Non-linear in-plane analysis and buckling of pinned–fixed shallow arches subjected to a central concentrated load

This paper is concerned with an analytical study of the non-linear elastic in-plane behaviour and buckling of pinned–fixed shallow circular arches that are subjected to a central concentrated radial load. Because the boundary conditions provided by the pinned support and fixed support of a pinned–fixed arch are quite different from those of a pinned–pinned or a fixed–fixed arch, the non-linear behaviour of a pinned–fixed arch is more complicated than that of its pinned–pinned or fixed–fixed counterpart. Analytical solutions for the non-linear equilibrium path for shallow pinned–fixed circular arches are derived. The non-linear equilibrium path for a pinned–fixed arch may have one or three unstable equilibrium paths and may include two or four limit points. This is different from pinned–pinned and fixed–fixed arches that have only two limit points. The number of limit points in the non-linear equilibrium path of a pinned–fixed arch depends on the slenderness and the included angle of the arch. The switches in terms of an arch geometry parameter, which is introduced in the paper, are derived for distinguishing between arches with two limit points and those with four limit points and for distinguishing between a pinned–fixed arch and a beam curved in-elevation. It is also shown that a pinned–fixed arch under a central concentrated load can buckle in a limit point mode, but cannot buckle in a bifurcation mode. This contrasts with the buckling behaviour of pinned–pinned or fixed–fixed arches under a central concentrated load, which may buckle both in a bifurcation mode and in a limit point mode. An analytical solution for the limit point buckling load of shallow pinned–fixed circular arches is also derived. Comparisons with finite element results show that the analytical solutions can accurately predict the non-linear buckling and postbuckling behaviour of shallow pinned–fixed arches. Although the solutions are derived for shallow pinned–fixed arches, comparisons with the finite element results demonstrate that they can also provide reasonable predictions for the buckling load of deep pinned–fixed arches under a central concentrated load.     

The description of the characteristics of the structure and the quantity in fixed pansystems theorems

Pansymmetry is the abstract of symetry, stability and other concepts in physics and so on. Fixed pansystems theorems portray a typical pansymmetry of systemic structure. The present paper complements and extends the Work in concerned in fixed pansystems theorems. It gives in finite case the structural character of fixed subsets; the criterion of existence of the least fixed subset, and the numbering formula of fixed subsets and minimal fixed subsets.     

Some new fixed point theorems in probabilistic metric spaces

ＳＯＭＥＮＥＷＦＩＸＥＤＰＯＩＮＴＴＨＥＯＲＥＭＳＩＮＰＲＯＢＡＢＩＬＩＳＴＩＣＭＥＴＲＩＣＳＰＡＣＥＳｚｈｕＣｈｕａｎ－ｘｉ（朱传喜）（ＭａｔｈｅｍａｔｉｅｓＤｉｖｉｓｉｏｎ,Ｎａｎｃｈａｎｇ．Ｕｎｉｖｅｒｓｉｔｙ,Ｎａｎｃｈａｎｇ）（Ｒｅｃｅｉｖ...     

流形元法固定边界约束处理研究

在数值流形方法中,对于材料的固定边界,一般采用罚函数的方法进行处理,即在固定边界上设置刚性弹簧约束其位移来实现固定约束条件的近似满足。罚函数法在理论上不是严格的固定约束处理方法,罚弹簧的布置与弹簧刚度的大小对模拟的效果都会产生影响。基于流形单元上位移函数的组成提出了流形方法固定边界约束处理的新方法,在组成流形单元的物理覆盖上,通过取消相应的覆盖函数在流形单元位移函数中的组成来实现双向固定的约束条件,通过使用只包含单方向位移的覆盖函数使x向固定约束条件和y向固定约束条件得到实现,推导了相应固定约束条件下的流形单元刚度矩阵的数值计算格式。该方法严格满足固定约束的物理意义,简化了固定边界的处理,并经算例证明是有效和准确的,有利于数值流形方法的程序实现和工程应用。     

一类碰撞振动系统在内伊马克沙克-音叉分岔点附近的局部两参数动力学

考虑一类具有对称性的三自由度碰撞振动系统.系统的庞加莱映射在一定条件下存在对称不动点,对应于系统的对称周期运动.根据对称性导出庞加莱映射P是另外一个隐式虚拟映射Q的二次迭代.推导了庞加莱映射对称不动点的解析表达式.根据映射不动点的稳定性及分岔理论,映射P的对称不动点发生内伊马克沙克-音叉(Neimark--Saker-pitchfork)分岔对应于映射Q发生内伊马克沙克-倍化(Neimark--Sakerflip)分岔.利用隐式虚拟映射Q,通过对范式作两参数开折分析,研究了映射P的对称不动点在内伊马克沙克-音叉分岔点附近的局部动力学行为.碰撞振动系统在这个余维二分岔点附近的局部动力学行为可能表现为投影后的庞加莱截面上的单一对称不动点、一对共轭不动点、单一对称拟周期吸引子以及一对共轭拟周期吸引子.数值模拟得到了内伊马克沙克-音叉分岔点附近的各种可能情况.内伊马克沙克-分岔和音叉分岔互相作用可能产生新的结果:对称不动点虽然首先分岔为两个共轭不动点,但是这两个共轭不动点是不稳定的,最终收敛到同一个对称拟周期吸引子.     

