phase and the sph liquid phase are coupled using the local averaging technique described by lagrangian approaches where both the continuity equation and the interaction force i e drag force are connected with the local mean voidage conservative forms of momentum transformation are derived for the dem sph interaction via a variational approach by introducing a correction to the sph approximation with explicit inclusion of boundary information arbitrary boundaries can be modeled without any extra wall particles where the boundary is used commonly for both dem and sph phases we deploy level set distance functions to efficiently construct and evaluate this boundary model to examine the validity of the present method we perform three dimensional simulations of a dynamic flow in a solid liquid dam break and a quasi steady flow in a rotating cylindrical tank and we conduct validation experiments to justify the simulation results in the dam break problem positions of wave fronts during the collapse are computed and compared with experimental measurements for the circulating tank some macroscopic aspects of the steady flow e g the shape dimension and velocity profile of the solid bed are obtained for validation data in both cases the simulation results are in good agreement with those of the experiment consequently the dem sph method is proved to be adequate in modeling solid liquid flows through this study

a unified stability analysis of meshless particle methods a uni ed stability analysis of meshless methods with eulerian and lagrangian kernels is presented three types of instabilities were identi ed in one dimension an instability due to rank de ciency a tensile instability and a material instability which is also found in continua the stability of particle methods with eulerian and lagrangian kernels is markedly di erent lagrangian kernels do not exhibit the tensile instability in both kernels the instability due to rank de ciency can be suppressed by stress points in two dimensions the stabilizing e ect of stress points is dependent on their locations it was found that the best approach to stable particle discretizations is to use lagrangian kernels with stress points the stability of the least squares stabilization was also studied copyright 2000 john wiley sons ltd

an hourglass control algorithm for lagrangian smooth particle hydrodynamics abstract this paper presents a stabilization scheme which addresses the rank deficiency problem in meshless collocation methods for solid mechanics specifically smooth particle hydrodynamics sph in the total lagrangian formalism is considered this method is rank deficient in the sense that the sph approximation of the deformation gradient is not unique with respect to the positions of the integration points the non uniqueness can result in the formation of zero energy modes if undetected these modes can grow and completely dominate the solution here an algorithm is introduced which effectively suppresses these modes in a fashion similar to hour glass control mechanisms in finite element methods simulations utilizing this control algorithm exhibit much improved stability accuracy and error convergence properties in contrast to an alternative method which eliminates zero energy modes namely the use of additional integration points the here presented algorithm is easy to implement and computationally very efficient

a one parameter family of interpolating kernels for smoothed particle hydrodynamics studies a set of interpolating functions of the type f v email protected p2v n is analyzed in the context of the smoothed particle hydrodynamics sph technique the behaviour of these kernels for several values of the parameter n has been studied either analytically as well as numerically in connection with several tests carried out in two dimensions the main advantage of this kernel relies in its flexibility because for n 3 it is similar to the standard widely used cubic spline whereas for n 3 the interpolating function becomes more centrally condensed being well suited to track discontinuities such as shock fronts and thermal waves

suppressing local particle oscillations in the hamiltonian particle method for elasticity the governing equation of elasticity is discretized into motion equations of the particles in a hamiltonian system a weighted least square method is adopted to evaluate the green lagrange strain using a symplectic scheme for the hamiltonian system we obtain the property of energy conservation in the discretized calculations however local particle oscillations occur and they excessively decrease low frequency motion in this study we propose the use of an artificial potential force to suppress the local oscillations the accuracy of the model with and without the inclusion of the artificial force is examined by analyzing a cantilever beam and wave propagation with the inclusion of the artificial force the local oscillations are reduced while energy conservation is maintained

an improved sph method towards higher order convergence this paper evaluates various formulations of the sph method for solving the euler equations convergence and stability aspects are discussed and tested taking into account subtleties induced by the presence of a free surface the coherence between continuity and momentum equations is considered using a variational study the use of renormalization to improve the accuracy of the simulations is investigated and discussed a new renormalization based formulation involving wide accuracy improvements of the scheme is introduced the classical sph and renormalized approaches are compared to the new method using simple test cases thus outlining the efficiency of this new improved sph method finally the so called tensile instability is shown to be prevented by this enhanced sph method through accuracy increases in the gradient approximations

