Research On Fast Structural Dynamic Analysis Based On Real-time Computational Methods And Its Application

The problems considered in engineering practice and scientific research become more and more complex, as leading to the increasing in the scale of the associated approximate mathematics model. Rapid development in computer is surpassed by the increasing demand in the scale of problems. Thus methods that can significantly reduce the problem size and computational cost while retain the accuracy of the solution and the physics of the structures are highly desirable. The real-time calculation methods emerge as the time require. In this thesis, the reported research from literatures about real-time calculation method is introduced. Based on the basic theory, real-time calculation methods are proposed for the structural dynamic anlysis. High efficiency is achieved both in time-space domain and frequency domain problems. The works of this thesis are summarized as following:1. A sensitivity analysis method is adopted to overcome the low efficiency in the reanalysis of structures. In this method, the sensitivity is performed to find the design parameter. The approximation of natural frequencies is given by the Taylor expansion with respect to the design parameter. Then it is easy to obtain the required natural frequency by modifying the structures and avoid fussy work. This method can be extanded to analysis and design of actual structures. At the same time, radial point intepolation method (RPIM) is suggested to solve the foregoing problem. The approximation of field variable by RPIM is performed in a parameter domain. The shape function of RPIM possess Delta function's property. This method is applied to fast analysis the wave characteristics in a composite material laminated plate. To reduce the error in the approximation, an adaptive method is presented for RPIM.2. Real-time calculation based on reduced basis method (RBM) for structural dynamic analysis is studied. The formulations are developed for modal superposition and direct integration, respectively. For the former, generalized eigenvalue problem and standard eigenvalue problem are studied according to the parameter dependence of stiffness and mass matrices. Corresponding to sample set, the reduced basis space is constructed by extracting the truncated eigenvectors. The efficiency improvement is achieved through a Galerkin projection of eigenvalue problem onto the reduced basis space. Newmark method is adopted to develop the formulation of real-time calculation method based on direct integration. To construct a time-independent reduced basis space, the time step is added into the parameter domain. The reduced Newmark incremental formula is obtained by projecting the full system onto the reduced basis space, as leading to effectively solution of the dynamic equilibrium equation.3. Different sampling of parameter is adopted to test the real-time calculation method based on RBM. In the numerical application, the pre-sampling technique is proposed to replace the sensitivity analysis. Greedy algorithm is suggested to construct the reduced basis space adaptively. In this algorithm, the variable vector corresponding to one arbitrary point in the pre-sampling set initializes the reduced basis space. By comparing the exact solution set and the reduced basis approximation in the pre-sampling set, it regards the point with maximum error as the next sample point, and the corresponding vector is extracted to enlarge the reduced basis space. This procedure will not terminate until it is convergent. Due to the adaptively sampling, it will generate a reduced basis space with suitable size, as avoiding the tradeoff between efficiency and accuracy.