V.V. Zozulya¹

CMES-Computer Modeling in Engineering & Sciences, Vol.42, No.3, pp. 187-216, 2009, DOI:10.3970/cmes.2009.042.187

Abstract The mathematical statement for contact problem with unilateral restrictions and friction is done in classical and weak forms. Different variational formulation of unilateral contact problems with friction based on principles of virtual displacements and virtual stresses are considered. Especially boundary variational functionals that are used with boundary integral equations have been established. Nonsmooth optimization algorithms of Udzawa type for solution of unilateral contact problem with friction have been developed. Some theoretical results of existence and uniqueness in elastostatic unilateral contact problem with friction are outlined. 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 a reasonable number… More >

M. Steffen¹, P.C. Wallstedt², J.E. Guilkey^2,3, R.M. Kirby¹, M. Berzins¹

CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.2, pp. 107-128, 2008, DOI:10.3970/cmes.2008.031.107

Abstract The Material Point Method (MPM) has shown itself to be a powerful tool in the simulation of large deformation problems, especially those involving complex geometries and contact where typical finite element type methods frequently fail. While these large complex problems lead to some impressive simulations and solutions, there has been a lack of basic analysis characterizing the errors present in the method, even on the simplest of problems. The large number of choices one has when implementing the method, such as the choice of basis functions and boundary treatments, further complicates this error analysis.\newline In this paper we explore some… More >

X.Y. Cui^1,2, G. R. Liu^2,3, G. Y. Li¹, X. Zhao², T.T. Nguyen², G.Y. Sun¹

CMES-Computer Modeling in Engineering & Sciences, Vol.28, No.2, pp. 109-126, 2008, DOI:10.3970/cmes.2008.028.109

Abstract A smoothed finite element method (SFEM) is presented to analyze linear and geometrically nonlinear problems of plates and shells using bilinear quadrilateral elements. The formulation is based on the first order shear deformation theory. In the present SFEM, the elements are further divided into smoothing cells to perform strain smoothing operation, and the strain energy in each smoothing cell is expressed as an explicit form of the smoothed strain. The effect of the number of divisions of smoothing cells in elements is investigated in detail. It is found that using three smoothing cells for bending strain energy integration and one… More >

H. Nguyen-Van¹, N. Mai-Duy², T. Tran-Cong³

CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.3, pp. 209-222, 2008, DOI:10.3970/cmes.2008.023.209

Abstract This paper reports a study of linear elastic analysis of two-dimensional piezoelectric structures using a smoothed four-node piezoelectric element. The element is built by incorporating the strain smoothing method of mesh-free conforming nodal integration into the standard four-node quadrilateral piezoelectric finite element. The approximations of mechanical strains and electric potential fields are normalized using a constant smoothing function. This allows the field gradients to be directly computed from shape functions. No mapping or coordinate transformation is necessary so that the element can be used in arbitrary shapes. Through several examples, the simplicity, efficiency and reliability of the element are demonstrated.… More >

Yan Liu¹, Xiong Zhang¹, K. Y. Sze², Min Wang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.3, pp. 177-192, 2007, DOI:10.3970/cmes.2007.020.177

Abstract In molecular simulations, the frequencies of the low-frequency modes are many orders of magnitude lower than those of the high-frequency modes. Compared with the amplitudes of the low-frequency modes, the amplitudes of the high-frequency modes are often negligible and, thus, least interesting. As dictated by the period of the highest frequency mode, the critical time step for stable time integration can be significantly increased by suppressing the negligible high-frequency modes yet the solution remains virtually intact. In this light, a smoothed molecular dynamics (SMD) approach is proposed to eliminate the high-frequency modes from the dynamical system through the use of… More >

Paulo Santos, Julieta António, António Tadeu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 79-98, 2000, DOI:10.3970/cmes.2000.001.531

Abstract This paper presents the three-dimensional scattering field obtained when 2D smooth topographical deformations are subjected to a dilatational point load placed at some point in the medium. The solution is formulated using boundary elements for a wide range of frequencies and spatially harmonic line loads, which are then used to obtain time series by means of (fast) inverse Fourier transforms into space-time. The topographical surface is modeled with a number of boundary elements, defined according to the excitation frequency of the harmonic source, and in such a way that the free surface can be discretized along a sufficient distance to… More >

K. Bououni¹, T. Jaber¹, S. Elbehissy¹

FDMP-Fluid Dynamics & Materials Processing, Vol.13, No.2, pp. 127-141, 2017, DOI:10.3970/fdmp.2017.013.127

Abstract The economic progress in the United Arab Emirates (UAE) induces to a significant increase in the demand for agricultural development. In Emirates the majority of the farms are irrigated by underground water, characterized by a high level of salinity. Liwa, Al Ain and Al Khatem areas are suffering from high water well salinity that exceeds 20,000 ppm. This work focuses on this problem and suggests a suitable solution allowing the use of renewable energy (Solar Photovoltaic) to drive RO desalination units. An optimal design of RO/PV unit adapted to a typical farm in Abu Dhabi was suggested using a model… More >

Robert Rundqvist¹, Andreas Mark¹, Fredrik Edelvik¹, Johan S. Carlsson¹

FDMP-Fluid Dynamics & Materials Processing, Vol.7, No.3, pp. 259-278, 2011, DOI:10.3970/fdmp.2011.007.259

Abstract Multiphase flow simulation using Smoothed Particle Hydrodynamics (SPH) has gained interest during recent years, mostly due to the inherent flexibility of the method and the physically rather intuitive formulation of extra constitutive equations needed when dealing with for instance non-Newtonian flows. In the work presented here, simulations based on an SPH model implemented in the flow solver IBOFlow has been used for simulation of robotic application of sealing material on a car body. Application of sealing materials is done in order to prevent water leakage into cavities of the body, and to reduce noise. In off-line programming of the robots… More >

H. Nguyen-Van¹, N. Mai Duy², T. Tran-Cong ³

CMC-Computers, Materials & Continua, Vol.6, No.3, pp. 159-176, 2007, DOI:10.3970/cmc.2007.006.159

Abstract This paper reports the development of a simple but efficient and accurate four-node quadrilateral element for models of laminated, anisotropic plate behaviour within the framework of the first-order shear deformation theory. The approach incorporates the strain smoothing method for mesh-free conforming nodal integration into the conventional finite element techniques. The membrane-bending part of the element stiffness matrix is calculated by the line integral on the boundaries of the smoothing elements while the shear part is performed using an independent interpolation field in the natural co-ordinate system. Numerical results show that the element offered here is locking-free for extremely thin laminates,… More >