fuzzy maximal radical and primary ideals of a ring we introduce the concepts of fuzzy maximal ideal the fuzzy radical of a fuzzy ideal and fuzzy primary ideal of a ring we show that a fuzzy left right ideal a of a ring r is a fuzzy maximal ideal if and only a 0 1 and a x r a x a 0 is a maximal left right ideal of r we also show that a fuzzy ideal a of a commutative ring r with unity is a fuzzy primary ideal of r if and only a 0 1 a is two valued and a is a primary ideal of r

hamiltonian particle hydrodynamics abstract particle based hydrodynamics models offer distinct advantages over eulerian and lagrangian hydrocodes in particular shock physics applications particle models are designed to avoid the mesh distortion and state variable diffusion problems which can hinder the effective use of lagrangian and eulerian codes respectively however existing particle in cell and smooth particle hydrodynamics methods employ particles which are actually moving interpolation points the latter distinction has been emphasized in the more recent development of element free galerkin theory as a result general formulations of all of the aforementioned methods are based on the partial differential equation forms of the continuum balance laws which underlie conventional eulerian and lagrangian schemes an alternative modeling methodology based on the application of hamilton s equations to a system of deforming physical particles provides a fully lagrangian energy based approach to shock physics simulations neither interpolations of field variables nor continuum balance laws are used to establish the state equations for the particle system mechanical and thermal interaction of the particles is accounted for by nonholonomic constraints which determine both particle entropy evolution and particle collision loads application of the method is illustrated by simulation of a wall shock problem

studies on the output of fuzzy controller with multiple inputs abstract in this paper we discuss the output of a fuzzy controller in which an arbitrary number of fuzzy control inputs and an arbitrary number of fuzzy sets employed to fuzzify every linguistic variable are considered in the fuzzy control rules a rule base with a rule mapping concept is considered a defuzzifier with the general t norm and t conorm operators is formulated a triangular family is adopted so that the defuzzifier of the complete rule mapping is represented by a formula consisting of only some rules using a specific logic pair to evaluate values we derive that the output of the fuzzy controller can be simply represented by a linear parametric function of the inputs to the fuzzy controller

general analytical structure of typical fuzzy controllers and their limiting structure theorems abstract the fuzzy controllers studied in this paper have r input variables error rate change of error of process output etc n members of input fuzzy sets are employed to fuzzify the inputs nr nonlinear control rules represented by an arbitrary function f are used which are evaluated by any type of fuzzy logic in conjunction with any inference method the center of gravity algorithm is utilized for defuzzification the author proves that the general analytical structure of the fuzzy controllers is the sum of a global f dependent nonlinear controller and a local nonlinear controller which locally adjusts control action of the global controller as n the global nonlinear controller approaches a global f dependent nonlinear controller while the local nonlinear controller disappears a necessary and sufficient condition is obtained for judging convergence of limiting structure of the fuzzy controllers if linear control rules are used the global controller is a global r dimensional multilevel relay which approaches a global linear controller as n two illustrative examples which deal with linear product maximum and minimum control rules are given

a weighted least squares particle in cell method for solid mechanics a novel meshfree method is proposed that incorporates features of the material point mpm and generalized interpolation material point gimp methods and can be used within an existing mpm gimp implementation weighted least squares kernel functions are centered at stationary grid nodes and used to approximate field values and gradients integration is performed over cells of the background grid and material boundaries are approximated with an implicit surface the proposed method avoids nearest neighbor searches while significantly improving accuracy over mpm and gimp implementation is discussed in detail and several example problems are solved including one manufactured solution which allows measurement of dynamic non linear large deformation performance advantages and disadvantages of the method are discussed copyright 2010 john wiley sons ltd

