distinct variants of the kdv equation with compact and noncompact structures in this paper we examine three distinct variants of the generalized kdv equation both the compact and the noncompact structures are treated for these variants we also emphasize the different physical structures of the two classes the focusing branch and the defocusing branch

design sensitivity analysis for rate independent elastoplasticity abstract a new incremental direct differentiation method for design sensitivity analysis of structures with rate independent elastoplastic behavior is presented we formulate analytical sensitivity expressions that are consistent with numerical algorithms for elastoplasticity that use implicit methods to integrate the constitutive equations and return mappings to enforce the consistency conditions the sensitivity expressions can be evaluated with only a modest increase in computational expense beyond the cost of simulation combined with the inherent advantages of implicit integration strategies this represents a significant improvement over previous sensitivity formulations for history dependent materials first order sensitivity expressions involving the complete set of design variables including shape design variables are derived for a generic response functional the reduced form of the consistent tangent stiffness matrix obtained at the end of each time or load step in the finite element procedure is used to update the response sensitivities for that time step no iterations are needed in the sensitivity computations a numerical example demonstrates the accuracy and efficiency of the new sensitivity analysis method for an elastoplastic analysis problem explicit sensitivities from the new method are confirmed by finite difference estimates

nonseparable spaceability and strong algebrability of sets of continuous singular functions abstract let cbv denote the banach algebra of all continuous real valued functions of bounded variation defined in 0 1 we show that the set of strongly singular functions in cbv is nonseparably spaceable we also prove that certain families of singular functions constitute strongly c algebrable sets the argument is based on a criterion of strong c algebrability using compositions with exponential like functions

c stationarity for optimal control of static plasticity with linear kinematic hardening an optimal control problem is considered for the variational inequality representing the stress based dual formulation of static elastoplasticity the linear kinematic hardening model and the von mises yield condition are used existence and uniqueness of the plastic multiplier is rigorously proved which allows for the reformulation of the forward system using a complementarity condition in order to derive necessary optimality conditions a family of regularized optimal control problems is analyzed wherein the static plasticity problems are replaced by their viscoplastic approximations by passing to the limit in the optimality conditions for the regularized problems necessary optimality conditions of c stationarity type are obtained

strong c algebrability of strong sierpinski zygmund smooth nowhere analytic and other sets of functions abstract we present a useful technique of proving strong c algebrability as an outcome we obtain the strong c algebrability of the following sets of functions strong sierpinski zygmund nowhere holder bruckner garg nowhere monotone differentiable a certain baire class smooth and nowhere analytic functions

structural aspects of the non uniformly continuous functions and the unbounded functions within c x abstract we prove in this paper that if a metric space supports a real continuous function which is not uniformly continuous then under appropriate mild assumptions there exists in fact a plethora of such functions in both topological and algebraical senses corresponding results are also obtained concerning unbounded continuous functions on a non compact metrizable space

lineability criteria with applications lineability is a property enjoyed by some subsets within a vector space x a subset a of x is called lineable whenever a contains except for zero an infinite dimensional vector subspace if additionally x is endowed with richer structures then the more stringent notions of dense lineability maximal dense lineability and spaceability arise naturally in this paper several lineability criteria are provided and applied to specific topological vector spaces mainly function spaces sometimes such criteria furnish unified proofs of a number of scattered results in the related literature families of strict order integrable functions hypercyclic vectors non extendable holomorphic mappings riemann non lebesgue integrable functions sequences not satisfying the lebesgue dominated convergence theorem nowhere analytic functions bounded variation functions entire functions with fast growth and peano curves among others are analyzed from the point of view of lineability

a level set method for structural topology optimization this paper presents a new approach to structural topology optimization we represent the structural boundary by a level set model that is embedded in a scalar function of a higher dimension such level set models are flexible in handling complex topological changes and are concise in describing the boundary shape of the structure furthermore a well founded mathematical procedure leads to a numerical algorithm that describes a structural optimization as a sequence of motions of the implicit boundaries converging to an optimum solution and satisfying specified constraints the result is a 3d topology optimization technique that demonstrates outstanding flexibility of handling topological changes fidelity of boundary representation and degree of automation we have implemented the algorithm with the use of several robust and efficient numerical techniques of level set methods the benefit and the advantages of the proposed method are illustrated with several 2d examples that are widely used in the recent literature of topology optimization especially in the homogenization based methods

