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Article
Publication date: 1 December 2004

Gh. R. Heravi and R. Attarnejad

The purpose of this paper is to improve the effectiveness of ordinary reduction methods performance, in nonlinear dynamic analysis. In this paper, the error vector due to…

Abstract

The purpose of this paper is to improve the effectiveness of ordinary reduction methods performance, in nonlinear dynamic analysis. In this paper, the error vector due to linear and nonlinear dynamic analysis in generalized subspaces is extracted, and is decomposed into two independent components, namely outside and inside components. Based on the inside error component, a new iterative reduction method, one‐dimensional generalized subspace procedure (ODGS), is proposed where an innovative criterion is defined for updating the base vectors necessary for stiffness changes in nonlinear dynamic analysis. In this study, the performance of ODGS for linear and nonlinear analysis of elastodynamic systems including non‐proportional damping based on the Ritz generalized subspace has been proposed. Numerical examples show the competency of the proposed method in both economy and exactness. Time saving gained from the ODGS method could be recompensed to get much more accurate results consuming the same CPU time. This iterative method is more effective than the ordinary reduction methods. Since the method is directly derived from the discrete model based on the finite element method (FEM), the complexity of the structure does not affect directly the effectiveness of ODGS. Therefore, whenever the FEM is effectively capable to represent the topology of the structure, the ODGS results will also represent the system response properly. Same as any other reduction methods, accuracy of this iterative reduction method is directly related to the number of selected Ritz vectors, according to convergence criterion.

Details

Engineering Computations, vol. 21 no. 8
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 24 August 2010

Reza Attarnejad

Purpose — Analysis of nonprismatic members has received a great deal attention from designers and engineers due to their ability in satisfaction of architectural and…

Abstract

Purpose — Analysis of nonprismatic members has received a great deal attention from designers and engineers due to their ability in satisfaction of architectural and aesthetic necessities. Using these structural members in complex structures such as aircrafts, turbine blades and space vehicles, exact static and dynamic analyses of these members become more significant. Based on structural/mechanical principles, the purpose of this paper is to present a new method to evaluate exact structural matrices for nonprismatic Euler‐Bernoulli beam elements. Design/methodology/approach — Through introducing the concept of basic displacement functions (BDFs), it is shown that exact shape functions are derived in terms of BDFs. BDFs and their derivatives have structural interpretations; therefore, they are obtained via application of flexibility method. Unlike the conventional methods, which are almost categorized as displacement‐based methods, the flexibility basis of the method ensures the true satisfaction of equilibrium equations at any interior point of the element. Findings — The exact shape functions and consequently structural matrices are derived for general nonprismatic beam elements. Numerical examples are carried out to determine static deflection and natural frequencies, and the results are highly competent with the other methods in literature. Research limitations/implications — The method can be extended to structural analysis of curved beams, plates and shells as well. Moreover, it is possible to derive exact dynamic shape functions via BDFs by solving the governing equation for transverse vibration of beams. Theoretically, the method faces limitation in analysis of nonprismatic beams that converge to a point where cross‐sectional area and moment of inertia are equal to zero. Practical implications — The development of this idea, i.e. BDFs seems to lead to promotive novel approaches for structural analysis and could be a breaking point for developing new elements for plates and shells as it was shown for beam elements. Originality/value — The paper's introduction of special functions, namely BDFs and their application, in both static and dynamic analyses of structures, could be a breaking point in analysis procedures.

Details

Engineering Computations, vol. 27 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 17 July 2009

Latif Ebrahimnejad and Reza Attarnejad

The purpose of this paper is to introduce a novel approach to solving linear systems arising from applying a Boundary Element Method (BEM) to elasticity problems.

Abstract

Purpose

The purpose of this paper is to introduce a novel approach to solving linear systems arising from applying a Boundary Element Method (BEM) to elasticity problems.

Design/methodology/approach

The key idea is based on using wavelet transforms as a tool to change dense and fully populated matrices of BEM systems into sparse matrices. Wavelets are then used again to produce an algorithm to solve the resultant sparse linear systems. The wavelet transformation part of the method can be added as a black box to existing BEM codes.

Findings

Numerical results focusing on the sensitivity of the solution for various physical variables to the thresholding parameters, and savings in computer time and memory are presented. The results show that the proposed method is efficient for large problems.

Research limitations/implications

Application of the proposed method is restricted to problems with number of DOF equal to an integer power of 2.