a method for deriving the analytical structure of a broad class of typical interval type 2 mamdani fuzzy controllers type 2 t2 fuzzy controllers are emerging as the related t2 fuzzy logic and algorithms have recently been advancing rapidly at present a t2 fuzzy controller is viewed and used as a black box function generator that produces a desired nonlinear mapping between the input and output of the controller we call the mapping analytical structure the mathematical expression of the analytical structure however is not explicitly known to the controller designer this is in sharp contrast with the analytical structure of a conventional controller which is not only always explicitly known but serves as a starting point for system analysis and design obviously the knowledge of a t2 fuzzy controller s analytical structure can have significant benefits they include 1 understanding more precisely how the controller works in the same sense as we understand how a conventional controller e g the pid controller functions 2 making t2 fuzzy control more acceptable to safety critical fields such as biomedicine 3 taking advantage of the well developed nonlinear control theory to develop better analysis and design methods for t2 control systems e g less conservative system stability criteria and 4 permitting rigorous comparative exploration on differences between the t2 and type 1 t1 fuzzy controllers and their relative merits and pitfalls e g performance and structural complexity in this paper we develop an innovative technique which is capable of deriving the analytical structure for a wide class of interval t2 mamdani fuzzy controllers the configuration of the controllers is typical and is substantially more general than the related efforts in the literature it uses any number and types of interval t2 input fuzzy sets any number and types of general or interval t2 output fuzzy sets arbitrary fuzzy rules zadeh and operator karnik mendel center of sets type reducer and the centroid defuzzifier we show in detail how the derivation method works in a general setting and provide the analytical structure of an example t2 controller as well in addition we utilize the method to prove that a subset of the t2 fuzzy controllers are the sum of two nonlinear pi or pd controllers each of which has a variable proportional gain and a variable integral gain or derivative gain plus a variable offset if and only if the input fuzzy sets are piecewise linear e g triangular and or trapezoidal the sum of the two nonlinear pi or pd controllers is a new discovery relative to the current literature

a stable sph discretization of the elliptic operator with heterogeneous coefficients smoothed particle hydrodynamics sph has been extensively used to model high and low reynolds number flows free surface flows and collapse of dams study pore scale flow and dispersion elasticity and thermal problems in different applications it is required to have a stable and accurate discretization of the elliptic operator with homogeneous and heterogeneous coefficients in this paper the stability and approximation analysis of different sph discretization schemes traditional and new of the diagonal elliptic operator for homogeneous and heterogeneous media are presented the optimum and new discretization scheme of specific shape satisfying thetwo point flux approximation nature is also proposed this scheme enhances the laplace approximation brookshaw s scheme 1985 and schwaiger s scheme 2008 used in the sph community for thermal viscous and pressure projection problems with an isotropic elliptic operator the numerical results are illustrated by numerical examples where the comparison between different versions of the meshless discretization methods are presented

conservative smoothing with b splines stabilizes sph material dynamics in both tension and compression smooth particle hydrodynamics sph is a grid free method for material dynamics which appears to have potential advantages over fixed grid methods with respect to grid tangling standard sph with stress s and interpolation weight w has instabilities of two types when sw 0 and tension s 0 in theory conservative smoothing can stabilize both types but carefully controlling smoothing to prevent excessive loss of fine detail had been found to be difficult in some numerical experiments here we present an easy natural way of using the sph b spline finite interpolation method to introduce sufficient conservative smoothing to stabilize sph material dynamics in both tension and compression we present numerical results for both tension and compression which provide evidence of the efficacy of this approach

regular paper the takagi sugeno fuzzy controllers using the simplified linear control rules are nonlinear variable gain controllers takagi sugeno ts for short fuzzy controllers have been used and treated as black box controllers and there exists no explicit structure of any ts fuzzy controller in the literature in this paper we investigate the analytical structure of the ts fuzzy controllers that use our newly introduced simplified ts control rule scheme our scheme requires that all the rule consequent employ a common linear function and be proportional to one another the scheme drastically reduces the number of adjustable parameters required by the original ts rule scheme product fuzzy logic and was employed in the rule antecedents we theoretically proved that the ts controllers using the simplified rule scheme were nonlinear variable gain controllers the proportionality of the rule consequent parameterized the gain variation characteristics as special cases the ts controllers with three or two input variables and the simplified linear rule consequent were nonlinear variable gain pid pi or pd controllers as an illustration we mathematically analyzed the nonlinear variable gain pi controllers and revealed that the gain variation empowered the controllers to outperform their linear counterparts stability of the nonlinear pi control systems was also addressed a practical example is given to show how to achieve the desired characteristics of the gain variation by properly designing the simplified rules

