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.
Highlights
Truss systems are commonly implemented in several structural systems including space structures, high-span bridge systems and bracing the skeleton buildings
To compare the applicability of the proposed method with commonly used analysis methods in the nonlinear behavioral assessment of space trusses, four numerical examples are considered in a microcomputer environment. 32-bit Pentium 1.66 GHz processors (2 CPUs) is used for solving the numerical examples
It can be concluded that the PM method for this example is able to precisely evaluate the behavior reduction computational and 29.0%
Summary
Truss systems are commonly implemented in several structural systems including space structures, high-span bridge systems and bracing the skeleton buildings. It is reported that the implementation of the linear analysis to investigate the structural applications is not sufficiently reliable without considering nonlinearities [1,2,3,4]. The linear theory is used for structures that are under service loads, but if there were slender elements in the structure or external loads exceeding the design loads (e.g., buckling load in the case of structural stability), ignorance of nonlinear behavior would cause considerable errors in a computational process due to large nonlinear deflections. Several studies in nonlinear analysis methods are presented [5,6,7,8,9], in which the stability of trusses under static and dynamic loads is investigated. Zhu et al [10] studied geometric and material nonlinearity for space trusses
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