Caristi type hybrid fixed point theorems in menger probabilistic metric space

I.IntroductionandPreliminariesInl976,CaristiprovedtheCaristi'sfixedpointtheoreminIll.Becausethistheoremdoesnotrequirethecontinuityofthemapping.ittindsapplicationsinmanyfields.Inl99l,S.S.Changetal.l'l,broughtforwardCaristi'sfixedpointtheoremandEkeland'svar…     

A solution for an isotropic sector under anti-plane shear loadings

In this study, the problem of an isotropic sector subjected to anti-plane shear loadings is investigated. The loadings were applied to the arc of the sector, and the radial edges of the sector were under traction-free or fixed conditions. Depending on these conditions, three problems, namely, free–free, fixed–free, and fixed–fixed edges were studied. A procedure using the finite Mellin transform combined with the Laplace transform was proposed for solving these problems. Explicit closed form solutions for the displacement and stress fields throughout the sector were obtained. The stress intensity factor (SIF) for each problem was analyzed using the obtained stress fields. It was determined that the SIF disappeared under the special condition of a fixed–fixed edge. Other special cases having anti-symmetric conditions were deduced from the derived solutions, and the results of these verified those cited in the literature as well as those obtained using finite element analysis (FEA).     

PANSYMMETRY AND FIXED PANSYSTEMS THEOREMS OF A CLASS OF PANSYSTEMS RELATIONS

In this paper. some results of pansymmetry and fixed pansystems theorems areextended to the case of a class of binary relations under the framework of pansystemsmethodology It is concretely discussed when a class of binary relations has a common fixedsubset on a finite universal set. Several simple but comprehensive decisive theorems areobtained which can be determined if a class of binary relations has a common fixed subset.Asaresult the main decisive theorem-Markov-Kakutani Theorem-is extended whichis in traditionally fixed point theory and can be determined if a class of mappings has acommon fixed point.     

Thermophoretic effects on nano-particle deposition in channel flow

In this study, deposition of particles with diameters of 3, 5, and 10 nm in a finite-length heated channel flow is numerically studied under both molecular diffusion and thermophoretic effects. Two types of thermal conditions were examined. The first condition involved various inlet temperatures with a fixed wall temperature. The second condition involved various wall temperatures and a fixed inlet temperature. For a finite channel length, higher particle deposition can be obtained for the various inlet temperature and fixed wall temperature cases. However, for the same temperature ranges, complete particle collection on the wall can only be achieved under various wall temperatures and fixed inlet temperature cases when the channel length is long enough. This is because a temperature gradient appears in these cases. The temperature gradient in the various inlet wall temperatures and fixed wall temperature cases is zero when the flow is thermally fully developed.     

Fixed point index of uniform limit of set-Valued strict set-contractive mappings and its applications

In this paper,the class of uniform limit mappings of set-valued,strick set-contractivemappings is discussed.Furthermore,the fixed point index theory for the uniform limitmappings is established.Using the fixed point index theory,some positive fixed pointtheorems are proved.Our theorems generalize some results in[1,4,5,7].     

Global synchronization in fixed time for semi-Markovian switching complex dynamical networks with hybrid couplings and time-varying delays

This paper is concerned with the global synchronization in fixed time for semi-Markovian switching complex dynamical networks with hybrid couplings and time-varying delays in the presence of disturbances. Firstly, the property with respect to the global stability in fixed time is developed for semi-Markovian switching nonlinear systems. Subsequently, a novel sliding manifold with double integration is presented based on the proposed principle of convergence in fixed time. Under the designed sliding mode controller, the state trajectory of synchronization error system is driven to the prescribed sliding manifold in fixed time. In addition, the global stability in fixed time of sliding mode dynamics is proved analytically. By means of the stochastic Lyapunov–Krasovskii functional approach, the synchronization condition is established in terms of linear matrix inequalities; moreover, the stochastic fixed settling-time can be determined to any desired values in advance, via the configuration of parameters in the proposed controller. Finally, two numerical examples are provided to demonstrate the validity of the theoretical results and the feasibility of the proposed approach.

     

Minimal and maximal fixed point theorems and iterative technique for nonlinear operators in product spaces

In this paper, we study minimal and maximal fixed point theorems and iterative technique for nonlinear operators in product spaces. As a corollary of our result, some coupled fixed point theorems are obtained, which generalize the coupled fixed point theorems obtained by Guo Da-jun and Lankshmikanthamt and the results obtained by Lan in, and.     