an accurate multi regime sph scheme for barotropic flows abstract this paper focuses on the use of a mesh less numerical method to solve barotropic fluid flows smooth particle hydrodynamics sph such methods suffer from a severe lack of accuracy when evaluating state variables as the pressure field sph ale methods based on riemann solvers significantly improve this evaluation but increase the scheme complexity and low mach issues are difficult to prevent we propose an alternative scheme called s p h a l e relying on the combination of the sph ale formalism and a finite volume stabilizing low mach scheme applied to monophasic barotropic euler equations its characteristics are detailed and evaluated through a nonlinear stability analysis highlighting cfl like conditions on the scheme parameters as far as we know it is the first time such nonlinear analysis is performed on a sph ale scheme finally its implementation on several academic test cases reveals that the proposed scheme actually increases both stability and accuracy in reduced computation time with respect to sph ale riemann solvers

analytical structure and characteristics of symmetric karnik mendel type reduced interval type 2 fuzzy pi and pd controllers this paper presents the analytical structure of a class of interval type 2 it2 fuzzy proportional derivative pd and proportional integral pi controllers that have symmetrical rule base and symmetrical consequent sets two assumptions are made 1 the zadeh and operator is employed as the t norm operator 2 type reduction is performed by the karnik mendel km type reduction method the main contributions are the methodology that identifies the input conditions where the km algorithm uses a new switch point to compute the bounds of the type reduced set the closed form expressions that relate the inputs and output of an it2 fuzzy controller and insights into the potential performance improvement because of the inclusion of the footprint of uncertainty fou compared with its t1 counterpart two additional fou parameters generate 31 extra local regions each providing a unique relationship between the inputs and output signals the generation of a relatively large number of local regions at the cost of two extra design parameters indicates that an it2 fuzzy controller may be able to provide better performance furthermore by comparing the analytical structure with the corresponding t1 counterpart the potential advantages to use the it2 over the t1 fuzzy controller are studied four interesting characteristics are identified and they provide insights into why the it2 fuzzy controller may better balance the conflicting aims of fast rise time and small overshoot

fuzzy control theory a nonlinear case abstract sources of nonlinearity in a fuzzy controller include the fuzzification algorithm used for the controller inputs fuzzy control rules type of fuzzy logic used for evaluating the fuzzy control rules and the defuzzification algorithm used for the controller output we analyze the performance of a simple fuzzy controller with linear and nonlinear defuzzification algorithms we prove theoretically that such a fuzzy controller the smallest possible with two inputs error and rate change of error and a nonlinear defuzzification algorithm is equivalent to a nonfuzzy nonlinear proportional integral pi controller with proportional gain and integral gain changing with error and rate change of error about a setpoint furthermore this fuzzy controller is precisely equivalent to a conventional linear pi controller if a linear defuzzification algorithm is employed computer simulation showed that the performance of the fuzzy controller was almost the same as that of the pi controller when first order and second order linear processes were used furthermore the fuzzy controller was significantly better when a first order with a time delay model was used more importantly the simulated result illustrated that the fuzzy controller was stable when a nonlinear process model was controlled but the pi controller was unstable

sph with dynamical smoothing length adjustment based on the local flow kinematics abstract due to the lagrangian nature of smoothed particle hydrodynamics sph the adaptive resolution remains a challenging task in this work we first analyse the influence of the simulation parameters and the smoothing length on solution accuracy in particular in high strain regions based on this analysis we develop a novel approach to dynamically adjust the kernel range for each sph particle separately accounting for the local flow kinematics we use the okubo weiss parameter that distinguishes the strain and vorticity dominated regions in the flow domain the proposed development is relatively simple and implies only a moderate computational overhead we validate the modified sph algorithm for a selection of two dimensional test cases the taylor green flow the vortex spin down the lid driven cavity and the dam break flow against a sharp edged obstacle the simulation results show good agreement with the reference data and improvement of the long term accuracy for unsteady flows for the lid driven cavity case the proposed dynamical adjustment remedies the problem of tensile instability particle clustering

