Qiuxia Fan^1,*, Jianyu Li¹, Xinqi Zhang¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.31, No.1, pp. 1-1, 2024, DOI:10.32604/icces.2024.012048

Abstract In this paper, a series of smoothed finite element methods for the electromagnetic field distribution of non-contact LVDT are proposed. Firstly, the problem domain is discretized into a set of four-node tetrahedral elements, and the linear shape function is used to interpolate the domain variables. Then, the smooth region is further constructed by combining the nodes, edges and surfaces of the unit. Gradient smoothing technique is used to smooth the magnetic vector potential and scalar potential on each smooth domain. Based on the generalized smooth Galerkin weak form, the discretization system expression is derived and More >

K. Wang, S.J. Zhou, Z.F. Nie

The International Conference on Computational & Experimental Engineering and Sciences, Vol.18, No.4, pp. 115-116, 2011, DOI:10.3970/icces.2011.018.115

Abstract The natural neighbour Galerkin method is tailored to solve boundary value problems of the couple-stress elasticity to model the size dependent behaviour of materials. This method is based on the displacement-based Galerkin approach, and the calculation of the global stiffness matrix is performed using gradient smoothing technique combined with the non-Sibsonian partition of unity approximation scheme. This method possesses the following properties: the complex C1-continuous approximation scheme is avoided without using either Lagrange multipliers or penalty parameters; no domain integrals involved in the assembly of the global stiffness matrix; and the imposition of essential boundary More >

K. Wang¹, S.J. Zhou^2,3, Z.F. Nie⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.1, pp. 77-102, 2011, DOI:10.3970/cmes.2011.073.077

Abstract The natural neighbour Galerkin method is tailored to solve boundary value problems of the couple-stress elasticity to model the size dependent behaviour of materials. This method is based on the displacement-based Galerkin approach, and the calculation of the global stiffness matrix is performed using gradient smoothing technique combined with the non-Sibsonian partition of unity approximation scheme. This method possesses the following properties: the complex C1-continuous approximation scheme is avoided without using either Lagrange multipliers or penalty parameters; no domain integrals involved in the assembly of the global stiffness matrix; and the imposition of essential boundary More >

X.Y. Cui^1,2, G. R. Liu^2,3, G. Y. Li^1,4, G. Zheng¹

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.3, pp. 217-230, 2008, DOI:10.3970/cmes.2008.038.217

Abstract In this paper, a gradient smoothed formulation is proposed to deal with a fourth-order differential equation of Bernoulli-Euler beam problems for static and dynamic analysis. Through the smoothing operation, the C¹ continuity requirement for fourth-order boundary value and initial value problems can be easily relaxed, and C⁰ interpolating function can be employed to solve C¹ problems. In present thin beam problems, linear shape functions are employed to approximate the displacement field, and smoothing domains are further formed for computing the smoothed curvature and bending moment field. Numerical examples indicate that very accurate results can be yielded when More >