Sharif Digital Repository

In this paper, the dynamic characteristics of skewed bridges are explored analytically. Closed form solutions for translational and torsional periods of free vibration and mode shapes are given for slab-girder skewed bridges. Moreover, the seismic displacement of the deck of skewed bridges is calculated using the response spectrum method and its skew term is compared with the requirement of AASHTO. The effects of seismic force resisting elements, such as elastomeric bearings and end diaphragms are included. It is shown that the skew term in AASHTO's equation can underestimate the seat width requirement for some bridges. A new skew term for the bridge seat width requirement is suggested  

A fast statistical method for the analysis of the Read SNM of a 6 T SRAM cell in near/subthreshold region is proposed. The method is based on the nonlinear behavior of the cell. DIBL and body effects are thoroughly considered in the derivation of an accurate closed form solution for the Read Static Noise Margin (SNM) of the near/subthreshold SRAM cell. This method uses the state space equation to derive the Read SNM of the cell as a function of threshold voltage of cell transistors. This function shows the dependency of the Read SNM on sizing, VDD, temperature, and threshold voltage variations. It provides a fast reliability analysis for a cell array of a given size and a supply voltage. It... 

Non-linear bending analysis of tapered functionally graded (FG) beam subjected to thermal and mechanical load with general boundary condition is studied. The governing equations are derived and a discussion is made about the possibility of obtaining analytical solution. In the case of no axial force along the beam, a closed form solution is presented for the problem. For the general case with axial force, the Galerkin technique is employed to overcome the shortcoming of the analytical solution. Moreover, the Generalized Differential Quadrature (GDQ) method is also implemented to discretize and solve the governing equations in the general form and validate the results obtained from two other... 

ABSTRACT Disc rheological parameters regulate the mechanical and biological function of intervertebral disc. The knowledge of effects of degeneration on disc rheology can be beneficial for the design of new disc implants or therapy. We developed two material property identification protocols, i.e., inverse poroelas-tic finite element analysis, and biphasic closed form solution. These protocols were used to find the material properties of intact, moderate and severe degenerated porcine discs. Comparing these two computational protocols for intact and artificial degenerated discs showed they are valid in defining bi-phasic/poroelastic properties. We found that enzymatic agent disrupts the... 

MIMO radar is the next generation radar which transmits arbitrary waveforms at each one of its apertures. It has been shown that the design of waveforms for MIMO radars in order to synthesize a desired spatial beampattern is mapped into a waveform correlation matrix R design in the narrowband case. As of now, given a desired beampattern or estimated locations information of targets, calculating R has been modeled as an optimization problem like semi-definite programming. Also, in some special cases like rectangular beampattern, closed-form solutions for R has been proposed. In this paper, we introduce a fast algorithm which is capable of designing R in order to achieve more arbitrary... 

A closed form solution is presented in this paper to study the dynamics of a composite beam with a single delamination under the action of a moving constant force. The delaminated beam is divided into four interconnected beams using the delamination limits as their boundaries. Governing motion equations are derived in which the differential stretching and the bending-extension coupling are considered. The method of modal analysis is adopted to derive analytically the dynamic response of each beam. The obtained results for the free vibrations of delaminated beam are verified against reported similar results in the literature. Moreover, the maximum dynamic response of such a beam is compared... 

The current paper uses the Extended Kantorovich Method (EKM) to analytically solve the problem of squeezed film damping in micromirrors. First a one term Galerkin approximation is used and following the extended Kantorovich procedure, the solution of the Reynolds equation which governs the squeezed film damping in micromirrors is reduced to solution of two uncoupled ordinary differential equation which can be solved iteratively with a rapid convergence for finding the pressure distribution underneath the micromirror. It is shown that the EKM results are independent of the initial guess function. It is also shown that EKM is highly convergent and practically one iterate is sufficient for... 

In this paper, the strain gradient theory, a non-classical continuum theory capable of capturing the size effect observed in micro-scale structures, is employed in order to investigate the size-dependent mechanical behavior of microbars. For a strain gradient bar, the governing equation of motion and classical and non-classical boundary conditions are derived using Hamilton's principle. Closed form solutions have been analytically obtained for static deformation, natural frequencies and mode shapes of strain gradient bars. The static deformation and natural frequencies of a clamped-clamped microbar subjected to a uniform axial distributed force are derived analytically and the results are... 

Consider a set of (N+1)-phase concentric spherical ensemble consisting of a core region encased by a sequence of nested spherical layers. Each phase is spherically isotropic and is functionally graded (FG) in the radial direction. Determination of the elastic fields when the outermost spherical surface is subjected to a nonuniform loading and the constituent phases are subjected to some prescribed nonuniform body force and eigenstrain fields is of interest. When the outermost layer is an unbounded medium with zero eigenstrain and body force fields, then an N-phase multi-inhomogeneous inclusion problem is realized. Based on higher-order spherical harmonics, presenting a three-dimensional... 

