Improved Homotopy Perturbation Method for Geometrically Nonlinear Analysis of Space Trusses

Abstract

The objective of this study is to explore a noble application of the improved homotopy perturbation procedure bases in structural engineering by applying it to the geometrically nonlinear analysis of the space trusses. The improved perturbation algorithm is proposed to refine the classical methods in numerical computing techniques such as the Newton–Raphson method. A linear of sub-problems is generated by transferring the nonlinear problem with perturbation quantities and then approximated by summation of the solutions related to several sub-problems. In this study, a nonlinear load control procedure is generated and implemented for structures. Several numerical examples of known trusses are given to show the applicability of the proposed perturbation procedure without considering the passing limit points. The results reveal that perturbation modeling methodology for investigating the structural performance of various applications has high accuracy and low computational cost of convergence analysis, compared with the Newton–Raphson method.

An Efficient Two-Step Iterative Technique for Solving Non-Linear Equations

“…Researchers have been focused on these approximate solutions to non-linear problems and during the last few decades, analytical solutions to these problems have been extensively studied. The researchers aimed at designing iterative methods with a high convergence order and requiring fewer calculations [7,1,3,17], some work for the numerical solutions of different daily life problems using the homotopy perturbation method is published in recent years [9,18,5,15,2,6]. For numerical solutions of non-linear equations, He [10], Rafiq and Rafiullah [19], Golbabai and Javidi [7,8], Noor and Noor [16], and Basto et al [3] presented various techniques.…”

Beton-dolgulu çelik tüplü kompozit kısa kolonların nihai yük taşıma kapasitesinin ilgililik vektör makinesine dayalı tahmini için modelleme yaklaşımı

“…The significant feature of the RVM is that it uses very few kernel functions so that it will be computationally efficient. RVM concepts were used by many researchers in different domains for developing a model [23][24][25][26][27][28][29]. The applications of RVM concepts for the structural engineering domain are found to be scarce.…”

Adaptation of the Newton-Raphson and Potra-Pták methods for the solution of nonlinear systems

“…Mohit; Sharifi; Tavakoli (2020) proposed three-step iterative techniques, with fourth-order convergence, for solving nonlinear equations used for geometrically nonlinear analysis of space truss. Dehghani et al (2020) proposed an improved perturbation algorithm to refine the classical methods in numerical computing techniques such as the Newton-Raphson method.…”