梁類結(jié)構(gòu)幾何非線性大變形問題優(yōu)化算法的研究.pdf

1、沈陽建筑大學(xué)碩士學(xué)位論文梁類結(jié)構(gòu)幾何非線性大變形問題優(yōu)化算法的研究姓名：尤超申請學(xué)位級別：碩士專業(yè)：固體力學(xué)指導(dǎo)教師：侯祥林2008-02碩士研究生學(xué)位論文 Abstract III Abstract Nonlinearity exists in all engineering problems, and nonlinear factors are included in varied degrees. Con

2、sequently, it is necessary to develop nonlinear analysis. With the availability of the computer and the appearance of the FEM, now nonlinear analysis has obtained gigantic achievement. At the p

3、resent time, FEM is the one of most effectively numerical calculation method. FEM is that a series of modified linear approximation solutions approach the solution of nonlinear problem step by

4、 step, which means that a series of linear problems are analyzed by the iterative method. Compared to the previous geometry nonlinear analysis this paper selects out the elementary theory and c

5、omputational method suitable for this topic research .The article proposes a new method -final state large deformation direct analysis optimization algorithm. Based on optimization theory, direct

6、analysis optimization algorithm in final state is proposed to solve the geometrically nonlinear problem and achieves direct analysis calculation of structural deformation in equilibrium state. The

7、 algorithm in this paper analyzes the cantilever beam and the simply- supported beam. The structure in equilibrium after large deformation is studied and divided into some slight segments. Then,

8、 the endpoint coordinates of slight segments are given through coordinate recursion formulae so as to establish an objective function in terms of unknown endpoint coordinates of slight segments.

9、 Thus, make sure of optimization problem of the geometrically nonlinear analysis of material structure, and write a program. The state of the equilibrium of beams are completely analyzed and de

10、duced by the algorithm proposed in the paper. Applied the algorithm, the accuracy of the direct analysis optimization algorithm is verified on the condition that analysis of the small deformati

11、on of the structure of the beam, and then the process of the large deformation direct analysis optimization algorithm is described. Numerical examples are given and the results are analyzed in

12、 comparison with those by FEM, which shows that the algorithm in this paper is reliable and verifies the correctness of nonlinear geometrical relationship.. In the paper ,using the proposed alg

13、orithm study the deformation and the rotation of the beam in a simple indeterminate circumstances, and by analyzing typical example to FEM results, which show the method handle the large defor

14、mation structure also validity and accuracy Because the paper chooses the equilibrium state after deformation as the object, which will enhance the result accuracy of algorithm in this paper and

15、 make the results approach true values. Therefore, the algorithm in this paper is suitable for nonlinear analysis and has the significance reference to the large span bridge design in present