Sharif Digital Repository

Automatic theorem proving has been attractive in artificial intelligence (AI). The aim of the usual automatic theorem proving methods is applying of the mathematical logic rules to decide intelligently, and reasoning automatically. In contrast the aim of our research is to apply computers abilities and artificial intelligence methods to simulate human abilities to prove mathematical theorems. For this purpose, we invent a typed formal language (TFL) to describe mathematical theories. The language must be clearly computable and should cover the First Order Logic (FOL) and the usual mathematical sentences. Then some algorithms and inference rules to compare sentences conceptually are... 

Design, analysis and practical implementation of the filter trust-region algorithms are investigated. First, we introduce two filter trust-region algorithms for solving the unconstrained optimization problem. These algorithms belong to two different class of optimization algorithms: (1) The monotone class, and (2) The non-monotone class. We prove the global convergence of the sequence of the iterates generated by the new algorithms to the first and second order critical points. Then, we propose a filter trust-region algorithm for solving bound constrained optimization problems and show that the algorithm converges to a first order critical point. Moreover, we address some well known... 

This world’s commercial and competitive space force’s designers and manufactures to produce and supply products with high quality and low price at desirable level of reliability. On the other hand, during the design and production process, Engineers are always faced with uncertainty. Essentially, uncertainties can be divided into two categories: aleatory and epistemic. Aleatory uncertainties are due to changes in design conditions, material properties, physical dimensions of components and operating conditions. This kind of uncertainty will not be reduced during the life.on the otherhand, Epistemic uncertainties that are due to lack of knowledge about physical nature of systems can be... 

Ti-UIO-66(Zr) nanocomposites have been prepared via a modified one-step solvothermal methodology and evaluated in photocatalytic oxidative desulfurization. Extensive characterization by X-ray diffraction (XRD), Fourier transforms infrared spectroscopy (FT-IR), field emission scanning electron microscopy (FESEM), transmission electron microscopy (TEM), Energy-dispersive X-ray spectroscopy (EDX), ultraviolet-visible diffuse reflectance spectroscopy (UV-vis DRS), photoluminescence spectroscopy (PL), nitrogen adsorption-desorption, and thermogravimetric analysis (TGA), have revealed the role of Ti loading, on Ti speciation and the structure of the composite materials. Their performance have been... 

The use of steel as one of the most widely used materials in the construction of structures is accompanied by problems and among them the problem of establishing stability in structure is important. To provide stability in the structure as a whole and for each of its elements, the new edition of the American Specification for Structural Steel Buildings, has introduced three general methods based on the elastic analysis. It includes, direct analysis method, effective length method and first-order analysis method. Each method has advantages and disadvantages. The present study is divided into two parts. The first part gives an overview of the behavior of structures and methods of determining... 

In this thesis, a new method has been developed for tuning of fractional PI ( ) and fractional [PI] ( ) controllers for the first order plus dead-time ( ) systems. By using the performance-map method ( ) and based on phase and gain margins' criteria, a formula which is function of fractional order ( ) and normalized dead-time ( ) has been proposed for the proportional and integral coefficients. In addition, an equation has been given for the fractional order of controller to minimize the integrated absolute error ( ) index. Moreover, overshoot and settling-time of the step response of the system have been improved by dynamic setpoint weighting. Simulation results have shown that proposed... 

In this thesis we construct a bounded translation of intuitionistic predicate logic into Basic predicate logic with restricted use of universal quantifier and without equality inspired by papers [1] and [2]  

The object of this study is to determine the buckling load of reinforced composite conical shells under axial compression. . Shells are reinforced by stringers and rings and the boundary conditions are assumed to be simply supported. At first the equilibrium equations are obtained using the first order shear deformation theory (FSDT), smeared stiffener technique and principle of minimum potential energy. In the following, the resulting equations which are the system of five variable coefficient partial differential equations in terms of displacement components are investigated by generalized differential quadrature method (GDQM). Finally the standard eigenvalue equation is formed and the... 

Based on the modified couple stress and Mindlin plate theories, a Levy type solution is presented for bending and vibration analysis of rectangular isotropic micro plates with simple supports at opposite edges and different boundary conditions at the other two ones. Modified couple stress theory is taken into account to capture the size effect and the governing equations are derived using Hamilton's principle, and solved by Levy solution and space-state method. The results are verified with the existing ones in the literature. As a benchmark, additional tables for vertical deflections and free vibrations of plate with various boundary conditions are presented  

The primary objective of this research is probabilistic quantification of the fatigue life of tension-leg platforms (TLP) using reliability methods. The need for such methods stems from the significant uncertainty in the loads exerted on offshore structures. The scope of this paper is limited to the study of fatigue in TLP tendons. For this purpose, nonlinear force time history response of the TLP tendon under random wave loads is computed and the damage due to fatigue is estimated in accordance with the Palmgren-Miners rule. Assuming a Rayleigh distribution for stress variation and eight different sea states, the ultimate fatigue damage is computed by accumulating the damage over all... 

