Asymptotic-numerical method for buckling analysis of shell structures with large rotations
Journal of Computational and Applied Mathematics - Special issue: Selected papers from the 2nd international conference on advanced computational methods in engineering (ACOMEN2002) Liege University, Belgium, 27-31 May 2002
Forced harmonic response of viscoelastic structures by an asymptotic numerical method
Computers and Structures
Journal of Computational Physics
Nonlinear forced vibration of damped plates by an asymptotic numerical method
Computers and Structures
Nonlinear vibrations of simply-supported plates by the p-version finite element method
Finite Elements in Analysis and Design
Projection techniques to improve high-order iterative correctors
Finite Elements in Analysis and Design
A harmonic balance approach for large-scale problems in nonlinear structural dynamics
Computers and Structures
Accurate reduced-order models for a simple rotor blade model using nonlinear normal modes
Mathematical and Computer Modelling: An International Journal
Hi-index | 0.00 |
This work concerns the computation of the nonlinear solutions of forced vibration of damped plates. In a recent work (Boumediene et al. in Comput Struct 87:1508---1515, 2009), a numerical method coupling an asymptotic numerical method (ANM), harmonic balance method and Finite Element method was proposed to resolve this type of problem. The harmonic balance method transforms the dynamic equations to equivalent static ones which are solved by using a perturbation method (ANM) and the finite element method. The numerical results presented in reference (Boumediene et al. in Comput Struct 87:1508---1515, 2009) show that the ANM is very efficient and permits one to obtain the nonlinear solutions with few matrix triangulation numbers compared to a classical incremental iterative method. However, putting a great number of harmonics (6 or greater) into the load vector leads to tangent matrices with a great size. The computational time necessary for the triangulation of such matrices can then be large. In this paper, reduced order models are proposed to decrease the size of these matrices and consequently the computational time. We consider two reduced bases. In the first one, the reduced basis is obtained by the resolution of a classical eigenvalue problem. The second one is obtained by using the nonlinear solutions computed during the first step of the calculus which is realized with the ANM. Several classical benchmarks of nonlinear damped plates are presented to show the efficiency of the proposed numerical methods.