fuzzy prime ideals of a ring abstract this paper characterizes all fuzzy prime ideals p of an arbitrary ring r we show that a nonconstant fuzzy ideal p of r is prime if and only if p0 x r p x p 0 is a prime ideal of r p is two valued and p 0 1 examples are given showing that p0 is a prime ideal is not sufficient for p to be a fuzzy prime ideal and that p0 may be a prime ideal of r with the image of p being of arbitrary finite cardinality or being countably infinite

isomorphism theorems and fuzzy k ideals of k semirings we define and study the fuzzy maximal k ideal of a k semiring also we characterize the quotient k semiring r a of a k semiring r by a fuzzy maximal k ideal a and we have some isomorphism theorems in commutative k semirings and further we have some properties of the quotient k semiring r a of all cosets of a fuzzy semiprimary semiprime primary prime k ideal a in a commutative k semiring r

fuzzy invariant subgroups and fuzzy ideals abstract the purpose of this paper is to introduce some basic concepts of fuzzy algebra as fuzzy invariant subgroups fuzzy ideals and to prove some fundamental properties in particular it will give a characteristic of a field by a fuzzy ideal

an adaptive sph method for strong shocks we propose an alternative sph scheme to usual sph godunov type methods for simulating supersonic compressible flows with sharp discontinuities the method relies on an adaptive density kernel estimation adke algorithm which allows the width of the kernel interpolant to vary locally in space and time so that the minimum necessary smoothing is applied in regions of low density we have performed a von neumann stability analysis of the sph equations for an ideal gas and derived the corresponding dispersion relation in terms of the local width of the kernel solution of the dispersion relation in the short wavelength limit shows that stability is achieved for a wide range of the adke parameters application of the method to high mach number shocks confirms the predictions of the linear analysis examples of the resolving power of the method are given for a set of difficult problems involving the collision of two strong shocks the strong shock tube test and the interaction of two blast waves

a constant density approach for incompressible multi phase sph a constant density approach which corrects intermediate density errors by adjusting the half time step velocity with exact projection is proposed for the multi phase sph method developed in our previous work x y hu n a adams an incompressible multi phase sph method j comput phys 227 2007 264 278 as no prescribed reference pressure is required the present approach introduces smaller numerical viscosity and allows to simulate flows with unprecedentedly high density ratios by the projection sph method numerical examples for taylor green flow capillary waves and for rayleigh taylor instability are presented and compared to theoretical solutions or references from the literature

theoretical analysis of crisp type fuzzy logic controllers using various t norm sum gravity inference methods the input output parametric relationship of a class of crisp type fuzzy logic controllers flcs using various t norm sum gravity inference methods is studied four most important t norms are used to calculate the matching level of each control rule and the explicit mathematical forms of reasoning surfaces obtained by using these four t norms are addressed reasoning surfaces of these crisp type flcs are proved to be composed of a two dimensional multilevel relay no matter which t norm is used and a local position dependent nonlinear compensator with output pattern influenced by the t norms is selected by analyzing the intrinsic operation of the four t norms the authors find that both standard intersection and algebraic product are suitable operators to perform the inference of the flc however bounded difference and drastic intersection are disqualified because they cannot satisfy some important criteria a measure of relative degree of nonlinearity is defined to examine the output figures of these crisp type flcs the ultimate behavior of these crisp type flcs as the number of linguistic terms approaches infinity is also explored the local stability criteria for the proportional integral pi type fuzzy control systems and the natural global stability characteristic for the proportional derivative pd type fuzzy control systems are also examined

towards a paradigm for fuzzy logic control the purpose of this paper is to lay a foundation for fuzzy logic control flc design constructing a class of fuzzy logic controllers that is suitable for a broad range of controls applications some scalar definitions in flc are extended to the n dimensional case including vector fuzzy number and membership vector a rigorous mathematical expression is given for the function g x called the reasoning surface manufactured by a fuzzy associative memory fam for the existence and uniqueness of solutions in any closed loop system with a fuzzy logic controller it is shown that the fam function g x must be lipschitz this places restrictions on the allowed rules in the flc it is argued that for effective control design the membership functions should not be uniformly spaced the triangular membership functions generally suffice and product inferencing should be used under these conditions the flc manufactures a piecewise multilinear lipschitz fam function g x that is a generalized proportional plus derivative plus offset controller the scalar and two dimensional cases are studied in detail