topology and shape optimization for elastoplastic structural response abstract it is a common practice to base both material topology optimization as well as a subsequent shape optimization on linear elastic response however in order to obtain a realistic design it might be essential to base the optimization on a more realistic physical behavior i e to consider geometrically or and materially nonlinear effects in the present paper an elastoplastic von mises material model with linear isotropic hardening softening for small strains is used the objective of the design problem is to maximize the structural ductility in the elastoplastic range while the mass in the design space is prescribed with respect to the specific features of either topology or shape optimization for example the number of optimization variables or their local global influence on the structural response different methods are applied for topology optimization problems the gradient of the ductility is determined by the variational adjoint approach in shape optimization the derivatives of the state variables with respect to the optimization variables are evaluated analytically by a variational direct approach the topology optimization problem is solved by an optimality criteria oc method and the shape optimization problem by a mathematical programming mp method in topology optimization a geometrically adaptive procedure is additionally applied in order to increase the efficiency and to avoid artificial stress singularities the procedures are verified by 2d design problems under plane stress conditions

elasto plastic shape optimization using the level set method this article focused on shape optimization of static perfect plasticity problems in the framework of the von mises criterion thanks to the level set method we circumvent the ill posedness of the model by using two regularized versions of the mechanical problem the rst one is the classical perzyna formulation which we regularize the second one is a new regularized formulation derived for the von mises criterion shape gradients are calculated thanks to the adjoint method to illustrate the validity of the method 2d examples are performed

linear subsets of nonlinear sets in topological vector spaces for the last decade there has been a generalized trend in mathematics on the search for large algebraic structures linear spaces closed subspaces or infinitely generated algebras composed of mathematical objects enjoying certain special properties this trend has caught the eye of many researchers and has also had a remarkable influence in real and complex analysis operator theory summability theory polynomials in banach spaces hypercyclicity and chaos and general functional analysis this expository paper is devoted to providing an account on the advances and on the state of the art of this trend nowadays known as lineability and spaceability

optimal control of quasi static plasticity with linear kinematic hardening part i existence and discretization in time in this paper we consider an optimal control problem governed by a time dependent variational inequality arising in quasi static plasticity with linear kinematic hardening we address certain continuity properties of the forward operator which imply the existence of an optimal control moreover a discretization in time is derived and we show that every local minimizer of the continuous problem can be approximated by minimizers of modified time discrete problems a correction is attached

polygonal finite elements for topology optimization a unifying paradigm in topology optimization literature the parameterization of design is commonly carried out on uniform grids consisting of lagrangian type finite elements e g linear quads these formulations however suffer from numerical anomalies such as checkerboard patterns and one node connections which has prompted extensive research on these topics a problem less often noted is that the constrained geometry of these discretizations can cause bias in the orientation of members leading to mesh dependent sub optimal designs thus to address the geometric features of the spatial discretization we examine the use of unstructured meshes in reducing the influence of mesh geometry on topology optimization solutions more specifically we consider polygonal meshes constructed from voronoi tessellations which in addition to possessing higher degree of geometric isotropy allow for greater flexibility in discretizing complex domains without suffering from numerical instabilities copyright 2009 john wiley sons ltd

application of exp function method to dullin gottwald holm equation in this paper we adopt the exp function method and the traveling wave transformation to study the so called dgh equation as a result a number of exact solutions of this equation have been found the family of solution including some exact solutions such as solitary wave pattern periodic traveling wave solution kink wave solution and new bounded wave solutions and explained some of the solutions physical meaning

quasistatic evolution problems for linearly elastic perfectly plastic materials the problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rate independent processes existence of solutions is proved through the use of incremental variational problems in spaces of functions with bounded deformation this approach provides a new approximation result for the solutions of the quasistatic evolution problem which are shown to be absolutely continuous in time four equivalent formulations of the problem in rate form are derived a strong formulation of the flow rule is obtained by introducing a precise definition of the stress on the singular set of the plastic strain

