CMES-Vol. 95, No. 3, 2013

Open Access

ARTICLE

On the Axisymmetric Time-harmonic Lamb’s Problem for a System Comprising a Half-space and a Covering Layer with Finite Initial Strains
S.D. Akbarov^1,2
CMES-Computer Modeling in Engineering & Sciences, Vol.95, No.3, pp. 173-205, 2013, DOI:10.3970/cmes.2013.095.173
Abstract By employing the Three-dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies (TLTEWISB) the time-harmonic Lamb’s problem for a system comprising a finite pre-strained half-space and finite pre-strained covering layer made of incompressible materials is examined for the case where the material of the covering layer is stiffer than that of the half-space material. It is assumed that on the upper free face plane of the covering layer the point-located time-harmonic force acts. The elasticity relations of the materials are described through Treloar’s potential. The corresponding boundary-value problem is solved by employing the Hankel… More >

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Constrained Optimization Multi-dimensional Harmonic Balance Method for Quasi-periodic Motions of Nonlinear Systems
Haitao Liao¹
CMES-Computer Modeling in Engineering & Sciences, Vol.95, No.3, pp. 207-234, 2013, DOI:10.3970/cmes.2013.095.207
Abstract The constrained optimization multi-dimensional harmonic balance method for calculating the quasi-periodic solutions of nonlinear systems is presented. The problem of determining the worst quasi-periodic response is transformed into a nonlinear optimization problem with nonlinear equality constraints. The general nonlinear equality constraints are built using a set of nonlinear algebraic equations which is derived using the multi-dimensional harmonic balance method. The Multi- Start algorithm is adopted to solve the resulting constrained maximization problem. Finally, the validity of the proposed method is demonstrated with a Duffing oscillator and numerical case studies for problems with uncertainties are performed More >

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ARTICLE

Numerical Integration with Constraints for Meshless Local Petrov-Galerkin Methods
L. Sun¹, G. Yang², Q. Zhang³
CMES-Computer Modeling in Engineering & Sciences, Vol.95, No.3, pp. 235-258, 2013, DOI:10.3970/cmes.2013.095.234
Abstract We propose numerical integration rules for meshless local Petrov- Galerkin methods (MLPG) employed to solve elliptic partial different equations (PDE) with Neumann boundary conditions. The integration rules are required to satisfy an integration constraint condition of Green’s formula type (GIC). GIC was first developed in [Babuska, Banerjee, Osborn, and Zhang (2009)] for Galerkin meshless method, and we will show in this paper that it has better features for MLPG due to flexibility of MLPG in choosing different trial and test function spaces. A general constructive algorithm is presented to design the integration rules satisfying GIC. More >

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