Showing papers by "Reza Attarnejad published in 2013"
TL;DR: In this paper, structural analysis of axially functionally graded tapered beams is studied from a mechanical point of view using a finite element method using the concept of basic displacement functions (BDFs).
Abstract: In this article, structural analysis of axially functionally graded tapered beams is studied from a mechanical point of view using a finite element method. Introducing the concept of basic displacement functions (BDFs), it is shown that exact shape functions could be explicitly obtained in terms of BDFs via application of basic principles of structural mechanics. BDFs are obtained using the unit-dummy-load method. Carrying out static analysis, it is verified that exact results are provided by applying one or a few elements. The competency of the present element in stability and free vibration analyses is verified through several numerical examples.
49 citations
TL;DR: In this article, a 2D-DTM was applied to derive the natural frequencies of variable thickness thin plates with different boundary conditions, and several numerical examples have been carried out to demonstrate the applicability and accuracy of the present method in free vibration analysis of both uniform and variable thickness.
Abstract: This paper aims at extending the application of two-dimensional differential transform method (2D-DTM) to study the free vibration of thin plates with arbitrarily varying thickness. First, the differential equation of motion governing thin plates with varying thickness is derived using Hamilton’s principle. Afterward, the 2D-DTM, a numerical method which is capable of reducing the size of computational work and can be applied to various types of differential equations, has been applied to derive the natural frequencies of variable thickness thin plates with different boundary conditions. Several numerical examples have been carried out to demonstrate the applicability and accuracy of the present method in free vibration analysis of both uniform plates and plates with variable thickness.
33 citations
TL;DR: In this paper, basic displacement functions (BDFs) were derived for arbitrarily curved non-uniform beams, including the effects of shear deformation and extensibility of neutral axis.
Abstract: Basic Displacement Functions (BDFs) are introduced and derived using the basic principles of structural mechanics. BDFs are then utilized to obtain new shape functions for arbitrarily curved non-uniform beams, including the effects of shear deformation and extensibility of neutral axis. The main virtue of the proposed shape functions is their susceptibility to the variations in cross-sectional area, moment of inertia, and curvature along the axis of the beam element. Competence of the present method in static and free vibration analyses, as well as its applicability to the special case of straight Timoshenko beam has been verified through several numerical examples.
22 citations
TL;DR: In this article, a finite element approach for free vibration analysis of rotating tapered beams made of functionally graded (FG) materials is presented. Butts et al. developed a new type of unit-dummy load method, namely, basic displacement functions (BDFs) derived from which the exact shape functions are obtained.
Abstract: Free vibration of rotating tapered beams made of functionally graded (FG) materials is studied through a finite element approach. A new element is introduced that takes advantage of the exact shape functions for nonrotating tapered FG beam elements. Developing a new type of unit-dummy-load method, special functions, namely, basic displacement functions (BDFs) are derived from which the exact shape functions are obtained. The element is employed in free vibration analysis where the effects of taper ratio, rotational speed, and hub radius are investigated. The present results could be efficiently used for future research works in this field.
20 citations