an energy based criterion of crack branching and its application on the multidimensional space method abstract in this paper a criterion of crack branching based on the energy release rate is proposed theory of multidimensional space method for crack branching is established in the framework of the extended finite element method xfem in which the formula of the boundary shift energy is deduced the boundary cracking energy is obtained because the boundary shift model is abstracted into the boundary cracking model the energy release rates of the crack branching in four quadrants are determined based on boundary cracking energy further the energy release rate of the crack branching is introduced into multidimensional space method to determine the crack branching if the crack tip branching the criteria of crack branching are applied to determine the direction of the branching cracks otherwise the criteria of maximum circumferential stress are applied to determine the direction of the cracks moreover a classical numerical example is investigated to verify the correctness of the criterion of crack branching in the framework of the multidimensional space method

a stabilized fractional step runge kutta taylor sph algorithm for coupled problems in geomechanics abstract failure of geomaterials with pores filled with fluids is an important research area in both civil and geological engineering many finite element formulations for coupled problems present difficulties such as overestimating failure loads or mesh alignment dependence resulting on spurious failure mechanisms moreover the spaces where field variables are approximated have to fulfill additional requirements ensuring stability stress velocity pore pressure formulations in fe analysis provide accurate results for wave propagation and failure analysis however finite elements present important limitations when deformations are large the purpose of this paper is to present a stabilized fractional step sph algorithm which combines the advantages of the sph method for large deformation problems with those of the taylor galerkin algorithm used within the finite element framework

analysis of the incompressibility constraint in the smoothed particle hydrodynamics method summary smoothed particle hydrodynamics sph is a particle based fully lagrangian method for fluid flow simulations in this work fundamental concepts of the method are first briefly recalled then we present a thorough comparison of two different incompressibility treatments in sph the weakly compressible approach where a suitably chosen equation of state is used and the truly incompressible method in two basic variants where the velocity field projection onto a divergence free space is performed a noteworthy aspect of the study is that in each incompressibility treatment the same boundary conditions are used and further developed that allows a direct comparison to be made two dimensional and three dimensional validation cases are studied problems associated with the numerical setup are discussed and an optimal choice of the computational parameters is proposed and verified the efficiency issues of the incompressibility treatments are considered and the speed up features are highlighted the results show that the present state of the art truly incompressible methods based on a velocity correction suffer from density accumulation errors to address this issue an algorithm based on a correction for both particle velocities and positions is presented the usefulness of this density correction is examined and demonstrated copyright 2012 john wiley sons ltd

a quasi static dual particle method for solids based on dual particle dynamics summary a dual particle method for problems in solid mechanics on the basis of dual particle dynamics is extended to applications of quasi static deformations of solids the general approach incorporates the discrete strong form of the governing equation a lagrangian representation of a moving least squares approximation of field variables and a spatial discretization comprised of two particle sets motion points and stress points the quasi static dual particle method introduced in this work incorporates geometric and material nonlinearities as well as a modified method for applying traction boundary conditions some computational exercises are performed to verify the correct implementation of the method show convergence behavior and demonstrate the improved performance of the modified traction boundary condition application method copyright 2012 john wiley sons ltd

stabilization algorithm for the optimal transportation meshfree approximation scheme abstract meshfree approximation schemes possess a high potential in computer aided engineering due to their large flexibility especially the tremendous progress in processor technology within recent years relativizes the increase in computation time due to the inherent search algorithm nevertheless meshfree approximation schemes are still faced with some challenges like imposition of dirichlet boundary conditions robustness of the algorithm and accuracy the recent developed optimal transportation meshfree otm method seemed to overcome most of these problems in this paper the otm solution scheme is combined with a standard search algorithm in order to allow a simple and flexible computation however this scheme is not stable for some examples of application hence an investigation is conducted which shows that the reason for this instability is due to underintegration based on this investigation a remedy to stabilize the algorithm is suggested which is based on well known concepts to control the hourglass effects in the finite element method in contrast to the original publication the otm algorithm is derived here from the principle of virtual work local maximum entropy shape functions are used which possess a weak kronecker property this enables a direct imposition of dirichlet boundary conditions if the boundary is convex the limitations of this basis function are also addressed in this paper additionally the search algorithm presented fulfills basic topological requirements several examples are investigated demonstrating the improved behavior of the stabilized otm algorithm

