In this paper a method for solving a General fuzzy linear system with crisp solution is considered. We consider the method in special case when the elements of the coefficient matrix and the right hand side are trapezoidal fuzzy numbers. The method in detail is discussed and followed by theorem and illustrated by solving some examples.

In this paper, a method is presented for the solution of General frictionless nonlinear contact-impact problems called "United Elements". In the fields of mechanics and structures, contact-impact problems are considered one of the most difficult fields. The reason is that in addition to the presence of material and geometric nonlinearities, the last possible nonlinearity, the boundary condition nonlinearity, enters the problem. In fact, the boundary condition will be obtained as a part of the solution. The usual methods for these problems stem from Lagrange Multipliers and Penalty Function methods, and in each method, the simultaneous satisfaction of contact constraints and equilibrium equations is sought. Both of these methods have some intrinsic mathematical and numerical deficiencies which relates to the quality of boundary condition exertion. Therefore, in this work, bayed on the physical concepts and mechanics principals, another method is used for the solution of contact-impact problems. The method is" not only suitable for computer programming but also compensates the deficiencies of the other methods.

A numerical method for solving nonlinear Fredholm-Volterra integral equations of General type is presented. This method is based on replacement of unknown function by truncated series of well known Chebyshev expansion of functions. The quadrature formulas which we use to calculate integral terms have been estimated by Fast Fourier Transform (FFT). This is a grate advantage of this method which has lowest operation count in contrast to other early methods which use operational matrices (with huge number of operations) or involve intermediate numerical techniques for evaluating intermediate integrals which presented in integral equation or solve special case of nonlinear integral equations. Also rate of convergence are given. The numerical examples show the applicability and accuracy of the method.

In this paper, an analytical formulation of FGM axisymmetric thick-walled cylinders, based on the first shear deformation theory (FSDT) is presented. The displacements and maximum stress in thick cylindrical shells are calculated. solutions are obtained under Generalized plane strain assumptions. It is assumed that the material is isotropic and heterogeneous with constant Poissn's ratio and radially varying elastic modulu. The results have been compared with findings of the plane elasticity theory (PET).