• Structural Engineering and Mechanics
• /
• 제25권2호
• /
• pp.201-217
• /
• 2007

A harmonic type differential quadrature approach for nonlinear dynamic analysis of multi-degree-of-freedom systems has been developed. A series of numerical examples is conducted to assess the performance of the HDQ method in linear and nonlinear dynamic analysis problems. Results are compared with the existing solutions available from other analytical and numerical methods. In all cases, the results obtained are quite accurate.

• Structural Engineering and Mechanics
• /
• 제22권3호
• /
• pp.331-349
• /
• 2006

The stresses and deflections in a laminated rectangular plate under thermal vibration are determined by using the moving least squares differential quadrature (MLSDQ) method based on the first order shear deformation theory. The weighting coefficients used in MLSDQ approximation are obtained through a fast computation of the MLS shape functions and their partial derivatives. By using this method, the governing differential equations are transformed into sets of linear homogeneous algebraic equations in terms of the displacement components at each discrete point. Boundary conditions are implemented through discrete grid points by constraining displacements, bending moments and rotations of the plate. Solving this set of algebraic equations yields the displacement components. Then substituting these displacements into the constitutive equation, we obtain the stresses. The approximate solutions for stress and deflection of laminated plate with cross layer under thermal load are obtained. Numerical results show that the MLSDQ method provides rapidly convergent and accurate solutions for calculating the stresses and deflections in a multi-layered plate of cross ply laminate subjected to thermal vibration of sinusoidal temperature including shear deformation with a few grid points.

• Structural Engineering and Mechanics
• /
• 제34권2호
• /
• pp.231-245
• /
• 2010

Vibration analysis of rotating beams is a topic of constant interest in mechanical engineering. The differential quadrature method (DQM) is used to obtain the natural frequencies of free transverse vibration of rotating beams. As it is known the DQM offers an accurate and useful method for solution of differential equations. And it is an effective technique for solving this kind of problems as it is shown comparing the obtained results with those available in the open literature and with those obtained by an independent solution using the finite element method. The beam model is based on the Timoshenko beam theory.

• Structural Engineering and Mechanics
• /
• 제37권5호
• /
• pp.529-542
• /
• 2011

Three dimensional solutions for free vibrations analysis of functionally graded fiber reinforced cylindrical panel are presented, using differential quadrature method (DQM). The orthotropic panel is simply supported at the edges and is assumed to have an arbitrary variation of reinforcement volume fraction in the radial direction. Suitable displacement functions that identically satisfy the simply supported boundary condition are used to reduce the equilibrium equations to a set of coupled ordinary differential equations with variable coefficients, which can be solved by differential quadrature method to obtain natural frequencies. The main contribution of this work is presenting useful results for continuous grading of fiber reinforcement in the thickness direction of a cylindrical panel and comparison with similar discrete laminate composite ones. Results indicate that significant improvement is found in natural frequency of a functionally graded fiber reinforced composite panel due to the reduction in spatial mismatch of material properties.

• Structural Engineering and Mechanics
• /
• 제75권6호
• /
• pp.737-746
• /
• 2020

This paper attempts to investigate the free vibration of functionally graded material beams with nonuniform width based on the nonlocal elasticity theory. The theoretical formulations are established following the Euler-Bernoulli beam theory, and the governing equations of motion of the system are derived from the minimum total potential energy principle using the nonlocal elasticity theory. In addition, the Differential Quadrature Method (DQM) is applied, along with the Chebyshev-Gauss-Lobatto polynomials, in order to determine the weighting coefficient matrices. Furthermore, the effects of the nonlocal parameter, cross-section area of the functionally graded material (FGM) beam and various boundary conditions on the natural frequencies are examined. It is observed that the nonlocal parameter and boundary conditions significantly influence the natural frequencies of the functionally graded material beam cross-section. The results obtained, using the Differential Quadrature Method (DQM) under various boundary conditions, are found in good agreement with analytical and numerical results available in the literature.

