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The purpose of this thesis is to introduce a very important and recent branch of probability, ”SLE”, its relation to some discrete models in statistical physics, motivation, geometrical intuition and some of its important properties. In chapter 1, we introduce three discrete models: Self Avoiding Walk (SAW), Loop Erased Random Walk (LERW), and Percolation that have an important role in the thesis. In chapter 2, we set up the concept of SLE on two of these models. Required preliminaries from complex analysis and Loewner equations will be studied in chapter 3, and then, in chapter 4 we will define Chordal and Radial SLE. Studying some important properties of SLE is the subject of chapter 5. In... 

Adobe structures are considered as masonry structures which are out of scope of 2800 Iranian code. Due to this code, since these structures are made of weak materials, they do not have a considerable resistance to earthquakes. Since these structures can be found all around Iran; therefore, seismic study of walls as an important component of these structures, is, indeed, necessary. During this study, cyclic tests on three types of adobe walls, without opening, with window-opening, and with door-and-window-opening with a scale of 2:3 were done to study their in-plane behavior and also their failure modes. Based on our observations, in these walls, because of small ratio of height to length,... 

Modeling is one of the most important steps in analysis and design of structures. Most of the time behavior of floor diaphragms is assumed completely rigid in their plane in order to simplicity in practical design. Although this assumption leads to acceptable results in analysis and design of conventional buildings, erroneous results may assess in some particular buildings—for instance narrow buildings with stiff end walls. Accordingly, behavior of these buildings in future earthquakes opposes those were predicted in design phase, and they are so vulnerable since in-plane deflection of floor diaphragms are striking which cannot be ignored. This thesis investigates the significance of... 

Nowadays, over seventy percent of buildings in the world are Structures which show a weak and often vulnerable behavior. Therefore, cognition and perception of the behavior of these types of structures are of important matters.Brick walls are the most important components of brick structures which have two in-plane and out-of-plane failure mode that are the common failure modes. Up to this point, lots of studies taking into account in-plane and out-of-plane behavior of brick walls individually have yet been carried out. However, the way these two modes could affect each other has not been studied effectively and there is no precise vision about this issue in the engineering society.... 

Based on Hamilton’s principle, a three-dimensional semi-analytical method for the analysis of free vibration of a nano-composite plate within the couple stress theory is developed. Computation of dynamic behavior as well as natural frequencies and mode shapes is interested. In this method, the mechanical displacement functions, in each layer, are defined as product of a base function and a three-dimensional polynomial with unknown coefficients. The base functions are defined with respect to the kinematical boundary condition and the domain geometry. The mode shapes will be obtained and the accuracy of the present approach is demonstrated by comparison it in both classical elasticity and... 

Adobe structures are considered as masonry structures which are out of scope of 2800 Iranian code. Due to this code, since these structures are made of weak materials, they do not have a considerable resistance to earthquakes. Since these structures can be found all around Iran; therefore, seismic study of walls as an important component of these structures, is, indeed, necessary. During this study, cyclic tests on three types of adobe walls, without opening, with window-opening, and with door-and-window-opening with a scale of 2:3 were done to study their in-plane behavior and also their failure modes. Based on our observations, in these walls, because of small ratio of height to length,... 

Here the differential equations of a Graphene sheet deformation is determined by making use of the most general form of first Strain Gradient Elasticity (SGE) theory. In order to derive the equations of in-plane and out-of-plane deformations, the matrix representation of Strain Gradient constitutive law is used. Vibration of the nano-plate is studied by modeling the plate based on Kirchhoff theory and application of variation of energy, therefor the in-plane and out-of-plane vibration of the nano-plate is found through Navier analytical solution. After all natural frequencies are obtained based on SGE parameters. SGE parameters are determined by calculating the potential of a representative... 

Wall systems are an essential part of the buildings and their capacity should be properly considered in their design. However, the seismic behavior of building systems with in-filled walls and their interaction is a very complex issue, yet to be understood. Using the in-filled walls in the buildings without including them in the design process changes the whole behavior of the structural system as well as their failure mechanism under earthquake excitations. On the other hand, there have been extensive researches on rehabilitation of the structures with in-filled walls or designing them as the main or one of the lateral load carrying systems against seismic input. In this research, first the... 

Nowadays, many structural engineers use fillet welds in their designs because of their high strength and affordability. In these welds, eccentric loadings either out-of-plane or in-plane create complex condition in welds from stress point of view. To determine the capacity of such fillet welds different methods have been proposed over time. For instance, the method approved by AISC is the Elastic method. This method when combined with load factors, as required by the LRFD design method, yields very conservative designs for fillet welds. Therefore, in this project, we try to propose the plastic method for welds under eccentric loadings. This method is more economical than the elastic method...