Many orthogonal methods have been used for nonlinear analysis of structures. Some of the most significant orthogonal methods are: normal plane, updated normal plane, and unbalance force orthogonal. It should be mentioned that most of them have inadequacies in analyzing some structures. In this paper, several new orthogonal methods have been offered. The aforementioned techniques are on the basis of previous methods parameter improvement and increase of converging rate. Ability of these techniques will be shown, by analyzing some sample structures.

Avoidance of symmetry in Seljuk brickwork is one of the accessible but Difficult to understand concepts of Islamic art. The use of bricks in a variety of geometric designs without observing the principle of symmetry in the edges of the building led to a dramatic change in the structure of the brick arrays of this period that has never been experienced in any historical period in Iran. Note that changes in the artistic structure of a traditional society do not simply take place, and the coincidence of these with the height and perfection of Iranian brick art has caused a contradiction in the art of this era that has so far received little attention. However, the Seljuk era brick work debate has been a highly repetitive topic in domestic and foreign research, and despite the principle of symmetry in Iranian art, little attention has been paid to the issue of Avoidance of symmetry in Seljuk-era brickwork Explaining and interpreting this deconstruction of the new social class (middle class) as the sponsor of production that followed a new taste is of great importance. Sponsors' taste and bricklayer enthusiasm for displaying their ability, created the style of pop art in brickwork of that era that's like all the pop arts was influenced by social structures and with the political and social changes after the Seljuk era Immediately forgotten. This research aims to reveal new aspects of Seljuk-era brick art that have been neglected so far. This research is based on historical-interpretive method and based on library resources.

The Buneh Kuh anticline (with 25 km length and 7 to 17 km width) is a NW-SE trending anticline in the Coastal Fars Sub-basin (Zagros simple folded belt). Gachsaran formation is cropping out in the core of this anticline. In this paper the elements of fold style and folding mechanism have been investigated in the Buneh Kuh anticline. It is an asymmetric detachment fold on the Hormoz Formation. Herang anticline is a NW continuation of the Buneh Kuh anticline. Sub-surface contour map on the top of the Dehram group (gas reservoir) was prepared and its western culmination (near to the DD’ cross section) could be recommended for drilling.

