The Application Of DQ And GDQR In Structural Analysis

DQM, which is the abbreviation of Differential Quadrature Method, is a numerical method specially analyzing partial differential equations, it's developing very fast in the past decades. Since just certain numerical values not all numerical values of the unknown functions are needed in engineering models often and DQM just meets the requirement. Compared with FEM, DQM is very simple, costing less computation, effortless understanding and not depending on varational method, so it's convenient to be used in engineering.DQ and GDQR are used in many fields and the GDQR is developed quickly in structural mechanics. Based in the history of DQM and GDQR(Generalized Differential Quadrature Rule), here some typical problems are analyzed in details: 1) Some typical non-linearity problem is analyzed by DQM. In this paper, buckling of column is considered. The displacement in any position and the critical value at the bifurcation point is achived by some programs. Numerical results show that the DQM possesses a higher accuracy and convenience as compared with the analytic solution and other approximate solutions for the problem. 2) DQ and GDQR applied in engineering together. Some problem can be dealt with both DQ and GDQR.. The nonlinear static beam simply supported is considered in this thesis. The paper provides two different equation for the problem, and they are settled by DQM and GDQR separately. It's inspiring that the above nonlinear static problem with axial forces considered is dealt by DQM, and it's unique in the validity and efficiency. 3) GDQR is the advanced DQM. In this paper, a storage tanks which is stepped wall thickness and banded in circumferential is considered to show GDQR more fitting for variable section problem solving. 4) Software designing based on GDQR. Usually a computing method is accepted by people through some software used widely which based on the numerical method. In some degree, GDQR is completely and software designing based on GDQR can be considered. In this paper, two types of software designing method is shown. In this paper, the DQM is considered profound for variable section models solving. And GDQR, the lastly computing theory which one based on DQM are more fit in this problem solving, and this theory can be used in many fields. What's more, the software designing in this paper based on GDQR may be lead to a commericial one.