In this paper, semi-analytical method for asymmetrical eccentrically stiffened FGM cylindrical shells under external pressure and surrounded by a linear and non-linear elastic foundation is presented. The proposed linear model is based on two parameter elastic foundation Winkler and Pasternak. According to the von Karman nonlinear equations and the classical plate theory of shells, strain-displacement relations are obtained. The smeared stiffeners technique and Galerkin method, used for solving nonlinear problem. To finding the nonlinear dynamic response of fourth order Runge-Kutta method is used. The effect of parameters asymmetrical eccentrically stiffened on the nonlinear dynamic buckling response of FGM cylindrical shells have been investigated.

The post-buckling behavior of rectangular frames in an elastic domain is studied in depth. In analysis, unsymmetrical geometry, sway possibility and support conditions are considered in order to find their influences on load-deflection paths and non-linear deformations. The static perturbation technique is used for analysis and discussion. The first, a second order perturbation problem as an accurate measurement for the frame, is solved and the solutions compared with previously published papers. The results reveal that symmetric frames with a sway movement, due to lack of an axial force in the beam in the first order perturbation analysis, have a symmetric bifurcation point. However, the post-buckling behavior of un-symmetric frames with or without sway is bifurcated in an asymmetric manner.

In this paper, solution of inverse problems in a plane linear elastic bodies are investigated. In recent years, many studies have been conducted to develop effective approaches for damage detection in structural components. The efforts made over the last decades to overcome the mathematical challenges encountered in non-linear inverse problems may be categorized in two procedures: traditional methods, and qualitative methods. Although satisfactory results can be obtained using traditional approaches, they impose long reconstruction times associated with necessity of an accurate initial guess. These schemes require a priori information that may not be necessarily available. Consequently, the mentioned limitations have led to the conceptually distinct class of inverse scattering solutions, known as “, qualitative methods. ”,These methods are based on non-iterative obstacle reconstruction from far-and/or near-field measurements of the scattered field which avoids incorrect model assumption. Qualitative methods may be considered as probe/sampling methods such as linear sampling method, topological sensitivity, factorization method, and point source method, which seek to determine the geometric properties of scatterers. In this regard, the LSM and the FM introduced in the inverse scattering literature of far-field acoustics for the first time, are particularly attractive. This is due to the abilities of these methods to provide accurate reconstruction of the location and shape of the unknown scatterer from measurements of near-or far-field patterns, by monitoring the behavior of the norm of regularized solution. This norm is bounded inside the targets and unbounded elsewhere. Moreover, the most interesting feature of qualitative methods is that they do not require a priori information/assumption on the scatterer and/or the investigation domain. In addition, these methods may handle multiple scatterers as easily as single ones. Furthermore, these methods involve relatively low computational cost and can be applied to various types of defects such as non-convex and not-connected ones. For this purpose, sampling method in frequency domain is introduced for cavity/crack detection in a structural element such as plate. This goal is followed by partitioning the investigated region into an arbitrary grid of sampling points, in which a linear equation is solved. The main idea of the linear sampling method is to search for a superposition of differential displacement fields which matches with a prescribed radiating solution of the homogeneous governing equation in Ω, (D), for each sampling point. Although this method has been used in the context of inverse problems such as acoustics, and electromagnetism, there is no specific attempt to apply this method to identification of crack/cavities in a structural component. This study emphasizes the implementation of the sampling method in the frequency domain using spectral finite element method. A set of numerical simulations on two-dimensional problems is presented to highlight many effective features of the proposed qualitative identification method.