Carpets with Medallion patterns are a wide and unique collection of Iranian carpets that received a lot of attention in the Safavid period. Since these carpets are among the most important Iranian carpets, it is necessary to analyze them from different aspects. Therefore, with the aim of studying the proportions and relationships in carpets with medallion designs in order to examine the layers of the presence of geometric-numerical proportions between the components of the carpet and the ratio of the area of each component to the analysis of symmetry, disciplinary lines and the presence of fractal geometry in 8 samples of the most famous carpets of the Safavid period with Medallion patterns, simultaneously an attempt has been made to answer the main questions of this research. Questions are 1- In what format and with what kind of composition are the issues of geometric proportions, order, disciplinary lines and symmetry seen in these designs? 2- How is the mystical concept of "from plurality to unity" and "from unity to plurality" manifested in these designs? 3- How is the presence of fractal geometry and its pattern similarities with the medallion design in Safavid period carpets analyzed? It is necessary to answer these questions and pay attention to the fact that in most researches related to Medallion Pattern in Safavid period carpets, only the proportions and numerical relations between the components and the whole carpet have been studied and the issues of symmetry, disciplinary lines and fractal geometry have not been studied; and the importance of this research becomes clear. This research has been done by descriptive and analytical methods and its information has been collected with a library method. Due to the importance of the design and role of Iranian carpets in the Safavid period - especially medallion pattern - the target community includes 8 examples of famous Safavid carpets all which have the same construction and 4 quarter-medallions, including: Sheikh Safi al-Din Ardebili carpet (530x1032cm) at the Victoria and Albert Museum in London, a carpet known as the Sea Wave, or Portuguese rug, Khorasan texture (313x680cm) at the Vienna Museum of Handicrafts, Chelsea rug (310x549cm) at the Victoria Museum of Western Iran (360x690cm) at the Petzoli Poldi Museum in Milan, Vase rug, Kerman texture probability (171x249cm) and three samples of Kashan silk carpets (165.1x243.8cm), (148.6x221cm), (146.7x207.6cm) at the New York Metropolitan Museum. Using the two-dimensional screen roller software from the computer screen, the dimensions of the proportions inside the frame and the dimensions of the frames include the ratio of width to text length, width to total length, border width to text width, border width to total width, medallion width to full text width and the width of the medallion is calculated to the total width of the carpet and the ratios related to the area of the various components of the samples. The golden ratio obtained from the square of the index is also shown as an example for the hunting rug of the Petzoli Poldi Museum of Milan. By drawing disciplinary lines in the carpet resulting from the intersection of the diameters of the index squares, the complementary rectangle, the diameters of the main frames and the lines of symmetry of the main place in the composition of these carpets are obtained. By examining the intersection points and the resulting composition, the relations governing it have been studied. Fractal specimens found in nature are similar to those found in rugs. The method of analysis in this research is that all the obtained data are arranged and prepared in tables. Then, the rules of traditional Iranian design, the rules of golden ratio and the basic features of fractal mathematics were applied and compared. The principles and relations governing this design are extracted and analyzed in terms of geometry and golden ratio laws. The results of this research indicate that the principles of symmetry and golden ratios have been observed in designing the dimensions of the main frame of the carpet for all samples. By drawing disciplinary lines, an environment is created that shows the main place in the composition of these carpets. The presence of these locations proves that these designs are legal and based on geometric divisions. By examining the fractal geometry and its patterns in the samples of carpets, it is determined that although the carpets are composed of thousands of small and large patterns and sometimes of repetitive patterns, all these elements are in a regulated and purposeful way in a single combination. Thus, in spite of the multiplicity of components, we are finally faced with a single and regular set.

The Chelounak area in northwest of Birjand located in the Sistan suture zone extremity with middle-upper Eocene sedimentary and pyroclastic rocks, folded with different axes and exposed between the Chahak-mosavieh and Mohammadieh-Hessarsangi faults. These folds have a dominant characteristic of the dispersion axis trends of NE-SW, NW-SE, and N-S. Geometric-Kinematic Analysis of these folds was carried out by data that taken from the structural interpretations, satellite images, geological maps, structural cross sections and mathematical functions. Aspect ratio, percent shortenings and the rotation folds axes are respectively for folds with NE-SW axis, 0.356-1.6, 20-77% and 28-40°; for folds with NW-SE axes0.352-0.620, 25-41% and 25-40°; and for folds with N-S axes 0.352, 25% and 24°. In this analysis the Chahak and Chelounak synclines and the Chahak anticline with NE-SW axis have maximum shortening and the Shavangan syncline with NW-SE axis has minimum shortening. This Study demonstrated the aspect ratio rises with increasing of shortening. Analysis of the structural elements demonstrates axis change of the Chelounak, Chahak and Hoj noj synclines and the Chahak and Chelounak anticlines with NE-SW Dominant axes affected by the Chahak-Mosavieh fault (~N-S trend) as well as the axis change of the Taj kouh, Shavangan and Hessar sangi synclines with NW-SE dominant axes affected by the Mohammadieh-Hessar sangi fault (~N-S trend). Dispersion of folds axial respect to compressive component has caused difference in aspect ratio, shortening and rotation of fold axes values.

Analyzing the nonlinear vibration of beams is one of the important issues in structural engineering. According to this, an impressive analytical method which is called modified iteration perturbation method (MIPM) is used to obtain the behavior and frequency of a cantilever beam with geometric nonlinear. This new method is combined by the Mickens and iteration methods. Moreover, this method does not require small parameter in the equation which is difficult to be found for nonlinear oscillation. The accuracy of the solution that is obtained by the use of MIPM has been shown graphically and compared with exact solution. Comparison shows that good adaptation is obtained and MIPM as a powerful method for solving the vibrational behavior of structures analytically.