An Analytic Iteration Method Of Geometrical Nonlinear Analysys

Structure analysis of considering the bending and deformation influence of the axial pressure to column must adopt the method of two step analysis, namely we can't neglect the influence of deformation to the effect of force and it is a geometrical nonlinear problem of the column system of the elastic material. The ordinary overlay principle that had been extensively applied hasn't been applied to this kind of nonlinear analysis in elastic theory.This thesis introduces mainly an analytic iterative method that can carry on the geometrical nonlinear analysis to complicated structure and programming. This method is derived, considering geometrical nonlinear influence in structural calculation, on foundation of the analytic method that expresses with curving line of deflection equation of pressed column with geometry parameter expression with the combination of traditional linear analysis method. The result of this method is accurate solution of differential equation because it is on the basis of analytic method. Compared with the value solutions, it has a lot of characteristics such as clear concepts, simple steps, quick convergence rate, etc. Not only are there iterative steps in the thesis, but also author edits a calculating application program of analysis iterative method that carries on the geometrical nonlinear analysis to the structure in the environment of MATLAB language to calculate displacement and force of column of considering the influence of the axial pressure. This program is also suitable to the situation of imposing on crosswise distribution load. Some illustrative examples of plane frame structure are given to show the potential of this kind of analysis iterative method and application of program.Through theoretical analysis and example that is expounded and proved, this thesis makes the analytic iterative method and application program of carrying on the geometrical nonlinear analysis have major theoretical meaning and extensive practical value. It may be considered as the supplements for the current energy method with extensive application that carries on nonlinear analysis. In operating aspect of the application program, preparation work is less, data and program separate, operation is simple and convenience, efficiency is high, so operator may save plenty of time and expenses in the period of structural analysis. It will change some foreign expensive nonlinear analysis software ANSYS etc. to occupy the market.