a variationally consistent streamline upwind petrov galerkin smooth particle hydrodynamics algorithm for large strain solid dynamics this paper presents a new smooth particle hydrodynamics sph computational framework for explicit fast solid dynamics the proposed methodology explores the use of the streamline upwind petrov galerkin supg stabilisation methodology as an alternative to the jameson schmidt turkel jst stabilisation recently presented by the authors in lee et al 2016 in the context of a conservation law formulation of fast solid dynamics the work introduced in this paper puts forward three advantageous features over the recent jst sph framework first the variationally consistent nature of the supg stabilisation allows for the introduction of a locally preserving angular momentum procedure which can be solved in a monolithic manner in conjunction with the rest of the system equations this differs from the jst sph framework where an a posteriori projection procedure was required to ensure global angular momentum preservation second evaluation of expensive harmonic and bi harmonic operators necessary for the jst stabilisation is circumvented in the new supg sph framework third the supg sph framework is more accurate for the same number of degrees of freedom than its jst sph counterpart and its accuracy is comparable to that of the robust but computationally more demanding petrov galerkin finite element method pg fem technique explored by the authors in lee et al 2014 gil et al 2014 2016 bonet et al 2015 as shown in the numerical examples included a series of numerical examples are analysed in order to benchmark and assess the robustness and effectiveness of the proposed algorithm the resulting supg sph framework is therefore accurate robust and computationally efficient three key desired features that will allow the authors in forthcoming publications to explore its applicability in large scale simulations

a new jameson schmidt turkel smooth particle hydrodynamics algorithm for large strain explicit fast dynamics this paper presents a new smooth particle hydrodynamics sph computational framework for large strain explicit solid dynamics a mixed based set of total lagrangian conservation laws bonet et al 2015 gil et al 2016 is presented in terms of the linear momentum and an extended set of geometric strain measures comprised of the deformation gradient its co factor and the jacobian taking advantage of this representation the main aim of this paper is the adaptation of the very efficient jameson schmidt turkel jst algorithm jameson et al 1981 extensively used in computational fluid dynamics to a sph based discretisation of the mixed based set of conservation laws with three key distinct novelties first a conservative jst based sph computational framework is presented with emphasis in nearly incompressible materials second the suppression of numerical instabilities associated with the non physical zero energy modes is addressed through a well established stabilisation procedure third the use of a discrete angular momentum projection algorithm is presented in conjunction with a monolithic total variation diminishing runge kutta time integrator in order to guarantee the global conservation of angular momentum for completeness exact enforcement of essential boundary conditions is incorporated through the use of a lagrange multiplier projection technique a series of challenging numerical examples e g in the near incompressibility regime are examined in order to assess the robustness and accuracy of the proposed algorithm the obtained results are benchmarked against a wide spectrum of alternative numerical strategies

explicit formulas for fuzzy controller abstract in this paper we present some explicit formulas of fuzzy control in the simple case of one condition these formulas are then used on the one hand to study the effects of some design factors inference operators number of partitions etc and on the other hand to carry out simulations

a stable sph with adaptive b spline kernel abstract tensile instability often observed in smoothed particle hydrodynamics sph is a numerical artifact that manifests itself by unphysical clustering or separation of particles the instability originates in estimating the derivatives of the smoothing functions which when interact with material constitution may result in negative stiffness in the discretized system in the present study a stable formulation of sph is developed where the kernel function is continuously adapted at every material point b spline basis function with a variable intermediate knot is used as the kernel function the shape of the kernel function is then modified by changing the intermediate knot position such that the condition associated with instability does not arise while implementing the algorithm the simplicity and computational efficiency of sph are not compromised one dimensional dispersion analysis is performed to understand the effect of adaptive kernel on the stability finally the efficacy of the algorithm is demonstrated through some benchmark elastic dynamics problems