Pansystems research on a type of fixed subsets

The present paper continues the pansystems research on fixed studies. Under the pansystems framework it gives the existence critertion of I-type fixed and the theorems about the relations between the classes of reflexive and equation one and fixed subsets: introdaces the concept of fixpoints of binary relations extstence theorems about fixpoints for a kind of panweighted netwest.     

An analytical approach for calculating natural frequencies of finite one-dimensional acoustic metamaterials

In this paper, an analytical matrix method is presented to drive closed-form characteristic equations for natural frequencies of finite monoatomic and diatomic metamaterials with various boundary conditions. Here, we extend the matrix method introduced by Louck for monoatomic lattice chains. The proposed method is used to calculate the vibration frequencies of the monoatomic metamaterials with fixed–fixed, fixed-free and free-free boundary conditions. In addition, the natural frequencies of fixed–fixed diatomic metamaterials are calculated. The existence of band gaps in the frequencies of the metamaterials is numerically shown.

     

An Optimal Control Approach to Minimum-Weight Vibrating Beam Design

ABSTRACT

A gradient projection algorithm is applied to a class of vibrating cantilever beam optimization problems which are formulated as optimal control problems. The cross-section area is distributed along the beam for minimum total weight subject to fixed natural frequency constraints and a minimum allowed area limit. Three topics receive major emphasis: the effects of shear deformation and rotary inertia, higher-mode frequency constraints, and multiple frequency constraints. Computational results are presented for the cases of fixed fundamental frequency, fixed second-mode frequency, and fixed fundamental and second-mode frequencies under a variety of conditions.     

Viscosity method for hierarchical fixed point and variational inequalities with applications

A viscosity method for a hierarchical fixed point solving variational inequality problems is presented. The method is used to solve variational inequalities, where the involved mappings are non-expansive. Solutions are sought in the set of the fixed points of another non-expansive mapping. As applications, we use the results to study problems of the monotone variational inequality, the convex programming, the hierarchical minimization, and the quadratic minimization over fixed point sets.     

SIMPLE SHAKEDOWN OF STRUCTURES UNDER VARIABLE MULTI-LOADINGS

The shakedown analysis of structures under variable multi-loadings is considered, and the corresponding simple shakedown condition is presented in this paper. Distribution of fixed stresses field is given, and the self-equilibrium of fixed stresses field is analyzed. Elastic shakedown and plastic shakedown conditions are presented based on the fixed stresses field. The theorem is convenient to evaluate the shakedown limit of structures under cyclical variable multiloadings through solving positive scalar fields and fixed stresses field factors at a series of dangerous positions of the structure, and tedious computations are avoided. Finally the theorem is applied to a thick-walled cylindrical tube under variable pressure and temperature, and the rolling contact problem. The results are in good agreement with some computational results.     

Viscosity method for hierarchical fixed point and variational inequalities with applications

A viscosity method for a hierarchical fixed point solving variational inequality problems is presented. The method is used to solve variational inequalities, where the involved mappings are non-expansive. Solutions are sought in the set of the fixed points of another non-expansive mapping. As applications, we use the results to study problems of the monotone variational inequality, the convex programming, the hierarchical minimization, and the quadratic minimization over fixed point sets.     

FIXED POINT THEOREMS FOR FUZZY MAPPINGS IN PROBABILISTIC METRIC SPACES

ＦＩＸＥＤ　ＰＯＩＮＴ　ＴＨＥＯＲＥＭＳ　ＦＯＲ　ＦＵＺＺＹ　ＭＡＰＰＩＮＧＳ　ＩＮ　ＰＲＯＢＡＢＩＬＩＳＴＩＣ　ＭＥＴＲＩＣ　ＳＰＡＣＥＳＺｈａｎｇＳｈｉｓｈｅｎｇ（张石生）；ＺｈａｎｇＹｉｎｇ（张颖）；ＹｕａｎＪｉａｗｅｉ（袁家玮）（Ｒｅｃｅｉｖ...     

Bifurcation and chaos in discrete-time BVP oscillator

In this paper, we investigate the discrete-time Bohöffer-Van der Pol (BVP) oscillator obtained by Euler method. We provide the sufficient conditions of existence, asymptotic stability of the fixed points, then give theoretical analysis for local bifurcations of the fixed points, and derive the conditions under which the local bifurcations such as pitchfork, saddle-node, flip and Hopf occur at the fixed points. Furthermore, we prove that the fixed point eventually evolves into a snap-back repeller which generates chaotic behavior in the sense of Marotto's chaos when certain conditions are satisfied. Finally, several numerical simulations are provided to demonstrate the theoretical results of the previous and to show the new complex dynamical behaviors of the system.