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 - 21 January 2021

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… More >

Özkan inik^1,∗, Erkan Ülker², ismail Koç²

Computer Systems Science and Engineering, Vol.35, No.6, pp. 431-440, 2020, DOI:10.32604/csse.2020.35.431

Abstract The location of knot points and estimation of the number of knots are undoubtedly known as one of the most difficult problems in B-Spline curve approximation. In the literature, different researchers have been seen to use more than one optimization algorithm in order to solve this problem. In this paper, Big Bang-Big Crunch method (BB-BC) which is one of the evolutionary based optimization algorithms was introduced and then the approximation of B-Spline curve knots was conducted by this method. The technique of reverse engineering was implemented for the curve knot approximation. The detection of knot 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 - 21 August 2020

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 More >

Hamid Ghasemi¹, Harold S. Park², Xiaoying Zhuang^{3, 4, *}, Timon Rabczuk^{5, 6}

CMC-Computers, Materials & Continua, Vol.65, No.2, pp. 1157-1179, 2020, DOI:10.32604/cmc.2020.08358 - 20 August 2020

Abstract Flexoelectricity is a general electromechanical phenomenon where the electric polarization exhibits a linear dependency to the gradient of mechanical strain and vice versa. The truncated pyramid compression test is among the most common setups to estimate the flexoelectric effect. We present a three-dimensional isogeometric formulation of flexoelectricity with its MATLAB implementation for a truncated pyramid setup. Besides educational purposes, this paper presents a precise computational model to illustrate how the localization of strain gradients around pyramidal boundary shapes contributes in generation of electrical energy. The MATLAB code is supposed to help learners in the Isogeometric More >

Tuanjie Li^1,*, Yan Zhang¹, Jiaxing Zhou¹

CMES-Computer Modeling in Engineering & Sciences, Vol.118, No.3, pp. 583-598, 2019, DOI:10.31614/cmes.2018.04891

Abstract In order to satisfy the high efficiency and high precision of collaborative robots, this work presents a novel trajectory planning method. First, in Cartesian space, a novel velocity look-ahead control algorithm and a cubic polynomial are combined to construct the end-effector trajectory of robots. Then, the joint trajectories can be obtained through the inverse kinematics. In order to improve the smoothness and stability in joint space, the joint trajectories are further adjusted based on the velocity look-ahead control algorithm and quintic B-spline. Finally, the proposed trajectory planning method is tested on a 4-DOF serial collaborative More >

Gang Xu^1,*, Yufan Zhu¹, Lishan Deng¹, Guozhao Wang², Bojian Li¹, Kin-chuen Hui³

CMC-Computers, Materials & Continua, Vol.58, No.3, pp. 879-892, 2019, DOI:10.32604/cmc.2019.03752

Abstract In this paper, we propose an efficient method to construct energy-minimizing B-spline curves by using discrete mask method. The linear relations between control points are firstly derived for different energy-minimization problems, then the construction of B-spline curve with minimal internal energy can be addressed by solving a sparse linear system. The existence and uniqueness of the solution for the linear system are also proved. Experimental results show the efficiency of the proposed approach, and its application in G¹ blending curve construction is also presented. More >

Jing Tang¹, Mei-e Fang^1,*, Guozhao Wang²

CMES-Computer Modeling in Engineering & Sciences, Vol.115, No.2, pp. 263-280, 2018, DOI:10.3970/cmes.2018.01702

Abstract ωB-splines have many optimal properties and can reproduce plentiful commonly-used analytical curves. In this paper, we further propose a non-stationary subdivision method of hierarchically and efficiently generating ωB-spline curves of arbitrary order of ωB-spline curves and prove its Ck−2-continuity by two kinds of methods. The first method directly prove that the sequence of control polygons of subdivision of order k converges to a Ck−2-continuousωB-spline curve of order k. The second one is based on the theories upon subdivision masks and asymptotic equivalence etc., which is more convenient to be further extended to the case of More >

Xing Wei^1,2, Wen Chen², Bin Chen^2,3, Bin Chen^1,4, Bin Chen², Bin Chen¹

CMC-Computers, Materials & Continua, Vol.52, No.1, pp. 53-71, 2016, DOI:10.3970/cmc.2016.052.053

Abstract A new wavelet finite element method (WFEM) is constructed in this paper and two elements for bending and free vibration problems of a stiffened plate are analyzed. By means of generalized potential energy function and virtual work principle, the formulations of the bending and free vibration problems of the stiffened plate are derived separately. Then, the scaling functions of the B-spline wavelet on the interval (BSWI) are introduced to discrete the solving field variables instead of conventional polynomial interpolation. Finally, the corresponding two problems can be resolved following the traditional finite element frame. There are More >

Xingwu Zhang¹, Jixuan Liu², Xuefeng Chen^1,3, Zhibo Yang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.109-110, No.5, pp. 405-425, 2015, DOI:10.3970/cmes.2015.109.405

Abstract Plane truss is widely used in mechanical engineering, building engineering and the aerospace engineering et al.. The precisely analysis of plane truss is very important for structural design and damage detection. Based on the generalized variational principle and B spline wavelet on the interval (BSWI), the multivariable wavelet finite element for plane truss is constructed. First, the wavelet axial rod element and the multivariable wavelet Euler beam element are constructed. Then the multivariable plane truss element can be obtained by combining these two elements together. Comparing with the traditional method, the generalized displacement and stress More >

Taku Itoh¹, Susumu Nakata²

CMES-Computer Modeling in Engineering & Sciences, Vol.107, No.3, pp. 187-199, 2015, DOI:10.3970/cmes.2015.107.187

Abstract To speed up generating a scalar field g(x) based on a piecewise polynomial, a new method for determining field values that are indispensable to generate g(x) has been proposed. In the proposed method, an intermediate for generating g(x) does not required, i.e., the field values can directly be determined from given point data. Numerical experiments show that the computation time for determining the field values by the proposed method is about 10.4–12.7 times less than that of the conventional method. In addition, on the given points, the accuracy of g(x) obtained by using the proposed More >