Xiaojun Huang¹, Liaojun Zhang^2,*, Hanbo Cui¹, Gaoxing Hu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.140, No.2, pp. 1647-1668, 2024, DOI:10.32604/cmes.2024.049124 - 20 May 2024

Abstract This study proposes an effective method to enhance the accuracy of the Differential Quadrature Method (DQM) for calculating the dynamic characteristics of functionally graded beams by improving the form of discrete node distribution. Firstly, based on the first-order shear deformation theory, the governing equation of free vibration of a functionally graded beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam axial displacement, transverse displacement, and cross-sectional rotation angle by considering the effects of shear deformation and rotational inertia of the beam cross-section. Then, ignoring the shear deformation of the… More >

Geeta Arora¹, Pinkey Chauhan², Muhammad Imran Asjad³, Varun Joshi¹, Homan Emadifar⁴, Fahd Jarad^5,6,7,*

Computer Systems Science and Engineering, Vol.45, No.3, pp. 2647-2658, 2023, DOI:10.32604/csse.2023.032404 - 21 December 2022

Abstract The term ‘optimization’ refers to the process of maximizing the beneficial attributes of a mathematical function or system while minimizing the unfavorable ones. The majority of real-world situations can be modelled as an optimization problem. The complex nature of models restricts traditional optimization techniques to obtain a global optimal solution and paves the path for global optimization methods. Particle Swarm Optimization is a potential global optimization technique that has been widely used to address problems in a variety of fields. The idea of this research is to use exponential basis functions and the particle swarm More >

Francesco Tornabene^*, Matteo Viscoti, Rossana Dimitri

CMES-Computer Modeling in Engineering & Sciences, Vol.133, No.3, pp. 719-798, 2022, DOI:10.32604/cmes.2022.022210 - 03 August 2022

Abstract The article proposes an Equivalent Single Layer (ESL) formulation for the linear static analysis of arbitrarily-shaped shell structures subjected to general surface loads and boundary conditions. A parametrization of the physical domain is provided by employing a set of curvilinear principal coordinates. The generalized blending methodology accounts for a distortion of the structure so that disparate geometries can be considered. Each layer of the stacking sequence has an arbitrary orientation and is modelled as a generally anisotropic continuum. In addition, re-entrant auxetic three-dimensional honeycomb cells with soft-core behaviour are considered in the model. The unknown… More > Graphic Abstract

Xiaojun Huang^1,2, Liaojun Zhang^1,*, Renyu Ge², Hanbo Cui², Zhedong Xu²

CMES-Computer Modeling in Engineering & Sciences, Vol.132, No.1, pp. 23-41, 2022, DOI:10.32604/cmes.2022.019765 - 02 June 2022

Abstract In the current research, an effective differential quadrature method (DQM) has been developed to solve natural frequency and vibration modal functions of circular section beams along radial functional gradient. Based on the high-order theory of transverse vibration of circular cross-section beams, lateral displacement equation was reconstructed neglecting circumferential shear stress. Two equations coupled with deflection and rotation angles were derived based on elastic mechanics theory and further simplified into a constant coefficient differential equation with natural frequency as eigenvalue. Then, differential quadrature method was applied to transform the eigenvalue problem of the derived differential equation… More >

Yongqiang Yang^1,2, Zhongmin Wang^3,*

Sound & Vibration, Vol.53, No.3, pp. 51-64, 2019, DOI:10.32604/sv.2019.04004

Abstract Transverse vibration and stability analysis of circular plate subjected to follower force and thermal load are analyzed . B ased on the thin plate theory in involving the variable temperature, the differential equation of transverse vibration for the axisymmetric circular plate subjected to follower force and thermal load is established. Then, the differential equation of vibration and corresponding boundary conditions are discretized by the differential quadrature method. Meanwhile, the generalized eigenvalue under three different boundary conditions are calculated. In this case, the change curve of the first order dimensionless complex frequency of the circular plate More >

Jiun-Yu Wu^1,2, Hui-Ching Wang¹, Ming-I Char¹, Bo-Chen Tai¹

CMC-Computers, Materials & Continua, Vol.28, No.3, pp. 261-280, 2012, DOI:10.3970/cmc.2012.028.261

Abstract In this paper, we use the Local adaptive differential quadrature method (La-DQM) to solve multi-dimensional inverse scattering problem (ISP) of wave propagation. The La-DQM uses fictitious points to tackle the high-order differential equations with multi-boundary conditions and numerical results can be obtain directly in the calculation process. Six examples show the effectiveness and accuracy of the La-DQM in providing excellent estimates of unknown wave propagation from the given data. We think that the scheme is applicable to the ISP of wave propagation. Numerical results show that the La-DQM is powerful method for solving the inverse More >

Ying-Hsiu Shen, Chein-Shan Liu

The International Conference on Computational & Experimental Engineering and Sciences, Vol.16, No.3, pp. 77-78, 2011, DOI:10.3970/icces.2011.016.077

Abstract When the local differential quadrature (LDQ) has been successfully applied to solve two-dimensional problems, the global method of DQ still has a problem by requiring to solve the inversions of ill-posed matrices. Previously, when one uses (n-1)th order polynomial test functions to determine the weighting coefficients with n grid points, the resultant nxn Vandermonde matrix is highly ill-conditioned and its inversion is hard to solve. Now we use (m-1)th order polynomial test functions by n grid points that the size of Vandermonde matrix is mxn, of which m is much less than n. We find More >

Jiun-Yu Wu^1,2, Chih-Wen Chang³

CMC-Computers, Materials & Continua, Vol.25, No.3, pp. 215-238, 2011, DOI:10.3970/cmc.2011.025.215

Abstract In this paper, we employ the differential quadrature method (DQM) to tackle the inverse heat conduction problem (IHCP) of heat source. These advantages of this numerical approach are that no a priori presumption is made on the functional form of the estimates, and that evaluated heat source can be obtained directly in the calculation process. Seven examples show the effectiveness and accuracy of our algorism in providing excellent estimates of unknown heat source from the given data. We find that the proposed scheme is applicable to the IHCP of heat source. Even though the noise More >

Ying-Hsiu Shen¹, Chein-Shan Liu^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.2, pp. 157-178, 2011, DOI:10.3970/cmes.2011.071.157

Abstract When the local differential quadrature (LDQ) has been successfully applied to solve two-dimensional problems, the global method of DQ still has a problem by requiring to solve the inversions of ill-posed matrices. Previously, when one uses (n-1)th order polynomial test functions to determine the weighting coefficients with n grid points, the resultant n ×n Vandermonde matrix is highly ill-conditioned and its inversion is hard to solve. Now we use (m-1)th order polynomial test functions by n grid points that the size of Vandermonde matrix is m×n, of which m is much less than n. We More >

Hua Li¹, Shantanu S. Mulay¹, Simon See²

CMES-Computer Modeling in Engineering & Sciences, Vol.54, No.2, pp. 147-200, 2009, DOI:10.3970/cmes.2009.054.147

Abstract In this paper, the stability characteristics of a novel strong-form meshless method, called the random differential quadrature (RDQ), are studied using the location of zeros or roots of its characteristic polynomials with respect to unit circle in complex plane by discretizing the domain with the uniform or random field nodes. This is achieved by carrying out the RDQ method stability analysis for the 1st-order wave, transient heat conduction and transverse beam deflection equations using both the analytical and numerical approaches. The RDQ method extends the applicability of the differential quadrature (DQ) method over irregular domain,… More >