stable particle methods based on lagrangian kernels abstract a large deformation particle method based on the krongauz belytschko corrected gradient meshfree method with lagrangian kernels is developed in this form the gradient is corrected by a linear transformation so that linear completeness is satisfied for the test functions shepard functions are used this guarantees that the patch test is met lagrangian kernels are introduced to eliminate spurious distortions of the domain of material stability a mass allocation scheme is developed that captures correct reflection of waves without any explicit application of traction boundary conditions in addition the lagrangian kernel versions of various forms of smooth particle methods sph including the standard forms and the randles libersky modification are presented and studied results are obtained for a variety of problems that compare this method to standard forms of sph the randles libersky correction and large deformation versions of the element free galerkin method

a general technique for deriving analytical structure of fuzzy controllers using arbitrary trapezoidal input fuzzy sets and zadeh and operator deriving the analytical structure of fuzzy controllers is very important as it creates a solid foundation for better understanding insightful analysis and more effective design of fuzzy control systems we previously developed a technique for deriving the analytical structure of the fuzzy controllers that use zadeh fuzzy and operator and the symmetric identical trapezoidal or triangular input fuzzy sets many fuzzy controllers use arbitrary trapezoidal triangular input fuzzy sets that are asymmetric at present there exists no technique capable of deriving the analytical structure of these fuzzy controllers extending our original technique we now present a novel method that can accomplish rigorously the structure derivation for any fuzzy controller mamdani type or ts type that employs the arbitrary trapezoidal input fuzzy sets and zadeh fuzzy and operator the new technique contains our original technique as a special case given the importance of pid control we focus on mamdani fuzzy pi and pd controllers in this paper and show in detail how to use the new technique for different configurations of the fuzzy pi pd controllers the controllers use two arbitrary trapezoidal fuzzy sets for each input variable four arbitrary singleton output fuzzy sets four fuzzy rules zadeh fuzzy and operator and the centroid defuzzifier this configuration is more general and complicated than the mamdani fuzzy pi pd controllers in the current literature it actually contains them as special cases we call this configuration the generalized fuzzy pi pd controller

modeling low reynolds number incompressible flows using sph the method of smoothed particle hydrodynamics sph is extended to model incompressible flows of low reynolds number for such flows modification of the standard sph formalism is required to minimize errors associated with the use of a quasi incompressible equation of state treatment of viscosity state equation kernel interpolation and boundary conditions are described simulations using the method show close agreement with series solutions for couette and poiseuille flows furthermore comparison with finite element solutions for flow past a regular lattice of cylinders shows close agreement for the velocity and pressure fields the sph results exhibit small pressure fluctuations near curved boundaries further improvements to the boundary conditions may be possible which will reduce these errors a similar method to that used here may permit the simulation of other flows at low reynolds numbers using sph further development will be needed for cases involving free surfaces or substantially different equations of state

a total lagrangian upwind smooth particle hydrodynamics algorithm for large strain explicit solid dynamics in previous work 1 2 lee et al introduced a new smooth particle hydrodynamics sph computational framework for large strain explicit solid dynamics with special emphasis on the treatment of near incompressibility a first order system of hyperbolic equations was presented expressed in terms of the linear momentum and the minors of the deformation namely the deformation gradient its co factor and its jacobian taking advantage of this representation the suppression of numerical deficiencies e g spurious pressure long term instability and or consistency issues was addressed through well established stabilisation procedures in reference 1 the adaptation of the very efficient jameson schmidt turkel algorithm was presented reference 2 introduced an adapted variationally consistent streamline upwind petrov galerkin methodology in this paper we now introduce a third alternative stabilisation strategy extremely competitive and which does not require the selection of any user defined artificial stabilisation parameter specifically a characteristic based riemann solver in conjunction with a linear reconstruction procedure is used with the aim to guarantee both consistency and conservation of the overall algorithm we show that the proposed sph formulation is very similar in nature to that of the upwind vertex centred finite volume method presented in 3 in order to extend the application range towards the incompressibility limit an artificial compressibility algorithm is also developed finally an extensive set of challenging numerical examples is analysed the new sph algorithm shows excellent behaviour in compressible nearly incompressible and truly incompressible scenarios yielding second order of convergence for velocities deviatoric and volumetric components of the stress