Cables have always been under consideration as a structural element because of important features such as large strength to weight ratios and long spans. Their equilibrium analysis is an important issue in this regard. But this analysis involves highly nonlinear equations arising from large deformations and material nonlinearity. Different methods have been under use for numerical analysis of such structures. Using the principle of minimum total potential energy is one of the common methods of analyzing the equilibrium configuration of structures. In this method, which is considered an alternative to direct solution of nonlinear equations of equilibrium analytically or numerically by finite element for example, the total potential energy of the structure is minimized using optimization techniques and forces and deformations corresponding to the equilibrium configuration are computed. In cable structures, which under ideal assumption cannot withstand compressive forces, the potential energy functional has discontinuous derivative and thus the classic methods of optimization, which make use of the derivative of the objective function, cannot be used in this case. Usually, the energy consideration is used as the basis of obtaining the equilibrium equations of the structure but rarely is it used as a function the numerical minimization of which gives the equilibrium configuration. In this paper a new method of solving nonlinear equations of elastic equilibrium of cable structures is presented. In this method, first the potential energy functional of the cable structure with large deformations is established. Then, the Powell algorithm of optimization, which doesn't depend on the derivatives of the objective function, is applied and the equilibrium configuration as the minimizer of the functional is obtained. The proposed method has the ability to determine the force in each cable and displacements of the cable junctions (nodes) and the slack cables (cables with no tension) with great speed and accuracy compared to the classic methods. This work consists of a brief explanation of different analyzing methods of cable structures currently in the market. Then, the potential energy for a single cable is obtained and is generalized for a cable network. After that, the Powell's minimization technique is explained. In the examples section, a very simple structure for which the analytical result is available is considered as a validating example. Following that, several illustrative examples are considered. The results are in good agreement with previous published ones.

Modeling of crack propagation by finite element method under mixed mode conditions is of prime importance in fracture mechanics. This paper describes an application of finite element method to the analysis of mixed mode crack growth in linear elastic fracture mechanics. Crack growth process is simulated by an incremental crack-extension analysis based on the maximum principal stress criterion, which is expressed in terms of the stress intensity factor.In this paper, a procedure to correct the direction of crack propagation in the analysis of finite element is presented to ensure that a unique final crack path is achieved for different analysis of a problem by using different increments of crack. For each increment of crack extension, finite element method is applied to perform a single region stress analysis of the cracked structure. Results of this incremental crack extension analysis are presented for several geometries.

Modeling of crack propagation by a finite element method under mixed mode conditions is of prime importance in the fracture mechanics. This article describes an application of finite element method to the analysis of mixed mode crack growth in linear elastic fracture mechanics. Crack - growth process is simulated by an incremental crack-extension analysis based on the maximum principal stress criterion which is expressed in terms of the stress intensity factor. In this paper a procedure is employed to correct direction of crack propagation to ensure that a unique final crack path is achieved for different analysis of a problem by using different increments of crack. For each increment of crack extension, finite element method is applied to perform a single - region stress analysis of the cracked structure. Results of this incremental crack – extension analysis are presented for several geometries.

Nowadays, functionally graded materials (FGM) are widely used in many industrial, aerospace and military fields. On the other hand, the interest in the use of shrink-fitted assemblies is increasing for designing composite tubes, high-pressure vessels, rectors and tanks. Although extensive researches exist on thick-walled cylindrical shells, not many researches have been done on shrink-fitted thick FGM cylinders. In this paper, an analytical formulation for shrink-fitted of axisymmetric thick-walled FGM cylinders based on the linear plane elasticity theory is presented. The stresses and displacement fields in thick cylindrical shells are calculated using the real, Repeated and complex roots of characteristic equation. The displacements and stresses resulted are depicted for a case study. The results show that the material composition variation had evident effects on shrink-fit pressure in the intersection area of two fitted tubes. The value of this pressure affects radial and hoop stress distribution in FG circular cylinders walls.

Determination of the deformation length is one of the first steps in roll forming design. Roll forming industries are very interested in explicit simple relationsfor prediction the deformation length without using trail-and-error methods at workshop or time consuming finite element simulations. In this paper, elastic properties and work-hardening behaviour of the strip are considered in addition to geometric specifications of a channel section in order to study the strip deformation. Some relations are introduced for the deformation work consumed during the longitudinal stretching of the flange and the transverse bending of the bend line for a linear hardening elastic-plastic strip. Finally, a relation are developed for the deformation length. Theoretical results show that the forming angle, the flange length and the Young’s modulus increase the deformation length and the strip thickness, the initial strength and the tangential modulus at the elastic-plastic range decrease the deformation length. The Poisson’s ratio has no effect on the deformation length. However, the bend radius to the strip thickness ratio increases the deformation length. The elastic properties and work-hardening behaviour result in a deformation length which is shorter than the rigid–perfectly plastic deformation length which was proposed by Bhattacharyya.