Yassin Belkourchia

The dynamic behavior of structures with piezoelectric patches is governed by partial differential equations with strong singularities. To directly deal with these equations, well adapted numerical procedures are required. In this work, the differential quadrature method (DQM) combined with a regularization procedure for space and implicit scheme for time discretization is used. The DQM is a simple method that can be implemented with few grid points and can give results with a good accuracy. However, the DQM presents some difficulties when applied to partial differential equations involving strong singularities. This is due to the fact that the subsidiaries of the singular functions cannot be straightforwardly discretized by the DQM. A methodological approach based on the regularization procedure is used here to overcome this difficulty and the derivatives of the Dirac-delta function are replaced by regularized smooth functions. Thanks to this regularization, the resulting differential equations can be directly discretized using the DQM. The efficiency and applicability of the proposed approach are demonstrated in the computation of the dynamic behavior of beams for various boundary conditions and excited by impulse and Multiharmonics piezoelectric actuators. The obtained numerical results are well compared to the developed analytical solution.

In this paper, the Particle Swarm Optimization (PSO) is used to determine a good shape parameter of meshfree method with radial basis function (RBF) to get distribution function of Fokker-Planck equation associated to nonlinear stochastic differential equations. Numerical procedures based on Kansa's method and particle swarm optimization are applied to Duffing oscillator model. This paper gives the best shape parameter by PSO by minimizing the Root Mean Square Error (RMSE). The effectiveness of the method is demonstrated and the obtained results are well compared to the available ones.

This paper introduces a new hybrid optimization procedure named GA-PSO-SQP for resolution constrained engineering design problems. Certifiable issues in the engineering field are typically expansive scale or nonlinear or constrained optimization problems, very well-designed numerical procedure is this way needed. This coupling is based on the genetic algorithm, the sequential quadratic programming and on the particle swarm optimization united with a projected gradient algorithm to deal constrained optimization problems. Numerical results based on well-known held back engineering design problems are reported and compared. The solutions acquired by the proposed technique are generally improved than those results given by other known methodologies in the open literature.

The study of fluid-structure interaction (FSI) energy harvesting using piezoelectric patch integrated on beam structures has received significant attention over the past decades. In this work a mathematical model based on the Stokes equation for the flow and the Euler-Bernoulli beam theory for the structure motion is presented. Hybrid optimization procedure is elaborated to find the optimal locations of the piezoelectric patches to calculate the maximum generated electric power. The finite element method (FEM) coupled with the quadratic differential method (QDM) is used to numerically solve the resulting partial differential equations with an implicit time scheme. The obtained numerical simulations are used to calculate the generated electric power. Hybrid optimization algorithm namely GA-PSO-SQP is applied to find the optimal locations of the piezoelectric patches to give maximum generated electric power. An adaptive numerical scheme is elaborated herein to solve the FSI model for energy harvesting from ocean wave motion. This algorithm is combined with optimization procedures and the study gives more insights on the understanding of such problems.

In recent years, energy generation and harvesting took the attention of many researchers, especially the piezoelectric materials for their unique characteristics. One of the promising techniques for energy harvesting is the ocean wave energy harvester resulting from the pressure coming from the ocean movement waves on a vertical cantilever with piezoelectric patches, this results in a fluid-structure interaction. A mathematical model is presented based on the Stokes equation for the flow and the Euler-Bernoulli beam theory for the structure motion. The finite element method (FEM) coupled with the quadratic differential method (QDM) are used to numerically solve the resulting partial differential equations with an implicit time scheme. The obtained numerical simulations are validated and discussed. Results show clear effect of the water pressure on the cantilever, as well as the pulsatile behavior of the water motion. This paper gives an adaptive numerical scheme to solve the FSI model for energy harvesting of ocean wave motion and the study gives more insights on the understanding of such problems.

The aim of this paper is the elaboration of a new hybrid optimization procedure based on a coupling methodological approach for solving global optimization problem and active vibration control. This coupling is based on the genetic algorithm, the sequential quadratic programming and on the particle swarm optimization combined with a projected gradient algorithm. The proposed methodological approach and its convergence to the global solution are proved through the tested solutions. The proposed methodological approach is applied to constrained optimal piezoelectric actuators location. The test results indicate that the proposed algorithm is extremely robust and can be successfully used to solve global optimization problems. Based on the obtained optimal location, active vibration control of beams with multi-piezoelectric patches is elaborated.