new periodic solitary wave solutions for the benjiamin ono equation in this paper the new periodic solitary wave and doubly periodic solutions for 1 1 dimensional benjiamin ono equation are obtained using the bilinear method and extended homoclinic test approach these results demonstrate that the integrable system has richly dynamical behavior even if it is 1 1 dimensional

peano curves on topological vector spaces the starting point of this paper is the existence of peano curves that is continuous surjections mapping the unit interval onto the unit square from this fact one can easily construct of a continuous surjection from the real line r to any euclidean space rn the algebraic structure of the set of these functions as well as extensions to spaces with higher dimensions is analyzed from the modern point of view of lineability and large algebras are found within the families studied we also investigate topological vector spaces that are continuous image of the real line providing an optimal lineability result

structural optimization using sensitivity analysis and a level set method in the context of structural optimization we propose a new numerical method based on a combination of the classical shape derivative and of the level set method for front propagation we implement this method in two and three space dimensions for a model of linear or nonlinear elasticity we consider various objective functions with weight and perimeter constraints the shape derivative is computed by an adjoint method the cost of our numerical algorithm is moderate since the shape is captured on a fixed eulerian mesh although this method is not specifically designed for topology optimization it can easily handle topology changes however the resulting optimal shape is strongly dependent on the initial guess

peakons kinks compactons and solitary patterns solutions for a family of camassa holm equations by using new hyperbolic schemes in this paper a family of camassa holm equations with distinct parameters is investigated new solitary wave solutions that include peakons kinks compactons solitary patterns solutions and plane periodic solutions are formally derived new schemes that rest mainly on hyperbolic functions are employed to achieve our goal the work highlights the qualitative change in the physical structures of the obtained solutions

tangent operators and design sensitivity formulations for transient non linear coupled problems with applications to elastoplasticity tangent operators and design sensitivities are derived for transient non linear coupled problems the solution process and the formation of tangent operators are presented in a systematic manner and sensitivities for a generalized response functional are formulated via both the direct differentiation and adjoint methods the derived formulations are suitable for finite element implementations analyses of systems with materials that exhibit history dependent response may be obtained directly by applying the analyses of transient non linear coupled systems rate independent elastoplasticity is investigated as a case study and a problem with an analytical solution is analysed for demonstration purposes

integrability of displacement and stresses in linear and nonlinear elasticity with mixed boundary conditions abstract equations of linear and nonlinear infinitesimal elasticity with mixed boundary conditions are considered the bounded domain is assumed to have a lipschitz boundary and to satisfy additional regularity assumptions w 1 p regularity for the displacements and l p regularity for the stresses are proved for some p 2

b and strong stationarity for optimal control of static plasticity with hardening optimal control problems for the variational inequality of static elastoplasticity with linear kinematic hardening are considered the control to state map is shown to be weakly directionally differentiable and local optimal controls are proved to verify an optimality system of b stationary type for a modified problem local minimizers are shown to even satisfy an optimality system of strongly stationary type

shape optimization of elasto plastic structures and continua this article is concerned with the sensitivity analysis and optimization of elasto plastic bodies when isotropic strain hardening takes place the elasto plastic behaviour of the material is governed by a nonlinear complementarity problem after discretization the evolutionary state problem associated with the optimal shape problem is formulated as a sequence of nonsmooth equations and a general form of the optimal design problem is treated by using a nonsmooth approach the sensitivity analysis based on the adjoint variable technique is derived for a history dependent problem as applications optimal design problems are solved for an elasto plastic truss structure and for an elasto plastic continuum

symmetry reductions and new exact non traveling wave solutions of potential kadomtsev petviashvili equation with p power with the aid of maple symbolic computation and lie group method pkpp equation is reduced to some 1 1 dimensional partial differential equations in which there are linear pde with constant coefficients nonlinear pde with constant coefficients and nonlinear pde with variable coefficients using the separation of variables homoclinic test technique and auxiliary equation methods we obtain new abundant exact non traveling solutions with arbitrary functions for the pkpp

