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Based on previous results of the existence, uniqueness, and regularity conditions for a continuous dynamic model for a parallel-plate electrostatic micro-electron-mechanical-systems with the fringing field, the purpose of this paper concerns a Galerkin-FEM procedure for deformable element deflection recovery. The deflection profiles are reconstructed by assigning the dielectric properties of the moving element. Furthermore, the device’s use conditions and the deformable element’s mechanical stresses are presented and discussed.

The Galerkin-FEM approach is based on weighted residuals, where the integrals appearing in the solution equation have been solved using the Crank–Nicolson algorithm.

Based on the connection between the fringing field and the electrostatic force, the proposed approach reconstructs the deflection of the deformable element, satisfying the conditions of existence, uniqueness and regularity. The influence of the electromechanical properties of the deformable plate on the method has also been considered and evaluated.

The developed analytical model focused on a rectangular geometry.

The device studied is suitable for industrial and biomedical applications.

This paper proposed numerical approach characterized by low CPU time enables the creation of virtual prototypes that can be analyzed with significant cost reduction and increased productivity.

Automatic modulation recognition (AMR) is a challenging problem in intelligent communication systems and has wide application prospects. At present, although many AMR methods based on deep learning have been proposed, the methods proposed by these works cannot be directly applied to the actual wireless communication scenario, because there are usually two kinds of dilemmas when recognizing the real modulated signal, namely, long sequence and noise. This paper aims to effectively process in-phase quadrature (IQ) sequences of very long signals interfered by noise.

This paper proposes a general model for a modulation classifier based on a two-layer nested structure of long short-term memory (LSTM) networks, called a two-layer nested structure (TLN)-LSTM, which exploits the time sensitivity of LSTM and the ability of the nested network structure to extract more features, and can achieve effective processing of ultra-long signal IQ sequences collected from real wireless communication scenarios that are interfered by noise.

Experimental results show that our proposed model has higher recognition accuracy for five types of modulation signals, including amplitude modulation, frequency modulation, gaussian minimum shift keying, quadrature phase shift keying and differential quadrature phase shift keying, collected from real wireless communication scenarios. The overall classification accuracy of the proposed model for these signals can reach 73.11%, compared with 40.84% for the baseline model. Moreover, this model can also achieve high classification performance for analog signals with the same modulation method in the public data set HKDD_AMC36.

At present, although many AMR methods based on deep learning have been proposed, these works are based on the model’s classification results of various modulated signals in the AMR public data set to evaluate the signal recognition performance of the proposed method rather than collecting real modulated signals for identification in actual wireless communication scenarios. The methods proposed in these works cannot be directly applied to actual wireless communication scenarios. Therefore, this paper proposes a new AMR method, dedicated to the effective processing of the collected ultra-long signal IQ sequences that are interfered by noise.

The main aim of the current paper is to find a numerical plan for hydraulic fracturing problem with application in extracting natural gases and oil.

First, time discretization is accomplished via Crank-Nicolson and semi-implicit techniques. At the second step, a high-order finite element method using quadratic triangular elements is proposed to derive the spatial discretization. The efficiency and time consuming of both obtained schemes will be investigated. In addition to the popular uniform mesh refinement strategy, an adaptive mesh refinement strategy will be employed to reduce computational costs.

Numerical results show a good agreement between the two schemes as well as the efficiency of the employed techniques to capture acceptable patterns of the model. In central single-crack mode, the experimental results demonstrate that maximal values of displacements in x- and y- directions are 0.1 and 0.08, respectively. They occur around both ends of the line and sides directly next to the line where pressure takes impact. Moreover, the pressure of injected fluid almost gained its initial value, i.e. 3,000 inside and close to the notch. Further, the results for non-central single-crack mode and bifurcated crack mode are depicted. In central single-crack mode and square computational area with a uniform mesh, computational times corresponding to the numerical schemes based on the high order finite element method for spatial discretization and Crank-Nicolson as well as semi-implicit techniques for temporal discretizations are 207.19s and 97.47s, respectively, with 2,048 elements, final time T = 0.2 and time step size τ = 0.01. Also, the simulations effectively illustrate a further decrease in computational time when the method is equipped with an adaptive mesh refinement strategy. The computational cost is reduced to 4.23s when the governed model is solved with the numerical scheme based on the adaptive high order finite element method and semi-implicit technique for spatial and temporal discretizations, respectively. Similarly, in other samples, the reduction of computational cost has been shown.

This is the first time that the high-order finite element method is employed to solve the model investigated in the current paper.

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.