Originality/value

The novel algorithm to solve transformed algebraic linear equations uses NS‐form of the modified matrix, taking the advantage of the hierarchical nature of Multi‐Resolution Analysis (MRA) to decompose a parent system into descendant systems with reduced size. These smaller systems are then solved iteratively using generalized minimal residual method.

Details

Engineering Computations, vol. 26 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 9 March 2010

M.R. Koohkan, R. Attarnejad and M. Nasseri

The purpose of this paper is to propose a semi‐analytical method for studying the interaction between reservoir and concrete gravity dams.

Abstract

Purpose

The purpose of this paper is to propose a semi‐analytical method for studying the interaction between reservoir and concrete gravity dams.

Design/methodology/approach

The reservoir is assumed to be unbounded at the far end and the solution is sought for incompressible and in‐viscid fluid. A concrete gravity dam is assumed to behave as a cantilever beam of variable section, and the inclination of the neutral axis is ignored.

Findings

It is shown that use of the differential quadrature method (DQM), with a few grid points in conjunction with the finite difference method (FDM), yields an acceptable convergence of results. Comparing the results of the proposed method with those of the literature shows the competency of the method.

Originality/value

DQM for space derivatives and FDM for time derivatives are used to discretize the partial differential equation of motion.

Details

Engineering Computations, vol. 27 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 2 October 2018

Anup Pydah and Aditya Sabale

There exists a clear paucity of models for curved bi-directional functionally graded (BDFG) beams wherein the material properties vary along the axis and thickness of the…

Abstract

Purpose

There exists a clear paucity of models for curved bi-directional functionally graded (BDFG) beams wherein the material properties vary along the axis and thickness of the beam simultaneously; such structures may help fulfil practical design requirements of the future and improve structural efficiency. In this context, the purpose of this paper is to extend the analytical model developed earlier to thick BDFG circular beams by using first-order shear deformation theory which allows for a non-zero shear strain distribution through the thickness of the beam.

Design/methodology/approach

Smooth functional variations of the material properties have been assumed along the axis and thickness of the beam simultaneously. The governing equations developed have been solved analytically for some representative determinate circular beams. In order to ascertain the effects of shear deformation in these structures, the total strain energy has been decomposed into its bending and shear components and the effects of the beam thickness and the arch angle on the shear energy component have been studied.

Findings

Closed-form exact solutions involving through-the-thickness integrals carried out numerically are presented for the bending of circular beams under the action of a variety of concentrated/distributed loads.

Originality/value

The results clearly indicate the importance of capturing shear deformation in thick BDFG beams and demonstrate the capability of tuning the response of these beams to fit a wide variety of structural requirements.

Details

Multidiscipline Modeling in Materials and Structures, vol. 15 no. 1
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 19 September 2017

Puneet Kumar and J. Srinivas

The purpose of this paper is to perform a numerical analysis on the static and dynamic behaviors of beams made up of functionally graded carbon nanotube (FG-CNT…

Abstract

Purpose

The purpose of this paper is to perform a numerical analysis on the static and dynamic behaviors of beams made up of functionally graded carbon nanotube (FG-CNT) reinforced polymer and hybrid laminated composite containing the layers of carbon reinforced polymer with CNT. Conventional fibers have higher density as compared to carbon nanotubes (CNTs), thus insertion of FG-CNT reinforced polymer layer in fiber reinforced composite (FRC) structures makes them sustainable candidate for weight critical applications.

Design/methodology/approach

In this context, stress and strain formulations of a multi-layer composite system is determined with the help of Timoshenko hypothesis and then the principle of virtual work is employed to derive the governing equations of motion. Herein, extended rule of mixture and conventional micromechanics relations are used to evaluate the material properties of carbon nanotube reinforced composite (CNTRC) layer and FRC layer, respectively. A generalized eigenvalue problem is formulated using finite element approach and is solved for single layer FG-CNTRC beam and multi-layer laminated hybrid composite beam by a user-interactive MATLAB code.

Findings

First, the natural frequencies of FG-CNTRC beam are computed and compared with previously available results as well as with Ritz approximation outcomes. Further, free vibration, bending, and buckling analysis is carried out for FG-CNTRC beam to interpret the effect of different CNT volume fraction, number of walls in nanotube, distribution profiles, boundary conditions, and beam-slenderness ratios.

Originality/value

A free vibration analysis of hybrid laminated composite beam with two different layer stacking sequence is performed to present the advantages of hybrid laminated beam over the conventional FRC beam.

Details

Multidiscipline Modeling in Materials and Structures, vol. 13 no. 4
Type: Research Article
ISSN: 1573-6105

Keywords

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