Resolution Of Nonlinear Problems Research Articles

A high-order finite element continuation for buckling analysis of porous FGM plates

This work presents an effective approach to investigating the buckling and post-buckling behavior of porous FGM plates. The main objective of the present analysis is to use a High Order Continuation based on the Asymptotic Numerical Method with the Finite Element Method for nonlinear behaviors of a Porous Functionally Graded Material plate (PFGM) with different porosity distributions under various types of transverse loads. In our study, we will take into account the lack of uniform and non-uniform porosity using a Higher-order Shear Deformation Theory (HSDT). The adapted solver proves to be more effective for analyzing non-linear mechanical phenomena and more precisely the post-buckling analysis of the PFGM plates. Indeed, this numerical high order algorithm presents an adaptive step length to the local nonlinearity of the solution branch and to detect easily the bifurcation points and bifurcated branches. When compared to iterative techniques like Newton–Raphson, the proposed high-order algorithm has the benefit of speeding up the resolution of nonlinear problems. The mathematical formulation is based on the higher-order shear deformation plate theory taking into consideration geometrical nonlinearity and initial imperfections. Numerical results of a parametric study on the effect of various types of load, porosity distribution, grading index, porosity index and different span-to-thickness ratios will be investigated.

Design of concentric ring arrays for low side lobe level using SQP algorithm

In this paper, an efficient method based on the sequential quadratic programming (SQP) algorithm for the pattern synthesis of concentric rings antenna arrays to reduce side lobe levels (SLL) by controlling only the amplitude excitations of each array element was presented. SQP algorithm is a deterministic method of multi-objective optimization. It is the most widely used for the resolution of nonlinear problems. It consists of transforming the nonlinear problem to sequence of quadratic sub-problems by using a quadratic approximation of the Lagrangian function. In order to illustrate the performance of the proposed method, several examples of planar concentric rings antenna array patterns with almost one-half wavelength spaced isotropic elements to reduce the SLL and to norrow the half power beam width are presented. The results shown in this paper and compared with those obtained by the application of uniform, Hamming and Blackman weighting, demonstrate the effectiveness of this optimization method based on the SQP algorithm.

Simulation of a natural circulation loop using a least squares hp-adaptive solver

In this work the implementation of a high-order method for the simulation of a natural circulation loop is discussed. An adaptive method is developed in order to improve both accuracy and computational time in the resolution of nonlinear problems. Finally, several numerical simulations are discussed in relation to the development of this kind of high-order adaptive methods for unstable thermo-hydraulic systems.