The asymmetric problem of lateral translation of an inextensible circular membrane embedded in a transversely isotropic half-space is addressed. With the aid of appropriate Green's functions, the governing equations of the problem are written as a set of coupled integral equations. With further mathematical transformations, the system of dual integral equations is reduced to two coupled Fredholm integral equations of the second kind which are amenable to numerical treatments. The exact closed-form solutions corresponding to two limiting cases of a membrane resting on the surface of a half-space and embedded in a full-space are derived. The jump behavior of results at the edge of the membrane... 

In this work an analytical solution is presented for a viscoelastic micro-beam based on the modified couple stress theory which is a non-classical theory in continuum mechanics. The modified couple stress theory has the ability to consider small size effects in micro-structures. It is strongly emphasized that without considering these effects in such structures the solution will be wrong and not suitable for designing systems in micro-scales. In this study correspondence principle is used for deriving constitutive equations for viscoelastic material based on the modified couple stress theory. Governing equilibrium equations are obtained by considering an element of micro-beam. Closedform... 

Rectangular plates on distributed elastic foundations are widely employed in footings and raft foundations of variety of structures. In particular, mounted columns and single footings may partially occupy the rectangular plate of any kind. This study deals with free vibration problem of thin rectangular plates on Winkler and Pasternak elastic foundation model which is distributed over a particular arbitrary area of the plate. Closed form solutions are developed through solving the governing differential equations of plates. Moreover, a novel mathematical approach is proposed to find the exact analytical solution of free vibration of plates with mixed or fully-clamped boundary conditions.... 

In this article, a constitutive model in the framework of continuum damage mechanics is proposed to simulate the elastic behavior of concrete in tension and compression states. We assume two parts for Gibbs potential energy function: elastic and damage parts. In order to obtain the elastic-damage constitutive relation with the internal variables, two damage thermodynamic release rates in tension and compression derived from the elastic part of Gibbs potential energy are introduced. Also, two anisotropic damage tensors (tension and compression) are defined which characterize the tensile and compressive behaviors of concrete. Furthermore, two different linear hardening rules for tension and... 

In addition to enhancement of the results near the point of application of a concentrated load in the vicinity of nano-size defects, capturing surface effects in small structures, in the framework of second strain gradient elasticity is of particular interest. In this framework, sixteen additional material constants are revealed, incorporating the role of atomic structures of the elastic solid. In this work, the analytical formulations of these constants corresponding to fee metals are given in terms of the parameters of Sutton-Chen interatomic potential function. The constants for ten fcc metals are computed and tabulized. Moreover, the exact closed-form solution of the bending of a... 

Elmore delay has been widely used as an analytical estimate of the interconnect delays in the performance-driven synthesis and layout of VLSI routing topologies. In this paper, Closed-form solutions for the 50% delay, rise time and overshoots of the step response of distributed Single Wall Carbon Nanotube (SWCNT), which consists RC and RLC parts, are presented for the first time. The proposed approach retains both efficiency and simplicity of the equivalent Elmore model with significantly improved accuracy, through surface fitting (3D) instead of curve fitting (2D)  

In this paper, nonlinear thermo-mechanical free vibration analysis of functionally graded (FG) beams investigated. Euler-Bernoulli assumptions together with Vo n Karman's strain-displacement relation are employed to derive the nonlinear governing partial differential equation (PDE) of motion. He's variational method is employed to obtain a simple and efficient approximate closed form solution of the nonlinear governing equation. Comparison between results of the present work and those available in literature shows the accuracy of presented technique. Some new results for the nonlinear natural frequencies of the FG beams such as the effect of vibration amplitude, material inhomogeneity and... 

In the current paper, analytical solutions are presented for the nonlinear problem of electrostatically actuated torsional micromirrors considering the bending of the torsional beams. Energy method is used for finding the equilibrium equations. Then the explicit function theorem is utilized for finding the equations governing the instability mode of the mirror. The presented results show that neglecting the bending effect in electrostatic torsion micro actuators can cause to several hundred percent of overestimation of the stability limits of the device. In order to study the voltage-angle and voltage-displacement behavior of the micromirror, equilibrium equations are solved using HPM.... 

The current paper deals with the problem of static instability of Micro/Nano mirrors under the combined effect of capillary force and van der Waals force. First the governing equations of the statical behavior of Micro/Nano mirrors under the combined effect of capillary force and casimir force is obtained using the newtons first law of motion. The dependence of the critical tilting angle on the physical and geometrical parameters of the nano/micromirror and its supporting torsional beams is investigated. It is found that existence of vdW torque can considerably reduce the stability limits of the nano/micromirror. It is also found that rotation angle of the mirror due to capillary force... 

In the current paper, Extended Kantorovich Method (EKM) has been utilized to analytically solve the problem of squeezed film damping in micromirrors. A one term Galerkin approximation is used and following the extended Kantorovich procedure, the solution of the Reynolds equation which governs the squeezed film damping in micromirrors is reduced to solution of two uncoupled ordinary differential equation which can be solved iteratively with a rapid convergence for finding the pressure distribution underneath the micromirror. It is shown that the EKM results are independent of the initial guess function. It is also shown that since EKM is highly convergent, practically one iterate is...