The Fast Analysis Of Dynamic Responses For Beam Structures Based On Reduced-basis Method

In the modern design and analysis, when comes to response analysis of structures,we need to apply numerical computation method to the problem and discrete theoriginal structure into multi degrees of freedom (DOF) systems so as to make itfeasible to calculate through finite element method (FEM). Generally, thecomputational costs involved in such problems are vast because the practicalproblems are complicated, as a result the scale of the discrete structures are very large.With the development of hardware technology, the calculating speed is improving.However, only relying on the enhancement of hardware is not enough. We shouldmeantime find a rapid calculation method to improve the speed of engineeringcalculations. To solve this problem, many domestic and alien scholars have presentedseveral methods, among which the reduced-basis method (RBM) is a typical one.RBM aims to transfer a high-dimensional problem into a low-dimensional problemthrough explicit the design parameters in the structure matrix and build thereduced-basis space according to certain sampling method. It can improve thecomputational efficiency and save the computer’s memory space without reducingaccuracy. In this paper, RBM is applied to a rapid calculation problem concerning thedynamic response of the structure. The main woks are as follows:(1)Dynamic equations were established for the transient response analysis.Newmark method was employed to solve the equations. The approximate solution wasachieved by introducing reduced-basis space to lower the dimension of the structure.This method was then used to analyze the two kinds of transient response under workloads, i.e. step load response and sinusoidal load response. Through numericalexamples, the approximate solution was verified and prove to be reliable and of goodaccuracy. Therefore, by employing this method can not only improve calculatingefficiency, but also save computer’s memory space.(2)For the modal analysis, Lanczos method was utilized in solving eigenvectorsand eigenvalues, through which the reduced-basis space was constructed. Theapproximate solution of modal was rapidly obtained after order reducing of theoriginal equations. This method was verified to be of high accuracy, calculation timeshortened and computer’s memory saved. In addition, a comparison betweenone-order modal analysis and multi-order modal analysis was conducted. It turned out that both methods had its strengths in modal solution.The rapid calculation method based on reduced-basis method which combinesNemark method and Lanczos method are tested by numberrical example.The resultscan guarantee the accuracy of the calculation while calculating time is obviouslyshortened in the analysis of transient responses and modal analysis by introducingRBM into the analysis of rapid computation of structual dynamic responses.At the endRBM has a great prosperity in the analysis of dynamic responses.