Improved Homotopy Perturbation Method for Geometrically Nonlinear Analysis of Space Trusses

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.

Chemical Reaction Influence on General Fluid

This paper focuses on unsteady, two-dimensional, flow boundary layer of a incompressible viscous electrically conducting and absorbing heat fluid along a semi-infinite vertical moving permeable plate in the presence of Chemical reaction and radiation effects. The dimensionless equations are analytically solved using perturbation procedure. The effects of the different flow fluid parameters on velocity, temperature and concentration fields with in the boundary layer have been examined with the help of graphs.

Analytical investigation of buckling of a cylindrical shell subjected to nonuniform external pressure

An analytical algorithm is proposed for studying the stability of a cylindrical shell subjected to nonuniform external pressure. The algorithm is based on a perturbation procedure and Padé approximants. Unlike the commonly used perturbation method, this approach is not limited by the smallness of the perturbation parameter. The approximate formulas obtained are sufficiently accurate and can be used in engineering practice.

A Perturbation Procedure for Limit Cycle and Heteroclinic Connection Analysis of Certain Self-Excited Oscillator

A perturbation procedure, in which the elliptic perturbation method and the hyperbolic perturbation method are applied, is presented for predicting heteroclinic connection of limit cycle or self-excited ocsillator. The limit cycle can be analytically constructed first by the elliptic perturbation method after Hopf bifurcation, in which the amplitude of limit cycle can be controlled by the modulus of elliptic functions. The heteroclinic trajectories, which are formed by the heteroclinic connection of limit cycle, can also be constructed by similar perturbation procedure but adopting the hyperbolic functions instead of elliptic functions. And the criterion of heteroclinic connection is given in the perturbation procedure. A typical self-excited oscillator is studied in detail to assess the present method.

Heteroclinic Bifurcation Analysis of Duffing-Van Der Pol System by the Hyperbolic Lindstedt-Poincaré Method

The heteroclinic bifurcation of the Duffing-Van der Pol oscillatory System is studied by the hyperbolic Lindstedt-Poincaré method. The heteroclinic solution can be solved analytically by the method. And the critical value of the bifurcation parameter under which heteroclinic orbit forms can be determined by the perturbation procedure. Typical applications are studied in detail and compared with numerical results to illustrate the accuracy of the present method.