Abstract
Based on the hybrid numerical method (HNM) combining with a reduced-basis method (RBM), the real-time transient response of a functionally graded material (FGM) plates is obtained. The large eigenvalue problem in wavenumber domain has been solved through real-time off-line/on-line calculation. At off-line stage, a reduced-basis space is constructed in sample wavenumbers according to the solved eigenvalue problems. The matrices independent of parameters are projected onto the reduced-basis spaces. At on-line stage, the reduced eigenvalue problems of the arbitrary wavenumbers are built. Subsequently, the responses in wavenumber domain are obtained by the approximated eigen-pairs. Because of the application of RBM, the computational cost of transient displacement analysis of FGM plate is decreased significantly, while the accuracy of the solution and the physics of the structure are still retained. The efficiency and validity of the proposed method are demonstrated through a numerical example.
Highlights
A complex structure is modeled by a discrete multi-degree-of-freedom system, and the dynamic analysis of them often requires solving a large set of equations
{ } At off-line stage, we introduce a sample set SG = μ1, μG m in the wavenumber domain, assuming G can be exactly divided by m. m denotes the number of truncated eigenvectors from Equation (13) associated with the desired accuracy of calculation
The present method is applied to an actual stainless steel-silicon nitride (SS-SN) functionally graded material (FGM) plate, in which the silicon nitride is considered as the inclusion material
Summary
A complex structure is modeled by a discrete multi-degree-of-freedom system, and the dynamic analysis of them often requires solving a large set of equations. The numerically solution of the transient structural response for such a large system is expensive; methods that can reduce significant-. In this paper we apply the reduced-basis method in wavenumber domain to the transient analysis of structures based on the modified HNM. The truncated eigenvectors corresponding to the carefully selected sample parameter points are extracted to construct the reduced-basis space onto which the original large system problem is projected. In this manner, a reduced system is obtained and the eigenvalue problem can be solved more effectively. The transient response in space-time domain is obtained through performing the inverse Fourier transform
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