•A semi-analytical method based on new Adomian polynomials is proposed.•Chaos in generalized Caputo fractional differential equations is numerically investigated.•Lyapunov stability is defined and a ...sufficient condition of asymptotic stability is given.
This paper investigates chaotic behavior and stability of fractional differential equations within a new generalized Caputo derivative. A semi–analytical method is proposed based on Adomian polynomials and a fractional Taylor series. Furthermore, chaotic behavior of a fractional Lorenz equation are numerically discussed. Since the fractional derivative includes two fractional parameters, chaos becomes more complicated than the one in Caputo fractional differential equations. Finally, Lyapunov stability is defined for the generalized fractional system. A sufficient condition of asymptotic stability is given and numerical results support the theoretical analysis.
•A generalized Gronwall inequality is given on finite time domain.•Finite-time stability of discrete fractional delay systems is discussed.•New finite-time stability criterion is provided.
This study ...investigates finite-time stability of Caputo delta fractional difference equations. A generalized Gronwall inequality is given on a finite time domain. A finite-time stability criterion is proposed for fractional differential equations. Then the idea is extended to the discrete fractional case. A linear fractional difference equation with constant delays is considered and finite-time stable conditions are provided. One example is numerically illustrated to support the theoretical result.
Fiber-reinforced polymer (FRP) composites have been widely used in civil engineering for either strengthening existing deteriorated reinforced concrete (RC) structures or constructing new structures. ...Recently, a new category of FRP composites with a large rupture strain (i.e., referred to as “LRS FRP” in this article) has become increasingly popular. In contrast with conventional FRP composites, LRS FRP composites possess a larger elongation and a lower modulus of elasticity. Since the ultimate state of structures with FRP strengthening generally depends on fracture of the FRP, it is expected that an increase in FRP rupture strain leads to a better performance of structures and LRS FRP composites are particularly suitable for enhancing ductility of structures. This paper presents a state-of-the-art review on the basic characteristics of LRS FRP composites and structural usage of LRS FRP composites (including concrete confined with LRS FRP composites), with further research opportunities associated with LRS FRP composites in structural engineering applications being identified.
Fractional standard and sine maps are proposed by using the discrete fractional calculus. The chaos behaviors are then numerically discussed when the difference order is a fractional one. The ...bifurcation diagrams and the phase portraits are presented, respectively.
•Fractional standard and sine maps are proposed by using the discrete fractional calculus.•The chaos behaviors are numerically discussed for various orders of difference operators.•The bifurcation diagrams and the phase portraits are presented, respectively.
•A transition portion is seen in the tensile stress–strain curves of PET FRP sheets after accelerated aging.•The tensile strength of PEN FRP sheets in 25 °C alkaline solution decreases by only ...5%.•The decrease in the tensile strength of PEN FRP sheets after aging in 40 °C alkaline solution and seawater are 13% and 4% respectively.•The alkaline resistance of PEN FRP composites is better than that of PET FRP composites.•The Arrhenius formula is adopted to predict the long-term tensile strength of LRS FRP sheets.
Large rupture strain (LRS) fiber-reinforced polymer (FRP) composites, including polyethylene naphthalate (PEN) FRP and polyethylene terephthalate (PET) FRP composites, have become increasing popular in civil construction. PET FRP and PEN FRP can be recyclable and thus they are environmentally friendly. However, the durability of LRS FRP composites under extreme environmental conditions (e.g., marine environment and high temperature) has not been understood. To this end, durability tests on 282 LRS FRP sheets after aging in alkaline/seawater solution with different temperatures (25℃, 40℃, 60℃) were conducted in this study. The microstructure of PEN FRP sheets was also analyzed using scanning electron microscope (SEM). The results show that the changes of the elastic modulus of the first linear portion and the elastic modulus of the second linear portion of PEN FRP sheets after aging in different aging temperatures are slight. For PEN FRP sheets with an aging period of 365 days in 60 °C solutions, the degradation rate of the tensile strength is around 10% for both alkaline (pH = 13.2) and seawater solutions, and the degradation rate of the tensile rupture strain is around 12.5%. Additionally, under a higher exposure temperature, there is a significant decrease in the tensile strength of LRS FRP composites. Furthermore, it shows that the durability of PEN FRP sheets was significantly affected in the alkaline environment compared to that in the seawater environment, and the alkaline resistance of PEN FRP composites is better than that of PET FRP composites.
A fractional difference is defined by the use of the right and the left Caputo fractional differences. The definition is a two-sided operator of Riesz type and introduces back and forward memory ...effects in space difference. Then, a fractional difference equation method is suggested for anomalous diffusion in discrete finite domains. A lattice fractional diffusion equation is proposed and the numerical simulation of the diffusion process is discussed for various difference orders. The result shows that the Riesz difference model is particularly suitable for modeling complicated dynamical behaviors on discrete media.
•A Riesz–Caputo fractional difference is proposed within the discrete fractional calculus.•A lattice diffusion equation is defined on discrete finite domains.•The fractional order is varied to numerically depict the diffusion behaviors of long interactions.
We consider a history-dependent variational–hemivariational inequality with unilateral constraints in a reflexive Banach space. The unique solvability of the inequality follows from an existence and ...uniqueness result obtained in Sofonea and Migórski (2016, 2018). In this current paper we introduce and study a generalized penalty method associated to the inequality. To this end we consider a sequence of generalized penalty problems, governed by a parameter λn and an operator Pn. We prove the unique solvability of the penalty problems as well as the convergence of corresponding solutions sequence to the solution of original problem. These results extend the previous results in Sofonea et al. (2018) and Xiao and Sofonea (2019). Finally, we illustrate them in the study of a history-dependent problem with unilateral boundary conditions which describes the quasistatic evolution of a rod–spring system under the action of given applied force.
The tool of the discrete fractional calculus is introduced to discrete modeling of diffusion problem. A fractional time discretization diffusion model is presented in the Caputo-like delta’s sense. ...The numerical formula is given in form of the equivalent summation. Then, the diffusion concentration is discussed for various fractional difference orders. The discrete fractional model is a fractionization of the classical difference equation and can be more suitable to depict the random or discrete phenomena compared with fractional partial differential equations.
Elliptical concrete-filled steel tube (ECFST) columns have been widely used, while they suffer deterioration due to various reasons. On the other hand, the concrete in ECFST columns is ineffectively ...confined due to the non-uniform confinement and the elliptical steel tube in ECFSTs is easy to experience buckling failure. To this end, fiber-reinforced polymer (FRP) jackets are proposed to strengthen the ECFST columns. In this study, axial compression tests on FRP-confined elliptical CFST (FCECFST) columns with a high-strength steel tube are carried out and the effects of the FRP jacket thickness (0, 1, 2, 3 layers) and the cross-sectional aspect ratio (1, 1.5 and 2) are investigated. The experimental results show that the elastic stifness, the ultimate axial load and ultimate axial strain of FCECFST columns increase with the FRP thickness at a given cross-sectional aspect ratio, while decrease with the cross-sectional aspect ratio at a given FRP jacket thickness. Also, FCECFST columns generally exhibit monotonic ascending load-strain behavior, implying that the performance of ECFST columns, which generally have a post peak descending load-strain behavior, is substantially enhanced. Given that the existing strength model is inaccurate and incapable to predict the ultimate condition of confined concrete in FCECFST, a new model of ultimate axial stress and ultimate axial strain is proposed and the verification demonstrates that the proposed model is of good accuracy.
