The Research Of Fast Reanalysis Algorithm For Structural Design Of Automobile Body

Structural design is essentially an iterative modification process. It is necessary to modify and analyze structures repeatedly during the design process due to the changes in design variables. The corresponding computational costs are expensive since the full analysis is commonly still repeatedly performed. Reanalysis is a fast computational technology to predict the response of a modified structure based on the initial analysis results. The most remarkable advantage of reanalysis technology is that reanalysis techniques attempt to analyze structures efficiently and avoid full analysis after modifications, so that a large amount of computational costs can be saved. Nowadays, reanalysis techniques have been successfully employed in various classes of structural reanalysis problems, such as static, dynamical and nonlinear problems. However, there are many unsolved problems and challenges for reanalysis technology. Firstly, there is no effective reanalysis method which could keep solutions exactly and efficiently for large changes in linear elastic problems. Secondly, for nonlinear problems, there is only a theoretical description that reanalysis method can solve geometric and material nonlinearity problems. Finally, for time-based dynamic problems, the main bottleneck is how to construct an effective reduced model as well as control the accumulated error properly. Thus, in this study, in order to overcome these bottlenecks and shortcomings, it is urgent and meaningful to find a highly efficient and accurate reanalysis method and develop corresponding software. And an effective tool to solve practical engineering problems is provided. Summarily, this paper conducts research on the basis of reanalysis method for automobile body structure design. Details of the research contents are described as follows:1) Application of combined approximation method with different elementsThe popular reanalysis methods, such as combined approximations(CA) method mainly focus on the truss and simple beam structures. It is not available for practical engineering structures, such as solid, shell and plate. The purpose of this study is to compare several types of elements of FEM in reanalysis procedure. These elements include truss, frame, beam, quadratic, plate and shell elements. And a reanalysis system is constructed with different elements. It has laid a solid foundation for further work. Nowadays, the CA method can quickly and accurately predict the modified response with small changes. However, the CA method can not guarantee the accuracy with the larger changes for every modifications.2) High accuracy block-based reanalysis methodDuring the design process for automobile, the changes of the structure will be enlarge with the repeatedly modification. The stability of predicted solution cannot necessarily be satisfied at each iteration step where the popular combined approximation(CA) method is employed. Thus, based on the block matrix inversion, an exact block-based reanalysis method for local modifications is proposed in this paper. Compared with direct method as Sherman-Morrison-Woodbury(SMW) formula, the presented method is more efficient when the change of stiffness matrix is large. For repeatedly modifications, the presented method can avoid leading to the different direction compared with full analysis which is due to the approximated method. In this study, the solving domain of modification can be classified into three parts, influenced region, stationary region and interface boundary between them. Based on the reverse Cuthill-Mckee algorithm(RCM), the main computational cost can concentrate on the influenced region by this specific blocked strategy. Thus, the proposed method can achieve an accurate response for large modification with lower computational cost. Several practical engineering problems such as car frame and inner door panel are analyzed and the results are exactly as those performed by full analysis. So the presented method is a capable reanalysis algorithm for ensuring solutions accurately and efficiently. At present, the proposed method can accurately and quickly calculate the modified response for large changes, but it still has limitations for the full rank change of the structure.3) A hybrid direct-CA method for geometric nonlinearity problemFor linear static problems, the reanalysis method can obtain accurate solutions efficiently for modifications. However, for geometric nonlinearity reanalysis problem, it is necessary to update linear equations and reanalyze repeatedly during the analysis process. Compared with initial analysis, the tangent stiffness matrix in current step has a full-rank change due to the large deformation. The popular CA method cannot guarantee the accuracy of approximations for repeated large modifications. With the number of load step increasing, the accumulated error is difficult to be compensated. Thus, an adaptive hybrid geometric nonlinearity reanalysis algorithm is proposed f or geometric nonlinearity reanalysis problem in this paper. It is the greatest advantage which a high accuracy reanalysis method is utilized. And a deformation criterion, an efficiency criterion and an adaptive strategy have been proposed to improve the accuracy, speed up the efficiency and control the error respectively. The initial analysis and initial displacement are adaptively updated by the error estimation, which ensures the accuracy of the geometric nonlinearity. In addition, in order to ensure the accuracy of the full-rank change of the tangent stiffness matrix, a hybrid direct and CA static reanalysis method(HDCA) is proposed. It is proved that the solutions by direct and CA method can be expressed as a linear combination of basis vector. And a hybrid reduced model is constructed based on the direct method and CA method. The HDCA method improves the efficiency of the direct method and the accuracy of the CA method. The applications of the dent resistance analysis for the automotive engine cover and the roof cover have shown that the adaptive hybrid geometric nonlinearity reanalysis algorithm can obtain accurate solutions. The method can be applied to large-scale and complex engineering problems.4) A time-based global method for dynamic reanalysisThe static and frequency-based dynamic reanalysis methods can be solved successfully. However, for time-based dynamic problems, a large number of computational effort and storage space are needed, which is spent on constructing the reduced model in each time step by using the reanalysis technique. Obviously, it is difficult to solve large-scale engineering problems in practical. Furthermore, once the time integration runs, the accumulated error is difficult to be compensated. Thus, an adaptive time-based global method(ATGR) for dynamic reanalysis for Newmark-β method is proposed in this paper. The global reduced model of the whole time domain is constructed by the Latin Hypercube Design(LHD) and Neumann series. Thus, this strategy can avoid the factorization of the effective stiffness matrix and improve the efficiency of the initialization and iterative process. In order to guarantee the accuracy of prediction, an adaptive strategy is used to minimize the accumulated error in time domain. A series of new basis vectors will be generated according to the error estimation and a corresponding reduced model will be updated. Numerical simple examples, such as trusses have shown that approximated solutions are accurate enough compared with full analysis and the method is a feasible method for d ynamical reanalysis problems in time domain. However, with the larger of the scale, the high accuracy of the dynamic reanalysis algorithm is still a challenge in the future.