Ola Ragb¹, Mokhtar Mohamed², Mohamed S. Matbuly¹, Omer Civalek^3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.3, pp. 2193-2217, 2023, DOI:10.32604/cmes.2023.028992

Abstract Four numerical schemes are introduced for the analysis of photocurrent transients in organic photovoltaic devices. The mathematical model for organic polymer solar cells contains a nonlinear diffusion–reaction partial differential equation system with electrostatic convection attached to a kinetic ordinary differential equation. To solve the problem, Polynomial-based differential quadrature, Sinc, and Discrete singular convolution are combined with block marching techniques. These schemes are employed to reduce the problem to a nonlinear algebraic system. The iterative quadrature technique is used to solve the reduced problem. The obtained results agreed with the previous exact one and the finite element method. Further, the effects… More > Graphic Abstract

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

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 optimization technique to find a… More >

Francesco Tornabene^*, Matteo Viscoti, Rossana Dimitri

CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.2, pp. 1393-1468, 2023, DOI:10.32604/cmes.2022.022237

Abstract In the present manuscript, a Layer-Wise (LW) generalized model is proposed for the linear static analysis of doublycurved shells constrained with general boundary conditions under the influence of concentrated and surface loads. The unknown field variable is modelled employing polynomials of various orders, each of them defined within each layer of the structure. As a particular case of the LW model, an Equivalent Single Layer (ESL) formulation is derived too. Different approaches are outlined for the assessment of external forces, as well as for non-conventional constraints. The doubly-curved shell is composed by superimposed generally anisotropic laminae, each of them characterized… 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

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 variables are described employing a… 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

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 into a set of algebraic… More >

Kamil Khan¹, Arshed Ali^1,*, Fazal-i-Haq², Iltaf Hussain³, Nudrat Amir⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.2, pp. 673-692, 2021, DOI:10.32604/cmes.2021.012730

Abstract This article studies the development of two numerical techniques for solving convection-diffusion type partial integro-differential equation (PIDE) with a weakly singular kernel. Cubic trigonometric B-spline (CTBS) functions are used for interpolation in both methods. The first method is CTBS based collocation method which reduces the PIDE to an algebraic tridiagonal system of linear equations. The other method is CTBS based differential quadrature method which converts the PIDE to a system of ODEs by computing spatial derivatives as weighted sum of function values. An efficient tridiagonal solver is used for the solution of the linear system obtained in the first method… More >

Siraj-ul-Islam¹, Arshed Ali^2,*, Aqib Zafar¹, Iltaf Hussain¹

CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.3, pp. 915-935, 2020, DOI:10.32604/cmes.2020.011218

Abstract Differential quadrature method is employed by numerous researchers due to its numerical accuracy and computational efficiency, and is mentioned as potential alternative of conventional numerical methods. In this paper, a differential quadrature based numerical scheme is developed for solving volterra partial integro-differential equation of second order having a weakly singular kernel. The scheme uses cubic trigonometric B-spline functions to determine the weighting coefficients in the differential quadrature approximation of the second order spatial derivative. The advantage of this approximation is that it reduces the problem to a first order time dependent integro-differential equation (IDE). The proposed scheme is obtained in… 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 subjected to the follower force… 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 that the (m-1)th order polynomial… More >

C. Shu^1,2, H. Ding², K.S. Yeo²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 195-206, 2005, DOI:10.3970/cmes.2005.007.195

Abstract Local radial basis function-based differential quadrature (RBF-DQ) method was recently proposed by us. The method is a natural mesh-free approach. It can be regarded as a combination of the conventional differential quadrature (DQ) method with the radial basis functions (RBFs) by means of taking the RBFs as the trial functions in the DQ scheme. With the computed weighting coefficients, the method works in a very similar fashion as conventional finite difference schemes. In this paper, we mainly concentrate on the applications of the method to incompressible flows in the steady and unsteady regions. The multiquadric (MQ) radial basis functions are… More >