• 한국소음진동공학회논문집
• /
• 제11권9호
• /
• pp.462-474
• /
• 2001

In this paper, Generalized Differential Quadrature Method is applied to the buckling analysis of built-up columns without or with stay plates. numerical analysis using GDQM is carried out for various boundary conditions(simply supported conditions, fixed conditions, fixed-simply supported conditions), dimensionless stiffness parameter and dimensionless inertia moment parameter. The accuracy and convergence of solutions are compared with exact solutions of Gjelsvik to validate the results of GDQM. Results obtained by this method are as follows. 91) This method can yield the accurate numerical solutions using few grid points. (2) The buckling load of built-up column increases as the dimensionless stiffness parameter decreases. (3) The effects of boundary conditions on the buckling load are not considerable as the dimensionless stiffness parameter increases. (4) The buckling load of built-up column increases due to the stay plate.

• Structural Engineering and Mechanics
• /
• 제10권5호
• /
• pp.451-462
• /
• 2000

Buckling loads are determined for thin isotropic circular cylindrical shell panels subject to radial pressure using the new differential quadrature method. The Budiansky stability theory serves as the basis of the analysis. For this problem involving four boundary lines a two-dimensional approach is used, and a detailed convergence study is carried out to determine the appropriate analysis parameters for the method. Numerical results are determined for a total of twelve cylindrical shell panel cases for a number of different boundary support conditions. The results are compared with analytical and finite element method results. Conclusions are drawn about the technical significance of the results and the solution process.

• 한국강구조학회 논문집
• /
• 제16권1호통권68호
• /
• pp.81-89
• /
• 2004

구조물과 같은 아치의 진동해석은 많은 산업분야에서 다양하게 적용되기 때문에 공학적 문제에 중요한 주제이다. 특히 변화하는 단면형상을 가지는 아치는 질량이나 강도를 최적화 하거나 특별한 구조물이나 요구조건들을 만족하기 위해서 폭넓게 사용되어 진다. 최근에는 일반화 미분구적법(GDQM)이나 미분변환법(DTM)은 각각 Shu와 Zou에 의해서 제안이 되었다. 연구에서는 변화하는 단면형상을 가지는 아치의 진동해석이 일반화 미분구적법과 미분변환법을 적용하였다. 변화하는 단면형상을 가지는 아치에 대하여 지배방정식이 유도되어졌으며, 미분변환과 일반화 미분구적법의 개념이 간단히 소개되었다. 변화하는 단면형상을 가지는 아치의 무차원화된 고유진동수가 다양한 경계조건에 대해서 구해졌으며, 이러한 방법들에 의해서 얻어지는 결과들은 선행연구와 비교 되어졌다. 일반화 미분구적법과 미분변환법은 변화하는 단면형상을 가지는 아치의 진동문제를 해석함에 있어서 빠른 수렴, 정확도, 효율성, 유효성을 보인다.

• 한국안전학회지
• /
• 제12권4호
• /
• pp.220-229
• /
• 1997

곡선보(curved beam)의 등분포 하중하에서 평면내(in-plane)와 평면의(out-of-plane)의 좌굴(buckling)을 해석하는데 differential quadrature method (DQM)을 이용하여 다양한 경계조건(boundary conditions)과 굽힘각(opening angles)에 따른 입계하중(critical loads)을 계산하였다. DQM의 해석결과는 해석적 해답(exact solution) 또는 다른 수지해석 결과와 비교하였으며, DQM은 적은 요소(grid points)를 사용하여 정확한 해석결과를 보여주었다. 두 경계조건(고정-고정, 고정-단순지지)하에서 새로운 결과를 또한 제시하였다.

• Steel and Composite Structures
• /
• 제2권2호
• /
• pp.99-112
• /
• 2002

The differential quadrature method (DQM) is a numerical technique of rather recent origin, which by its continually increasing applications in different problems of engineering, is a competing alternative to the conventional numerical techniques for the solution of initial and boundary value problems. The work of this paper concerns the application of the DQM in the area of the buckling of multi layered orthotropic composite plates with various boundary conditions the buckling of multi layered composite plates with constant and variable thickness under axial compressive static loading is considered. The effects of fiber orientation and boundary conditions on static behavior of composite plates are presented. The comparison of results from the present method and those obtained from NISA II software shows the accuracy and reliability of this method.