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

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 Analysis and Finite Elements Methods… 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 surface subdivision. And the problem… More >

S. Tanaka¹, H. Okada¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.4, pp. 217-224, 2007, DOI:10.3970/icces.2007.003.217

Abstract It has been recognized that the bottle-neck in solid/structural analyses using the finite element method is in their model generation phase. Methodologies that eliminate the needs for "elements" have been proposed by many researchers. They can be categorized into "meshless" and "virtually meshless" finite element methods. The "meshless" method may be represented by moving least square Ptrov-Galerkin (MLPG) method [1] and element free Galerkin Method (EFGM) [2]. The free-mesh method [3] and voxel finite element method [4], etc. are classified to be the "virtually meshless" approaches. The "meshless" methods eliminated needs for element connectivity information in their input data and… 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 robot. The experimental results indicate… 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 are treated as independent variables… 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 method is almost the same… More >

Hao Zuo^1,2, Zhi-Bo Yang^1,2,3, Xue-Feng Chen^1,2, Yong Xie⁴, Xing-Wu Zhang^1,2, Yue Liu⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.6, pp. 477-506, 2014, DOI:10.3970/cmes.2014.100.477

Abstract The application of B-spline wavelet on the interval (BSWI) finite element method for static, free vibration and buckling analysis in functionally graded (FG) beam is presented in this paper. The functionally graded material (FGM) is a new type of heterogeneous composite material with material properties varying continuously throughout the thickness direction according to power law form in terms of volume fraction of material constituents. Different from polynomial interpolation used in traditional finite element method, the scaling functions of BSWI are employed to form the shape functions and construct wavelet-based elements. Timoshenko beam theory and Hamilton’s principle are adopted to formulate… More >

P. K. Sahu¹, S. Saha Ray^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.2, pp. 91-112, 2013, DOI:10.3970/cmes.2013.093.091

Abstract In this paper, nonlinear integral equations have been solved numerically by using B-spline wavelet method and Variational Iteration Method (VIM). Compactly supported semi-orthogonal linear B-spline scaling and wavelet functions together with their dual functions are applied to approximate the solutions of nonlinear Fredholm integral equations of second kind. Comparisons are made between the variational Iteration Method (VIM) and linear B-spline wavelet method. Several examples are presented to compare the accuracy of linear B-spline wavelet method and Variational Iteration Method (VIM) with their exact solutions. More >

Zhibo Yang¹, Xuefeng Chen², Bing Li¹, Zhengjia He¹, Huihui Miao¹

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.2, pp. 129-156, 2012, DOI:10.3970/cmes.2012.085.129

Abstract The implementation of the B-spline Wavelet on the Interval (BSWI) for curved shell elements with rectangular planform is presented in this paper. By aid of the general shell theory, cylinder shells, doubly-curved shallow shells and hyperbolic paraboloidal shells BSWI elements are formulated. Instead of traditional polynomial interpolation, scaling functions at certain scale have been adopted to form the shape functions and construct wavelet-based elements. Because of the good character of BSWI scaling functions, the BSWI curved shell elements combine the accuracy of wavelet-based elements approximation and the character of B-spline functions for structural analysis. Different from the flat shell elements,… More >

Xiang Jiawei¹, Chen Xuefeng², Yang Lianfa³, He Zhengjia⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.1, pp. 1-12, 2008, DOI:10.3970/cmes.2008.023.001

Abstract A class of flat shell elements is constructed by using the scaling functions of two-dimensional tensor product B-spline wavelet on the interval (BSWI). Unlike the process of direct wavelets adding in the wavelet Galerkin method, the element displacement field represented by the coefficients of wavelets expansions was transformed from wavelet space into physical space via the constructed two-dimensional transformation matrix. Then, the BSWI flat shell element is constructed by the assembly of BSWI plane elastomechanics and Mindlin plate elements. Because of the good character of BSWI scaling functions, the BSWI flat shell element combine the accuracy of B-spline functions approximation… More >