a mixed variational formulation based on exact intrinsic equations for dynamics of moving beams abstract a nonlinear intrinsic formulation for the dynamics of initially curved and twisted beams in a moving frame is presented the equations are written in a compact matrix form without any approximations to the geometry of the deformed beam reference line or to the orientation of the intrinsic cross section frame in accordance with previously published work when effects of warping on the dynamics and local constraints on the cross sectional deformation are ignorable the in and out of plane st venant warping displacements which are fully coupled for nonhomogeneous anisotropic beams need only be included explicitly in the determination of a suitable elastic law a two dimensional problem and need not be considered explicitly in the one dimensional equations governing global deformation in this paper it is presupposed that such an elastic law is given as a one dimensional strain energy function thus the present equations which are based on only six generalized strain variables are valid for beams with closed cross sections and for which warping is unrestrained when simplified for various special cases they agree with similar intrinsic equations in the literature although the resulting equations are newtonian in structure closely resembling euler s dynamical equations for a rigid body the formulation adheres to a variational approach throughout thus providing a link between newtonian and energy based methods in particular the present development provides substantial insight into the relationships among variational formulations in which different displacement and rotational variables are used as well as between these formulations and newtonian ones for computational purposes a compact and complete mixed variational formulation is presented that is ideally suited for development of finite element analyses finally a specialized version of the intrinsic equations is developed in which shear deformations is suppressed

an enhancement of constraint feasibility in bpn based approximate optimization back propagation neural networks bpn have been extensively used as global approximation tools in the context of approximate optimization a traditional bpn is normally trained by minimizing the absolute difference between target outputs and approximate outputs when bpn is used as a meta model for inequality constraint function approximate optimal solutions are sometimes actually infeasible in a case where they are active at the constraint boundary the paper explores the development of the efficient bpn based meta model that enhances the constraint feasibility of approximate optimal solution the bpn based meta model is optimized via exterior penalty method to optimally determine interconnection weights between layers in the network the proposed approach is verified through a simple mathematical function and a ten bar planar truss problem for constrained approximate optimization design of rotor blade is conducted to support the proposed strategies

semi infinite programming theory methods and applications starting from a number of motivating and abundant applications in 2 including control of robots eigenvalue computations mechanical stress of materials and statistical design the authors describe a class of optimization problems which are referred to as semi infinite because their constraints bound functions of a finite number of variables on a whole region in 3 5 first and second order optimality conditions are derived for general nonlinear problems as well as a procedure for reducing the problem locally to one with only finitely many constraints another main effort for achieving simplification is through duality in 6 there algebraic properties of finite linear programming are brought to bear on duality theory in semi infinite programming section 7 treats numerical methods based on either discretization or local reduction with the emphasis on the design of superlinearly convergent sqp type methods taking this differentiable point of view this paper can be considered to be complementar

cross sectional analysis of composite beams including large initial twist and curvature effects an asymptotically exact methodology based on geometrically nonlinear three dimensional elasticity is presented for cross sectional analysis of initially curved and twisted nonhomogeneous anisotropic beams the analysis is subject only to the restrictions that the strain is small relative to unity and that the maximum dimension of the cross section is small relative to the wavelength of the deformation and to the minimum radius of curvature and or twist the final one dimensional strain energy per unit length exhibits asymptotically correct second order dependence of the initial curvature and twist parameters cross sectional constants of the one dimensional theory are obtained via finite element discretization over the cross sectional plane numerical results obtained for both isotropic and composite beams are compared with published results from special purpose analyses for initially twisted straight beams as well as initially curved untwisted beams the agreement with previously published results is excellent

solving min max problems and linear semi infinite programs abstract for a min max problem in the form of min x x max t t f t x the nondifferentiability of the max function f x max t t f t x presents special difficulty in finding optimal solutions we show that an entropic regularization procedure can provide a smooth approximation f p x that uniformly converges to f x over x as p tends to infinity in this way with p being sufficiently large minimizing the smooth function f p x over x provides a very accurate approximate solution to the min max problem when this approach is applied to solve linear semi infinite programming problems the previously proposed unconstrained convex programming approach is shown to be a special case

on asymptotically correct timoshenko like anisotropic beam theory abstract this paper presents a finite element cross sectional beam analysis capable of capturing transverse shear effects the approach uses the variational asymptotic method and can handle beams of general cross sectional shape and arbitrary anisotropic material the work builds on previous works which deal with development of the classical beam theory which includes only extension torsion and bending a timoshenko like formulation is sought to achieve a refined theory with simple boundary conditions apart from some simple special cases it is shown that this problem is overdetermined however it is possible to obtain the best possible solution using the least squares minimization technique the geometrical meaning of the shear variable for this formulation is also derived results are found to be in good agreement with published results for the shear stiffness coefficients for both isotropic and anisotropic beams

a smooth method for the finite minimax problem we consider unconstrained minimax problems where the objective function is the maximum of a finite number of smooth functions we prove that under usual assumptions it is possible to construct a continuously differentiable function whose minimizers yield the minimizers of the max function and the corresponding minimum values on this basis we can define implementable algorithms for the solution of the minimax problem which are globally convergent at a superlinear convergence rate preliminary numerical results are reported

