Jian Hua Rong^1,2,3, Zhi Jun Zhao⁴, Yi Min Xie⁵, Ji Jun Yi^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.90, No.3, pp. 211-231, 2013, DOI:10.3970/cmes.2013.090.211

Abstract Similar periodic structures have been widely used in engineering. In order to obtaining the optimal similar periodic structures, a topology optimization method of similar periodic structures with multiple displacement constraints is proposed in this paper. Firstly, in the proposed method, the design domain is divided into sub-domains. Secondly, a penalty term considering discrete conditions of density variables is introduced into the objective function, and the reciprocal density exponents of structural elements are taken as design variables. A topological optimization model of a similar periodic continuum structure with the objective function being the structural mass and the constraint functions being structural… More >

Chih-Ping Wu^1,2, Jian-Sin Wang², Yung-Ming Wang²

CMES-Computer Modeling in Engineering & Sciences, Vol.52, No.1, pp. 1-38, 2009, DOI:10.3970/cmes.2009.052.001

Abstract A meshless collocation method based on the differential reproducing kernel (DRK) interpolation is developed for the three-dimensional (3D) coupled analysis of simply-supported, functionally graded (FG) piezoelectric hollow cylinders. The material properties of FG hollow cylinders are regarded as heterogeneous through the thickness coordinate, and then specified to obey an exponent-law dependent on this. In the present formulation, the shape function for the reproducing kernel (RK) interpolation function at each sampling node is separated into a primitive function possessing Kronecker delta properties and an enrichment function constituting reproducing conditions. By means of this DRK interpolation, the essential boundary conditions can be… More >

J. Sladek¹, V. Sladek², P. Solek¹, S.N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.3, pp. 273-300, 2008, DOI:10.3970/cmes.2008.034.273

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed, to solve boundary and initial value problems of piezoelectric and magneto-electric-elastic solids with continuously varying material properties. Stationary and transient dynamic 2-D problems are considered in this paper. The mechanical fields are described by the equations of motion with an inertial term. To eliminate the time-dependence in the governing partial differential equations the Laplace-transform technique is applied to the governing equations, which are satisfied in the Laplace-transformed domain in a weak-form on small subdomains. Nodal points are spread on the analyzed domain, and each node is surrounded by a… More >

Y.C. Cai¹ and H.H. Zhu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.2, pp. 179-204, 2008, DOI:10.3970/cmes.2008.034.179

Abstract The popular Shepard PU approximations are easy to construct and have many advantages, but they have several limitations, such as the difficulties in handling essential boundary conditions and the known problem of linear dependence regarding PU-based methods, and they are not the good choice for MLPG method. With the objective of alleviating the drawbacks of Shepared PU approximations, a new meshless PU-based Shepard and Least Square (SLS) interpolation is employed here to develop a new type of MLPG method, which is named as Local Meshless Shepard and Least Square (LMSLS) method. The SLS interpolation possesses the much desired Kronecker-delta property,… More >

Zheng Juan^1,2,3, Long Shuyao^1,2, Xiong Yuanbo^1,2, Li Guangyao¹

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.2, pp. 137-154, 2008, DOI:10.3970/cmes.2008.034.137

Abstract In this paper, the meshless radial point interpolation method (RPIM) is applied to carry out a topology optimization design for the continuum structure. Considering the relative density of nodes as a design variable, and the minimization of compliance as an objective function, the mathematical formulation of the topology optimization design is developed using the SIMP (solid isotropic microstructures with penalization) interpolation scheme. The topology optimization problem is solved by the optimality criteria method. Numerical examples show that the proposed approach is feasible and efficient for the topology optimization design for the continuum structure, and can effectively overcome the checkerboard phenomenon. More >

J. Sladek¹, V. Sladek¹, Ch. Zhang², C.L. Tan³

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.1, pp. 57-68, 2006, DOI:10.3970/cmes.2006.016.057

Abstract The Meshless Local Petrov-Galerkin (MLPG) method for linear transient coupled thermoelastic analysis is presented. Orthotropic material properties are considered here. A Heaviside step function as the test functions is applied in the weak-form to derive local integral equations for solving two-dimensional (2-D) problems. In transient coupled thermoelasticity an inertial term appears in the equations of motion. The second governing equation derived from the energy balance in coupled thermoelasticity has a diffusive character. To eliminate the time-dependence in these equations, the Laplace-transform technique is applied to both of them. Local integral equations are written on small sub-domains with a circular shape.… More >

Jin Ma, Yang Liu, Hongbing Lu, Ranga Komanduri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.1, pp. 41-56, 2006, DOI:10.3970/cmes.2006.016.041

Abstract A multiscale simulation technique coupling three scales, namely, the molecular dynamics (MD) at the atomistic scale, the discrete dislocations at the meso scale and the generalized interpolation material point (GIMP) method at the continuum scale is presented. Discrete dislocations are first coupled with GIMP using the principle of superposition (van der Giessen and Needleman (1995)). A detection band seeded in the MD region is used to pass the dislocations to and from the MD simulations (Shilkrot, Miller and Curtin (2004)). A common domain decomposition scheme for each of the three scales was implemented for parallel processing. Simulations of indentation were… More >

J. Ma², H. Lu², B. Wang², R. Hornung³, A. Wissink³, R. Komanduri^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.2, pp. 101-118, 2006, DOI:10.3970/cmes.2006.014.101

Abstract A new method for multiscale simulation bridging two scales, namely, the continuum scale using the generalized interpolation material point (GIMP) method and the atomistic scale using the molecular dynamics (MD), is presented and verified in 2D. The atomistic strain from the molecular dynamics simulation is determined through interpolation of the displacement field into an Eulerian background grid using the same generalized interpolation functions as that in the GIMP method. The atomistic strain is consistent with that determined from the virial theorem for interior points but provides more accurate values at the boundary of the MD region and in the transition… More >

Jin Ma, Hongbing Lu, Ranga Komanduri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.3, pp. 213-228, 2006, DOI:10.3970/cmes.2006.012.213

Abstract The generalized interpolation material point (GIMP) method, recently developed using a C¹ continuous weighting function, has solved the numerical noise problem associated with material points just crossing the cell borders, so that it is suitable for simulation of relatively large deformation problems. However, this method typically uses a uniform mesh in computation when one level of material points is used, thus limiting its effectiveness in dealing with structures involving areas of high stress gradients. In this paper, a spatial refinement scheme of the structured grid for GIMP is presented for simulations with highly localized stress gradients. A uniform structured background… More >

L. Chen¹ J. H. Lee¹, C.-f. Chen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.3, pp. 199-224, 2012, DOI:10.3970/cmes.2012.086.199

Abstract This paper presents a numerical procedure to model surface tension using the Generalized Interpolation Material Point (GIMP) method which employs a background mesh in solving the equations of motion. The force due to surface tension is formulated at the mesh grid points by using the continuum surface force (CSF) model and then added to the equations of motion at each grid point. In GIMP, we use the grid mass as the color function in CSF and apply a moving average smoothing scheme to the grid mass to improve the accuracy in calculating the surface interface. The algorithm, named as GIMP-CSF,… More >