• Structural Engineering and Mechanics
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• v.72 no.1
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• pp.131-139
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• 2019

According to the properties of monoclinic materials, the normal and shear stresses are depending on both normal and shear strains. In the current investigation, the static analysis of monoclinic plates based on three dimensional elasticity theory is investigated. New governing equations and boundary conditions are derived for monoclinic plates and the Differential Quadrature Method (DQM) is used to solve the static problem. In our method of solution, no approximation is used and the DQM is adopted in all directions. By showing the differences between our results and the results for especially orthotropic plates, one can find that it is worth to investigate the monoclinic plates to have more accurate results.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.4
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• pp.629-638
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• 2002

This paper deals with the free vibration analysis of compressive tapered members resting on elastic foundation using the Differential Quadrature Method. Based on the differential equation subjected to the boundary conditions, adopted from the open literature, which governs the free vibrations of such member, this equation is applied to the Differential Quadrature Method. For computing natural frequencies, the numerical procedures are developed by QR Algorithm, in which the Chebyshev-Gauss-Lobatto method is used for choosing the grid points. The numerical methods developed herein for computing natural frequencies are programmed in FORTRAN code, and all solutions obtained in this study are quite agreed with those in the open literature.

• Journal of the Korean Society of Safety
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• v.17 no.1
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• pp.99-104
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• 2002

DQM(differential quadrature method) is applied to computation of eigenvalues of the equations of motion governing the free in-plane vibration for circular curved beams including mid-surface extension and the effects of rotatory inertia. Fundamental frequencies are calculated for the members with various end conditions and opening angles. The results are compared with numerical solutions by other methods for cases in which they are available. The differential quadrature method gives good accuracy even when only a limited number of grid points is used.

• Steel and Composite Structures
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• v.12 no.2
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• pp.129-147
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• 2012

In this paper, the thermal buckling analysis of rectangular composite laminated plates is investigated using the Differential Quadrature (DQ) method. The composite plate is subjected to a uniform temperature distribution and arbitrary boundary conditions. The analysis takes place in two stages. First, pre-buckling forces due to a temperature rise are determined by using a membrane solution. In the second stage, the critical temperature is predicted based on the first-order shear deformation theory. To verify the accuracy of the method, several case studies were used and the numerical results were compared with those of other published literatures. Moreover, the effects of several parameters such as aspect ratio, fiber orientation, modulus ratio, and various boundary conditions on the critical temperature were examined. The results confirm the efficiency and accuracy of the DQ method in dealing with this class of engineering problems.

• Structural Engineering and Mechanics
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• v.33 no.6
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• pp.675-696
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• 2009

In this paper, a unified solution method is presented for the classical beam theory. In Strength of Materials approach, the geometry, material properties and load system are known and related with the unknowns of forces, moments, slopes and deformations by applying a classical differential analysis in addition to equilibrium, constitutive, and kinematic laws. All these relations are expressed in a unified formulation for the classical beam theory. In the special case of simple beams, a system of four linear ordinary differential equations of first order represents the general mechanical behaviour of a straight beam. These equations are solved using the numerical differential quadrature method (DQM). The application of DQM has the advantages of mathematical consistency and conceptual simplicity. The numerical procedure is simple and gives clear understanding. This systematic way of obtaining influence line, bending moment, shear force diagrams and deformed shape for the beams with geometric and load discontinuities has been discussed in this paper. Buckling loads and natural frequencies of any beam prismatic or non-prismatic with any type of support conditions can be evaluated with ease.

• Structural Engineering and Mechanics
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• v.70 no.6
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• pp.765-779
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• 2019

Most of the existing evaluation criteria of vibration serviceability rely on the peak acceleration of the structure rather than that of the people keeping their own body unmoved on the structure who is the real receiver of structural vibrations. In order to accurately assess the vibration serviceability, therefore, a full path assessment approach of vibration serviceability based on vibration source, path and receiver is not only tentatively proposed in this paper, taking the peak acceleration of receiver into account, but also introduce a probability procedure to provide more instructive information instead of a single value. In fact, semi-rigid supported on both sides of the structure is more consistent with the actual situation than simply supported or clamped due to the application of the prefabricated footbridge structures. So, the footbridge is regarded as a beam with semi-rigid supported on both sides in this paper. The differential quadrature-integral quadrature coupled method is not only to handle different type of boundary conditions, but also after being further modified via the introduction of an approximation procedure in this work, the time-varying system problem caused by human-structure interaction can be solved well. The analytical results of numerical simulations demonstrate that the modified differential quadrature-integral quadrature coupled method has higher reliability and accuracy compared with the mode superposition method. What's more, both of the two different passive control measures, the tuned mass damper and semi-rigid supported, have good performance for reducing vibrations. Most importantly, semi-rigid supported is easier to achieve the objective of reducing vibration compared with tuned mass damper in design stage of structure.

• Structural Engineering and Mechanics
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• v.45 no.4
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• pp.569-594
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• 2013

The free vibration of axially functionally graded tapered arches including shear deformation and rotatory inertia are studied through solving the governing differential equation of motion. Numerical results are presented for circular, parabolic, catenary, elliptic and sinusoidal arches with hinged-hinged, hinged-clamped and clamped-clamped end restraints. In this study Differential Quadrature element of lowest order (DQEL) or Lagrangian Interpolation technique is applied to solve the problems. Three general taper types for rectangular section are considered. The lowest four natural frequencies are calculated and compared with the published results.

• Structural Engineering and Mechanics
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• v.22 no.3
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• pp.279-292
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• 2006

A new approach using the differential quadrature method (DQM) is derived for analysis of non-uniform beams resting on nonlinear media in this study. The influence of velocity dependent viscous damping and strain rate dependent viscous damping is investigated. The results solved using the DQM have excellent agreement with the results solved using the FEM. Numerical results indicated that the DQM is valid and efficient for non-uniform beams resting on non-linear media.

• Steel and Composite Structures
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• v.46 no.6
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• pp.759-772
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• 2023

This manuscript presents a comprehensive mathematical model to investigate buckling stability and postbuckling response of bio-inspired composite beams with helicoidal orientations. The higher order shear deformation theory as well as the Timoshenko beam theories are exploited to include the shear influence. The equilibrium nonlinear integro-differential equations of helicoidal composite beams are derived in detail using the energy conservation principle. Differential integral quadrature method (DIQM) is employed to discretize the nonlinear system of differential equations and solve them via the Newton iterative method then obtain the response of helicoidal composite beam. Numerical calculations are carried out to check the validity of the present solution methodology and to quantify the effects of helicoidal rotation angle, elastic foundation constants, beam theories, geometric and material properties on buckling, postbuckling of bio-inspired helicoidal composite beams. The developed model can be employed in design and analysis of curved helicoidal composite beam used in aerospace and naval structures.

• Structural Engineering and Mechanics
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• v.17 no.5
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• pp.671-690
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• 2004

A meshless method with novel variation of point collocation by finite mixture approximation is developed in this paper, termed the meshless finite mixture (MFM) method. It is based on the finite mixture theorem and consists of two or more existing meshless techniques for exploitation of their respective merits for the numerical solution of partial differential boundary value (PDBV) problems. In this representation, the classical reproducing kernel particle and differential quadrature techniques are mixed in a point collocation framework. The least-square method is used to optimize the value of the weight coefficient to construct the final finite mixture approximation with higher accuracy and numerical stability. In order to validate the developed MFM method, several one- and two-dimensional PDBV problems are studied with different mixed boundary conditions. From the numerical results, it is observed that the optimized MFM weight coefficient can improve significantly the numerical stability and accuracy of the newly developed MFM method for the various PDBV problems.