A Lower Bound Limit Analysis Algorithm And Its Implementation

The limit analysis as one kind of structural reliability analysis method since proposed has been taken seriously by international researchers. This article analyzes and summarizes the general situation of the research on this domain, as well as the meaning of this study. It makes the detailed thorough introduction to the elementary theory of the limit analysis, give out the mathematical model of upper and lower limit analysis. Introduce two kinds of calculation format: the calculation scheme I by using simplex finite element do mesh, and the calculation scheme II by using isoparametric element do mesh. Furthermore introduce one kind of step Newton iterative algorithm which corresponds with the calculation scheme I (in article becomes algorithm I). This algorithm's unknown quantity and objective function is represented by unified form, use simplex finite element do mesh, and use balance equation in differential form. It's considered that there are some deficiencies in algorithm I, this article introduces another step Newton iterative algorithm which corresponds with the calculation scheme II (in article becomes algorithm II). Algorithm II directly takes the overload factor as the objective function and the stress as the unknown quantity, and uses isoparametric element do mesh, and it derives the integral form balance equation by the principle of imaginary work. The main differences between algorithm I and algorithm II are the kind of element used to mesh is different, the balance equation expression way is different, and the objective function with unknown quantity separated or not. Because of these differences enable the algorithm II to have the following merits: needs few elements, better imitation in problems with complex boundary condition, and can use storage technique of the existing finite element program.Study and use the MATLAB coding to implement the algorithm II. The procedure is programmed by the article author, without referring to any existing finite element procedures. Use only MATLAB language to complete the whole treating processes (including the finite element treating process and iterative process). And use this procedure compute the chosen example. And then comparatively analyze the results of the algorithm II and the algorithm I, give out the conclusion.Furthermore, the article to each nonlinear programming algorithm which is used has carried on the brief introduction. And also summarize the programming language MATLAB which is used.