solving fuzzy inequalities with piecewise linear membership functions this paper deals with systems of fuzzy inequalities it shows that a system of fuzzy inequalities with piecewise linear membership functions can be converted to a one constraint nonlinear programming problem by employing the concepts of surrogate constraints and maximum entropy an augmented lagrangean algorithm is then applied to solve the resulting problem some computational results are included

explicit constraint approximation forms in structural optimization part 1 analyses and projections abstract an analytical study of several alternative forms of constraint approximation relevant to problems in structural design is presented limitations of the existing forms of the constraint approximations are stated and methods are outlined to improve them a new generalized form of constraint approximation is proposed for optimal design problems with and without design variable linking a power form of constraint approximation is derived for bending types of finite elements having nonlinear size stiffness relationships a detailed analysis to determine the relative effectiveness of the various forms is included a rating guideline is proposed to quantify the characteristics of chosen approximations or family of approximations on grounds of accuracy and of conservatism of remaining feasible

on timoshenko like modeling of initially curved and twisted composite beams abstract a generalized finite element based cross sectional analysis for nonhomogenous initially curved and twisted anistropic beams is formulated from geometrically nonlinear three dimensional 3 d elasticity the 3 d strain field is formulated based on the concept of decomposition of the rotation tensor and is given in terms of one dimensional 1 d generalized strains and a 3 d warping displacement that is obtained from the formulation not assumed the warping is found in terms of the 1 d strains via the variational asymptotic method vam in this paper a timoshenko like model is presupposed for a beam with cross sectional characteristic length h wavelength of deformation given by l and the magnitude of the radius of initial curvature and or twist is taken to be of the order r first a solution for the asymptotically correct refinement of classical anisotropic beam theory for initially curved and twisted beams through o h2 r2 is obtained next the o h2 l2 correction is computed it is known that timoshenko like theory is not capable of capturing all the o h2 l2 corrections for generally anisotropic beams however if all the o h2 l2 terms are known then the corresponding timoshenko like theory is uniquely defined numerical results are presented to illustrate the trends of the various classical extension twist bending twist and extension bending and nonclassical couplings extension shear bending shear and shear torsion as the initial twist and curvatures are varied

genetic algorithms in truss topological optimization the present paper describes the use of a stochastic search procedure that is the basis of genetic algorithms in developing near optimal topologies of load bearing truss structures the problem addressed is one wherein the structural geometry is created from a specification of load conditions and available support points in the design space the development of this geometry must satisfy kinematic stability requirements in addition to the usual requirements of structural strength and stiffness the approach is an adaptation of the ground structure method of topology optimization and is implemented in a two level genetic algorithm based search in this process the kinematic stability constraints are imposed at one level followed by the treatment of response constraints at a second level of optimization singular value decomposition is used to assess the kinematic stability constraints at the first level of design and results in the creation of a finite number of increasing weight stable topologies member sizing is then introduced at a second level of design where minimal weight and response constraints on stresses displacements and buckling are simultaneously considered at this level the only admissible topologies are those identified during the first stage and any stable combination thereof the design variable representation scheme allows for both the removal and addition of structural members during optimization

validation of the variational asymptotic beam sectional analysis the computer program vabs variational asymptotic beam section analysis uses the variational asymptotic method to split a three dimensional nonlinear elasticity problem into a twodimensional linear cross sectional analysis and a one dimensional nonlinear beam problem this is accomplished by taking advantage of certain small parameters inherent to beam like structures vabs is able to calculate the one dimensional cross sectional stiffness constants with transverse shear and vlasov refinements for initially twisted and curved beams with arbitrary geometry and material properties several validation cases are presented first an elliptic bar is modeled with transverse shear refinement using the variational asymptotic method and the solution is shown to be identical to that obtained from the theory of elasticity the shear center locations calculated by vabs for various cross sections agree well with those obtained from common engineering analyses comparisons with other composite beam theories prove that it is unnecessary to introduce ad hoc kinematic assumptions to build an accurate beam model for numerical validation values of the one dimensional variables are extracted from an abaqus model and compared with results from a one dimensional beam analysis using cross sectional constants from vabs furthermore point wise three dimensional stress and strain fields are recovered using vabs and the correlation with the three dimensional results from abaqus is excellent finally classical theory is shown to be insufficient for general purpose beam modeling appropriate refined theories are recommended for some classes of problems

on a basic model of a two disease epidemic this paper considers a basic model for a spread of two diseases in a population the equilibria of the model are found and their stability is investigated in particular we prove the stability result for a disease free and a one disease steady states bifurcation diagrams are used to analyse the stability of possible branches of equilibria and also they indicate the existence of a co infected equilibrium with both diseases present finally numerical simulations of the model are performed to study the behaviour of the solutions in different regions of the parameter space