For studying the hygrothermal deformation of generally laminated composite platesunder uniform temperature change and uniform moisture absorption change, by starting from the reduced form of elasticity displacement field for a long flat laminate, an analytical method is developed in order to accurately calculate the interlaminar stresses near the free edges of the laminate. The constant parameters appearing in the reduced displacement field, describe the global deformation of the laminate and appropriately obtained by employing an improved first-order shear deformation theory.For solving the coupled equilibrium equations of agenerally laminated composite plate, some of the stiffness... 

In the present study, an analytical solution is developed to calculate the interlaminar stresses in long generally cross-ply laminated composite plates subjected to bending. At first, upon the integration of the strain-displacement relations and using the existing patterns in deformation of the long laminate, the general displacement field is extracted and simplified to the final form. Presented solution is based on a combined method containing the equivalent single-layer (ESL) theories beside the Reddy’s layerwise theory. In this method, the equivalent single-layer theories are utilized because of their simplicity and low computational efforts rather than the layerwise theory in evaluation... 

In the present study, an analytical solution is developed to calculate the interlaminar stresses in long symmetric laminated composite plates subjected to shearing load. At first, upon the successive integrations of the strain-displacement relations and using the existing patterns in deformation of a long symmetric laminate, the general displacement field is extracted and simplified to the final form. Presented solution is based on a combined method containing the equivalent single-layer (ESL) theories beside the Reddy’s layerwise theory. In this method, the equivalent single-layer theories are utilized because of their simplicity and low computational efforts rather than the layerwise... 

Arcs and rings are used extensively in structures such as submarines and bridges due to their particular geometry. On the other hand, in multi-part rocket, due to the high temperature gradients, they form the fastening rings of functional materials (FGM). Considering the importance of this structural element, in this thesis, linear and nonlinear behavior (including bending and post-buckling) of rings made of functionally graded materials under different types of thermo-mechanical loading has been investigated. First, the governing equations are derived from the principle of minimum potential energy, based on the two theorems of Donnell and Love. Donnell's theory equations are solved... 

The current study is dedicated to free vibration analysis of a thin cylindrical shell with an oblique end. To this end, governing equations of motion and the corresponding boundary conditions are derived using Hamiltonian formulations. The differential form of equations is obtained by applying by part integration to the integral form of equations of motion. Equations of motions have been solved by Galerkin method for two different kinds of boundary conditions. Convergence process for different kinds of conditions has been done and results compared with papers. The effect of different parameters such as, length of cylinder, oblique angle, thickness etc. on the fundamental frequencies has been... 

The purpose of this study is to analytically study the aeroelastic characteristics of the cylindrical shells fully treated with passive constrained layer damping (PCLD) to indicate the effects of various parameters on the behavior of such structures. Constraining the viscoelastic layers increases the amount of dissipated energy and the bending stiffness of the structure without considerable change of the weight.
A thin shell theory in conjunction with the Donell assumptions is employed for the shell and the constraining layer (CL) and the first order shear deformation theory (FSDT) is used for the viscoelastic layer to construct the model. The effects of rotary inertia and shear... 

Due to major problems induced by delamination in laminated composites, functionally-graded materials (FGM) have been put to growing use in recent years. In the present research, dynamic stability of FGM cylindrical shells under axial follower loads is addressed. Loading was considered in three forms: concentrated (Beck’s problem), uniformly-distributed (Leipholz’s problem), and linearly-distributed (Hauger’s problem). In order to derive the governing equations, Love’s hypotheses and First-order Shear Theory (FST) were used. To solve the equations, polynomial mode shapes were used to approximate the displacements, and the extended Galerkin method was applied. The problem was solved for mild... 

In recent years, one of the important and challenging issues that has drawn many engineers’ attention is the system reliability. Generally, the possibility of the system’s satisfactory performance under specified operating conditions, for a given period of time, is defined as the System Reliability. Analytical and Simulation methods are two main reliability techniques. In the Analytical technique, mathematical models with some simplification are applied, whereas the Simulation technique utilizes significant number of experiments which are extremely costly and time-consuming. In spite of carrying out analytical methods for proving results, simulation is carried out in different analyses... 

In this study, free vibration analysis of moderately thick rectangular FG plates with general boundary conditions is investigated. Governing equations of motion are obtained based on the Mindlin plate theory. A semi analytical solution is presented for the governing equations using extended Kantorovich method (EKM). Results are compared and validated with available results in the literature. Effects of different parameters such as boundary conditions, material and geometrical parameters on natural frequencies of the FG plates are investigated  

In this study the free vibration of annular sector plates made of functional materials with using the extended Katrovich method is investigated for a variety of boundary conditions. For this purpose, based on the first order shear deformation theory and Hamilton's principle, equations of motion that they are five differential equations and coupled, are derived. Due to the difficulty of the equations obtained by applying extended kantrovich method on these equations, two ordinary differential equations obtained, the two categories combined fixed and simple boundary conditions will be solved by using generalized differential quadrature and in an iterative process system natural frequency is...