CMES-Vol. 88, No. 6, 2012

Open Access

ARTICLE

Analogy Between Rotating Euler-Bernoulli and Timoshenko Beams and Stiff Strings
A.S Vinod Kumar, Ranjan Ganguli²
CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.6, pp. 443-474, 2012, DOI:10.3970/cmes.2012.088.443
Abstract The governing differential equation of a rotating beam becomes the stiff-string equation if we assume uniform tension. We find the tension in the stiff string which yields the same frequency as a rotating cantilever beam with a prescribed rotating speed and identical uniform mass and stiffness. This tension varies for different modes and are found by solving a transcendental equation using bisection method. We also find the location along the rotating beam where equivalent constant tension for the stiff string acts for a given mode. Both Euler-Bernoulli and Timoshenko beams are considered for numerical results. More >

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Open Access

ARTICLE

Asymmetric Shell Elements Based on a Corrected Updated-Lagrangian Approach
P. Areias^1,2,3, T. Rabczuk⁴, D. Dias-da-Costa^5,6
CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.6, pp. 475-506, 2012, DOI:10.3970/cmes.2012.088.475
Abstract Surprisingly good displacement results are obtained by using the Petrov-Galerkin method with assumed and enhanced metric components in the test functions and enhanced metric components in the trial functions. Cartesian trial functions are required to ensure completeness and assumed/enhanced metric components are introduced to ensure high coarse-mesh accuracy. In the trial functions, the original incompatible-mode in-plane Q6 element by Wilson et al. can be used without violating the patch test. As a beneficial side-effect, Newton-Raphson convergence behavior for non-linear problems is improved. Transverse-shear and in-plane patch tests are satisfied while distorted-mesh performance is better than… More >

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ARTICLE

A New Anisotropic Local Meshing Method and Its Application in Parametric Surface Triangulation
W.W. Zhang¹, Y.F. Nie¹, Y.Q. Li¹
CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.6, pp. 507-530, 2012, DOI:10.3970/cmes.2012.088.507
Abstract A new algorithm for anisotropic triangular meshes generation in two dimension is presented. The inputs to the algorithm are the boundary geometry information and a metric tensor that specifies the desired element size and shape. The initial nodes are firstly distributed according to the above mentioned geometrical information, after bubble simulation, the optimized nodes set that meets the requirements of the metric tensor is obtained quickly. Then taking full advantage of the nodes set and the adjacency lists information provided by the process of node placement, a handful of non-satellite nodes are removed from the… More >

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ARTICLE

MLPG6 for the Solution of Incompressible Flow Equations
V. C. Loukopoulos¹, G. C. Bourantas²
CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.6, pp. 531-558, 2012, DOI:10.3970/cmes.2012.088.531
Abstract Meshless Local Petrov-Galerkin (MLPG) approach is used for the solution of the Navier-Stokes and energy equations. More specific as a special case we apply the MLPG6 approach. In the MLPG6 method, the test function is chosen to be the same as the trial function (Galerkin method). The MLPG local weak form is written over a local sub-domain which is completely independent from the trial or test functions. The sizes of nodal trial and test function domains, as well as the size of the local sub-domain over which the local weak-form is considered, can be arbitrary.… More >

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