A Temporally Adaptive Algorithm Based Investigation On Direct/Inverse Problems Of Beam/Plate Subjected To Moving/Fixed Loads

The numerical solutions of dynamic direct and inverse problems of structures have an important application background in engineering and research value in theory. The direct problem mainly concerns how to calculate the dynamic responses of structures accurately, and the inverse problem mainly concerns how to identify the structural constitutive parameters and dynamic loads from structural responses. One important issue in the numerical solution of direct problem is, how to keep steady computing accuracy when the size of time steps is difficult to be determined, and the computing accuracy of direct problem is also an important issue in the numerical solution of inverse problem because the direct problem usually needs to be solved continuously in the identification process. Moreover, when the gradient-type method is used in the solution of inverse problem, the numerical model of direct problem should provide the sensitivity information conviently and accurately. Hence, by taking the beam and plate as the study object, this thesis develops related research works, and the achievements include:1. Presenting a temporal piecewised adaptive numerical model to solve the dynamic responses of beam/plate subjected to moving/fixed loads, respectively. By expanding all variables at a discretized time interval, an initial and boundary value problem is decoupled into a series of recursive boundary value problems which can be solved by finite element method (FEM), and this model is convenient for sensitivity analysis. By an adaptive computation process, the computing accuracy can be ensured in the whole time history. The comparison with Runge-Kutta and Newmark methods based solutions indicate that the presented algorithm can better ensure the computing accuracy in the whole time history.2. Presenting a numerical model for solving the inverse problems of beam/plate subjected to moving/fixed loads, respectively. Based on the direct problem, an easy implementation of sensitivity analysis of unknown parameters can be provided. In the numerical solution of inverse problem, different additional information (e.g. displacement, velocity, acceleration) can be used for the identification of structural constitutive parameters and loads singly/simultaneously.3. Presenting a numerical model for solving the dynamic interval responses of a simply supported beam subjected to a moving load, considering the uncertain-but-bounded constitutive parameters and moving load. The upper and lower bounds of interval of structural responses can be calculated with the utilization of Taylor expansion and interval analysis. 4. Based on the interval direct problem, presenting a numerical model for the presented interval inverse problem of beam subjected to a moving load. The intervals of moving load and flexural rigidity of beam can be identified singly/simultaneously. The effects of different noise data on the identified results are considered, and satifactory results have been achieved.This thesis provides various numerical verifications and correlation analysis for the numerical models of direct and inverse problems considering the effects of many factors, and satisfactory results have been achieved.