optimal control of static elastoplasticity in primal formulation an optimal control problem of static plasticity with linear kinematic hardening and von mises yield condition is studied the problem is treated in its primal formulation where the state system is a variational inequality of the second kind first order necessary optimality conditions are obtained by means of an approximation by a family of control problems with state system regularized by huber type smoothing and a subsequent limit analysis the equivalence of the optimality conditions with the c stationarity system for the equivalent dual formulation of the problem is proved numerical experiments are presented which demonstrate the viability of the huber type smoothing approach

homoclinic breather wave solutions and doubly periodic wave solutions for coupled kdv equations abstract in this paper we first find out a proper variable transformation by the ideas of painleve expansion then we apply the extended homoclinic test approach to obtain two cycle breathing places wave solutions of eq 1 which describe interactions between two physical waves and these special solutions can be applied to explain the structure of certain physical phenomena thus this method can be applied to the study of other similar nonlinear coupled system

shape design sensitivity analysis and optimization of elasto plasticity with frictional contact a shape design sensitivity analysis and optimization are proposed for the ine nitesimal elasto plasticity with a frictional contact condition rate independent plasticity is considered with a return mapping algorithm and a von mises yield criterion the contact condition is formulated using the penalty method and the modie ed coulomb friction law a continuum based shape design sensitivity formulation is developed for structural and frictional contact variational equations the direct differentiation method is used to compute the displacement sensitivity and the sensitivities of various performance measures are computed from the displacement sensitivity path dependency of the sensitivity equation due to the constitutive relation and friction is discussed it is shown that no iteration is required to solve the sensitivity equation response analysis and the proposed sensitivity formulation are implemented using the mesh free method where the mesh distortion problem can be resolved numerical examples show accurate results of the proposed method compared to the e nite difference method dife culties in the sensitivity formulation for the e nite deformation problem are discussed i introduction b ecauseoftherecentdevelopmentofcomputationalmechanics it is now possible to analyze practical examples of complicated structural problems many design engineers who are not satise ed with response analysis alone have keen interests in the methodology of the design for more than two decades signie cant research efforthasbeen focused on the rate of response with respect to the changes in structural shape under shape design sensitivity analysis dsa analysis of the design sensitivity information is the most important and costly procedure in the automated optimum design process it supplies useful quantitative information to the design engineer about the direction of the desired design change in a classical linear problem dsa research has proved the differentiability of the solution of the response analysis using the linear operator theory and has derived specie c sensitivity expressions for variousproblems 1 aresultworthy of attention in linear dsais that theoriginalresponseandthesensitivityoftheresponsebelongtothe samekinematicallyadmissiblespaceandhavethesameregularities owing to the development of the response analysis capability engineers have directed their interest to the nonlinear problems that are dealt with efe ciently because many design application problems are accompanied by plastic deformation the design sensitivity of nonlinear problems has been actively developed and many research results are reported in the procedure of nonlinear response analysis the projection called a return mapping of the elastic trial stress is carried out to satisfy the variational inequality vi through an iteration in the stress space 2 the dsa on the other hand computes the rate of change of the projected response in the tangential direction of the constraint set without iteration note that the sensitivity analysis is linear and can be computed without iteration even thoughtheresponseanalysisisnonlinear 3 unlikethenonlinearelastic problem the sensitivity equation of the plastic problem requires sensitivity of the stress and internal evolution variables at the previous time the sensitivity equation is solved at each time without iteration and the sensitivity of the stress and evolution variables are

shape design sensitivity analysis of viscoplastic structures abstract design sensitivity analysis of nonlinear viscoplastic structures is developed in the continuum form starting from hamilton s principle constitutive models based on internal variable theory are incorporated in response analysis such models are described by a set of first order nonlinear differential equations with respect to time and some of them allow development of the yield surface the direct variation method is employed to obtain the sensitivity of the response discretization of the analysis and sensitivity equations and computer implementation aspects are discussed the discretized equations are implemented into a computer program and two numerical examples are solved to demonstrate the theory in the numerical examples only material nonlinearity under quasi static loading history is considered and the explicit integration method is employed to integrate the constitutive equations and their design variations the accuracy and efficiency of the developed sensitivity analysis are compared with the central finite difference method cyclic loading and loading rate effects are studied and discussed to show the general applicability of the developed sensitivity formulation