مهرداد فرید

In the present research, vibration behavior is presented for a thermally postbuckled double layered graphene sheet (DLGS). The DLGS is modeled as a nonlocal orthotropic plate which contains small scale effects. The formulations are based on the Kirchhoff's plate theory, and von Karman-type nonlinearity is considered in strain-displacement relations. The thermal effects, van der Waals forces between layers and chirality are also included and the material properties are assumed to be temperature-dependent. A semi analytical solution is obtained using multiple time scales method. The effects of variation of small scale parameter to the natural frequencies, deflections and response curve of DLGS are analyzed and the numerical results are obtained from the nonlocal plate model. Numerical results are compared with those of similar researches. Effects of various parameters on the postbuckled vibration of DLGS in thermal environments such as scale parameter, length and thermal load are presented. Stability of vibration modes around a buckled configuration is investigated. Results show that the scale parameter and thermal changes have important roles on nonlinear vibrational behavior of nano scale buckled structures.

In this syudy, a size-dependent modeling of micro plate with piezoelectric layers based on classical plate theory using modified couple stress theory is developed in this paper. Introducing only one material length scale parameter in modified couple stress theory to take into account the size effect of the system is one of the main advantage of this theory over other nonclassical continuum mechanics theories. Also, this theory is able to predict and interpret the size-dependent static and dynamic behavior of micro-scale structures with more accuracy and precision in comparison to classical continuum mechanics theory. The piezoelectric layers are modeled according to linear piezoelectricity theory and due to small thickness, the electric field is assumed to be constant over the layers. The equation of motion and its corresponding boundary conditions are derived using Hamilton principle. The equation of motion is solved numerically using finite element method and the effect of material length scale parameter and piezoelectric layers on free vibration and static deflection of micro-plate are investigated.

Shape Memory Alloys are widely used in the industry. Different researchers introduce successful models for phase transformation. In this work firstly the Lagoudas assumptionsis corrected and an enhanced model for phase transformation of these smart materials is introduced. Secondly we compare results of this model with cosine Liang-Rogers model. Results show a good consistency between this model and cosine Liang-Rogers model. Afterwards for the first time switching control for these operators is investigated. For this reason, special application of smart material is selected and a common Lyapunov function for all subsystems is selected to prove stability of the system under any arbitrary switching. Subsequently robust adaptive switching control is applied on it. Lastly, a time delay problem is supposed and it is shown that even by considering time delay for this switched system, it is globally asymptotically stable.

Boundary value problems involving contact are great importance in industries related to mechanical and civil engineering، also in environmental، medical، military and aerospace applications. In this paper، the nanoindentation contact problem between a rigid spherical indenter and surface of a viscoelastic half-space of arbitrary shape is considered under assumption of interfacial surfaces are frictionless. Deriving of the relations between the contact pressure distribution، the resultant force on the indenter and the penetration on viscoelastic surface is the main scope of presented study. By appropriate formulation of the viscoelastic constitutive equations، the problem can be solved numerically using the Matrix Inversion Method (MIM)، extended to viscoelastic indentation case and with exactly satisfying the boundary conditions. Comparison of the numerical results with analytical ones for loading-unloading procedure of spherical indenters، shows the efficiency of the method in case of a prescribed penetration as well as given load history.

The tribological aspects of contact systems are greatly affected by the friction and contact pressure distribution throughout the surface of the contact interface. Generally the contact of deformable bodies is a nonlinear problem and for the viscoelastic bodies it has a time-dependent response, since their viscous characteristics depends on time. The introduction of friction with its irreversible characteristic in contact surface makes the contact problem more difficult. The objective of this study is to develop a general augmented Lagrangian finite element formulation associated with an incremental adaptive procedure which established for analysis of frictional contact problems in viscoelastic systems. The contact behavior has been studied through an improved augmented Lagrangian approach. A generalized Maxwell model has been used to model the viscoelastic constitutive equations in which bulk and shear relaxation functions are represented by the sum of a series of decaying exponential functions of time. Based on the principle of virtual work, an effective finite element formulation associated with an incremental relaxation procedure has been developed. As an application of formulation, the numerical example has been presented to evaluate the numerical approach.

In this paper، the procedure of a novel computational solution for the formulation and analysis of nano-indentation contact problems between a viscoelastic half-space and a rigid indenter of any arbitrary geometry is presented. The main objective of this paper is to develop the relations which link the contact pressure distribution، the load on the indenter، and the indentation depth with assumption that the surfaces are frictionless. The viscoelastic indentation problem has been solved numerically employing a proper formulation in constitutive equations and applying a new matrix inversion approach satisfying the boundary conditions. The computational approach has been validated by comparing the numerical results to the analytic ones for loading and unloading process of a spherical nano-indenter.

The objective of this study is to develop a general finite element formulation associated with an incremental adaptive procedure established for the calculation of contact pressure distributions in viscoelastic structures. A generalized Maxwell model has been used to model the viscoelastic constitutive equations in which bulk and shear relaxation functions are represented by sum of a series of decaying exponential functions of time. Based on the principle of virtual work, an effective finite element formulation, associated with an incremental relaxation procedure, has been developed. The viscoelastic contact behavior has been studied through an improved augmented Lagrangian approach, based on kinematical conditions of contact bodies. The proper convergence caused by the numerical examples with those obtained from analytical results shows the applicability of presented finite element formulation.