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The paper aims to the size-dependent analysis of functionally graded materials in thermal environment based on the modified couple stress theory using finite element method.

The element formulation is developed within the framework of the penalty unsymmetric finite element method (FEM) in that the C¹ continuity requirement is satisfied in weak sense and thus, C⁰ continuous interpolation enhanced by independent nodal rotation is employed as the test function. Meanwhile, the trial function is designed based on the stress functions and the weighted residual method. Besides, the special Gauss quadrature scheme is employed for integrals of matrices in accordance with the graded variation of the material properties.

The numerical results reveal that in thermal environment, functionally graded materials exhibit better bending performance compared to homogeneous materials, Moreover, the findings also indicate that with an increase in MLSP, the natural frequencies of out-of-plane modes gradually increase, while the natural frequencies of in-plane modes show much less variation, leading to a mode switch phenomenon.

The work provides an efficient numerical tool for analyzing and designing the functionally graded structures in thermal environment in practical engineering applications.

The purpose of this paper is to propose a new temporal disaggregation method for time series based on the accumulated and inverse accumulated generating operations in grey modeling and the interpolation method.

This disaggregation method includes three main steps, including accumulation, interpolation, and differentiation (AID). First, a low frequency flow series is transformed to the corresponding stock series through accumulated generating operation. Then, values of the stock series at unobserved time is estimated through appropriate interpolation method. And finally, the disaggregated stock series is transformed back to high frequency flow series through inverse accumulated generating operation.

The AID method is tested with a sales series. Results shows that the disaggregated sales data are satisfactory and reliable compared with the original data and disaggregated data using a time series model. The AID method is applicable to both long time series and grey series with insufficient information.

The AID method can be easily used to disaggregate low frequency flow series.

The AID method is a combination of grey modeling technique and interpolation method. Compared with other disaggregation methods, the AID method is simple, and does not require auxiliary information or plausible minimizing criterion required by other disaggregation methods.