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• Open Access

ARTICLE

Application of the Differential Transform Method for Solving Periodic Solutions of Strongly Non-linear Oscillators

Hsin-Ping Chu1, Cheng-Ying Lo2
CMES-Computer Modeling in Engineering & Sciences, Vol.77, No.3&4, pp. 161-172, 2011, DOI:10.3970/cmes.2011.077.161
Abstract This paper presents the application of the differential transform method to solve strongly nonlinear equations with cubic nonlinearities and self-excitation terms. First, the equations are transformed by the differential transform method into the algebra equations in terms of the transformed functions. Secondly, the higher-order transformed functions are calculated in terms of other lower-order transformed functions through the iterative procedure. Finally, the solutions are approximated by the n-th partial sum of the infinite series obtained by the inverse differential transform. Two strongly nonlinear equations with different coefficients and initial conditions are given as illustrative examples. More >

• Open Access

ARTICLE

An Iterative Method for the Least-Squares Minimum-Norm Symmetric Solution

Minghui Wang1, Musheng Wei2, Shanrui Hu1
CMES-Computer Modeling in Engineering & Sciences, Vol.77, No.3&4, pp. 173-182, 2011, DOI:10.3970/cmes.2011.077.173
Abstract The mapping from the symmetric solution set to its independent parameter space is studied and an iterative method is proposed for the least-squares minimum-norm symmetric solution of AXB = E. Numerical results are reported that show the efficiency of the proposed methods. More >

• Open Access

ARTICLE

Experimental and Numerical Investigation of Instructions for Hyperelastic Membrane Inflation Using Fluid Structure Coupling

M.Souli1, F.Erchiqui2
CMES-Computer Modeling in Engineering & Sciences, Vol.77, No.3&4, pp. 183-200, 2011, DOI:10.3970/cmes.2011.077.183
Abstract During the design process of membrane structure to resist to high pressure loading, and the characterization of hyperelastic material, a structure made up of thin rubber undergoes large deformation and rotation under high pressure loading out of high pressurized gas. Until recently, to simulate the inflation of the hyperelastic membrane, a uniform pressure based on thermodynamic model or experimental tests is applied to the structure, as boundary conditions. From a computational time point of view, this approach is very fast, since no computational fluid dynamics is involved in the simulation. However, at the late stage of the membrane inflation, uniform… More >

• Open Access

ARTICLE

Mesh Simplification Method Using Principal Curvatures and Directions

V. Ungvichian1, P. Kanongchaiyos1
CMES-Computer Modeling in Engineering & Sciences, Vol.77, No.3&4, pp. 201-220, 2011, DOI:10.3970/cmes.2011.077.201
Abstract This paper describes an enhancement to Garland and Heckbert's mesh simplification method by using the principal curvatures and directions of each vertex. We calculate the values and directions, before using them to determine the absolute normal curvature in the direction of contraction, and multiplying the curvature with the edge length, the maximum absolute cosine of the angles between the edge and the normals of faces adjacent to either endpoint, and the quadric error of the collapse. We also apply penalties based on compactness and angular and dihedral deviations of the resulting faces. We have implemented these improvements and tested our… More >

• Open Access

ARTICLE

A simple locking-free discrete shear triangular plate element

Y.C. Cai1,2,3, L.G. Tian1, S.N. Atluri3
CMES-Computer Modeling in Engineering & Sciences, Vol.77, No.3&4, pp. 221-238, 2011, DOI:10.3970/cmes.2011.077.221
Abstract A new three node triangular plate element, labeled here as DST-S6 (Discrete Shear Triangular element with 6 extra Shear degrees of freedom), is proposed for the analyses of plate/shell structures comprising of thin or thick members. The formulation is based on the DKT (Discrete Kirchhoff Technique) and an appropriate use of the independent shear DOF(Degrees Of Freedom). The shear locking is completely eliminated in the DST-S6, without any numerical expediencies such as the reduce integration, the use of assumed strains/stresses, or the need for the stabilization of the attendant zero energy modes. It is shown that the present DST-S6 is… More >

• Open Access

ARTICLE

Modified Algorithm for Surface Tension with Smoothed Particle Hydrodynamics and Its Applications

H.F.Qiang1, F.Z.Chen1, W.R. Gao1
CMES-Computer Modeling in Engineering & Sciences, Vol.77, No.3&4, pp. 239-262, 2011, DOI:10.3970/cmes.2011.077.239
Abstract Based on smoothed particle hydrodynamics (SPH) method with surface tension proposed by Morris, this paper is intended to modify equations for surface tension by modifying normal and curvature with corrective smoothing particle method (CSPM). Compared with the continuum surface force (CSF) model for surface tension employed in the traditional SPH method, the accuracy in the present paper is much higher in terms of handling the problems with large deformation and surface tension. The reason is that in the traditional SPH method the deficiency of particles is near the boundary and sharp-angled areas, and it causes gross errors of curvature calculation.… More >

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