genetic algorithm perspective to identify energy optimizing inclusions in an elastic plate abstract analytical methods in optimization of elastic structures are often problematic due to the high order of the governing equations it is therefore useful to try various numerical schemes in parallel to better understand the optimized object behavior the paper describes the theoretical grounds and technical features that had to be introduced for effective implementation of a regular genetic algorithm ga to the shape optimization problems in planar elasticity these features concern the fitness calculation and imposing specific geometric constraints as a way to drastically reduce the computational efforts finally we demonstrate a successful ga application for numerical shape optimization of a hole or rigid inclusion in a plate arbitrarily loaded at infinity not only the known results have been reliably reproduced for the energy minimizing holes but this approach has allowed us to extend the findings for the worst energy maximizing inclusions as well

asymptotic construction of reissner like composite plate theory with accurate strain recovery abstract the focus of this paper is to develop an asymptotically correct theory for composite laminated plates when each lamina exhibits monoclinic material symmetry the development starts with formulation of the three dimensional 3 d anisotropic elasticity problem in which the deformation of the reference surface is expressed in terms of intrinsic two dimensional 2 d variables the variational asymptotic method is then used to rigorously split this 3 d problem into a linear one dimensional normal line analysis and a nonlinear 2 d plate analysis accounting for classical as well as transverse shear deformation the normal line analysis provides a constitutive law between the generalized 2 d strains and stress resultants as well as recovering relations to approximately but accurately express the 3 d displacement strain and stress fields in terms of plate variables calculated in the plate analysis it is known that more than one theory may exist that is asymptotically correct to a given order this nonuniqueness is used to cast a strain energy functional that is asymptotically correct through the second order into a simple reissner like plate theory although it is not possible in general to construct an asymptotically correct reissner like composite plate theory an optimization procedure is used to drive the present theory as close to being asymptotically correct as possible while maintaining the beauty of the reissner like formulation numerical results are presented to compare with the exact solution as well as a previous similar yet very different theory the present theory has excellent agreement with the previous theory and exact results

new findings on the dynamics of hiv and tb coinfection models abstract in this paper we study a model for hiv and tb coinfection we consider the integer order and the fractional order versions of the model let 0 78 1 0 be the order of the fractional derivative then the integer order model is obtained for 1 0 the model includes vertical transmission for hiv and treatment for both diseases we compute the reproduction number of the integer order model and hiv and tb submodels and the stability of the disease free equilibrium we sketch the bifurcation diagrams of the integer order model for variation of the average number of sexual partners per person and per unit time and the tuberculosis transmission rate we analyze numerical results of the fractional order model for different values of including 1 the results show distinct types of transients for variation of moreover we speculate from observation of the numerical results that the order of the fractional derivative may behave as a bifurcation parameter for the model we conclude that the dynamics of the integer and the fractional order versions of the model are very rich and that together these versions may provide a better understanding of the dynamics of hiv and tb coinfection

a dynamical model for hiv tb co infection abstract a nonlinear mathematical model is proposed and analyzed to study the dynamics of hiv tb and co infection the basic reproduction number for each of the two diseases hiv and tb is obtained four equilibrium points are found out of which one is disease free equilibrium while the remaining three equilibrium points are such that they are having at least one of the diseases hiv and or tb is present when the basic reproduction number of the two diseases is less than one then the disease free equilibrium point is stable this provides a threshold for the control of diseases when tb free equilibrium point exists then it is locally stable if the basic reproduction number of hiv is more than that of tb a condition for local stability of hiv free equilibrium point is also obtained there exist some situations in which bi stability is possible that is both of the diseases persist the conditions for global stability of these points are also established the conditions for existence of endemic equilibrium point are explored and it was found that it remains unstable whenever the endemic equilibrium point exists the instability of endemic equilibrium point is used to interpret that the co infection is not long lasting

solving a system of infinitely many fuzzy inequalities with piecewise linear membership functions abstract a cutting plane type algorithm for solving a system of infinitely many fuzzy inequalities with piecewise linear membership functions is proposed in each iteration we solve a finite nonlinear optimization problem and add one or two more constraints the iterative process ends when an optimal solution is identified a convergence proof under some mild conditions is given an efficient implementation based on the concepts of constraint surrogation and maximum entropy is included some computational results are also reported

solving fuzzy inequalities with concave membership functions abstract solving systems of fuzzy inequalities could lead to the solutions of fuzzy mathematical programs it is shown that a system of fuzzy inequalities with concave membership functions can be converted to a regular convex programming problem a method of centres with entropic regularization techniques is proposed for solving such a problem some computational results are included

a regularization method for solving the finite convex min max problem the finite min max problem min text max f i x i 1 cdots m is solved generating a sequence of differentiable subproblems mathop min limits x varphi v x mathop min limits x mathop text sup limits v u in u u t f x frac 1 2 left u v right 2 where u and v are variables in the dual space the method will minimize this smooth function until sufficient decrease of varphi v x is attained and then updates the parameter v convergence is proved assuming convexity and numerical results are given

linear programming with multiple fuzzy goals abstract this paper describes the use of fuzzy set theory in goal programming gp problems in particular it is demonstrated how fuzzy or imprecise aspirations of the decision maker dm can be quantified through the use of piecewise linear and continuous functions models are then presented for the use of fuzzy goal programming with preemptive priorities with archimedean weights and with the maximization of the membership function corresponding to the minimum goal examples are also provided