Large-scale Numerical Analysis And Design Sensitivities Computation Research On Thin-walled Structure

Because of its high load carrying efficiency, thin-walled structure is widely used in aviation, spaceflight, navigation, automobile engineering and so on. Due to the development of science and technology and the demand of modern industry, the finite element numerical analysis combined with engineering optimization is the typical technical characteristics of modern structural design, also is the important technology to realize high-precision and cost efficient design. Due to the inherent complexity of multi-disciplinary structural design, the modern structural numerical analysis and design demands refined, large-scale, multiple working cases and multi-solvers, which require the more accuracy of the large-scale engineering numerical calculation and the more high execution efficiency of computer software technology. Meanwhile, the influence of the multidisciplinary performance of sectional configuration parameters in engineering structures is the important information in engineering analysis and design, is also the necessary technical parameters for numerical optimization based on design sensitivity. The large-scale structural sensitivities calculation has a lot of responses and design variables, which also require the high-efficiency computer algorithms software platform. With 30 years'development, the international mainstream commercial structural software system has achieved the integration of these technologies function mentioned above. However, carefully analyze and study the modern commercial software systems and their computing performances, it can be found that there are still several aspects need to develop and improve. In addition, some important post-processing functions of structural software system are concerned by modern multidispline analysis and design, while which are ignored and lacked in the modern large-scale commercial structural engineering software system, such as determination of rigidity surface and elastic aix of wing structure and its stiffness distributed characteristics, the main research work is shown as follows:(1) Based on the sequence table data structure theory, the one-dimensional dynamic sequential table data storage technology is proposed, which implements efficient storage and assesses of original data and new data in the algorithm software system. In order to solve the large sparse system of linear equations and the large sparse matrix eigenvalue problems, the direct sparse solver DSS and the eigenvalue solver ARPACK are comprehensively analyzed and researched in the dissertation. In order to realize the efficient management of the decomposition stiffness matrix, the momery handle of DSS is used, which can not only avoid repeatly decomposing the global stiffness matrix, but also can release the momery space timely. To improve the efficiency of this algorithm system, two technical measures is adopted: Firstly, OpenMP parallel computing technique is introduced into the computation intensive code area, which can fully make use of the computing resourse of the modern multicore, large memory computer; Secondly, based on the algorithm framework, the targeted code optimization techniques are developed, including the reasonable useage of loop, improving the code utilization, and the high-efficient computation of matrix multiplication.(2) For realizing refined numerical analysis of large-scale thin-walled structure, three kinds of common thin-walled finite element (General Timoshenko beam element TM3, general triangle flat shell element OTS3 and general quadrilateral flat shell element QTS4) are adopted in the dissertation. To achieve the analysis of several kinds of structural performance and response, calculation formula of stress/strain, geometric stiffness and consistant mass matrix of the triangle common thin-walled element are developed.(3) To achieve high-efficient solution of multi-boundary model numerical analysis, the multi-boundary storage and dynamic assembly technique of the global stiffness matrix is proposed, which is based on the node-reordering technique. According to the multi-boundary processing technique, the multiple working cases solveing strategy is constructed, the boundary reaction force calculation formula and all kinds of load array expression are deduced. In order to obtain the more accurate torsional angle of wing section surface, the computing method based on unit load is developed.(4) Based on the analytical derivative of finite element, the analytical design sensitivity derivative of the large-scale thin-walled structure with multiple working condition and high-dimension variables is developed. The derivative expressiones of element-level matrix of the three common thin-walled structural element are deduced, including element stiffness matrix, the calculation formula of the stress/strain, geometric stiffness matrix and consistant mass matrix. To improve the design sensitivity derivative calculation efficiency of the algorithm software system, several technical strategies is employed:first, for different design sensitivity analysis model, the two analytical methods have different efficiency. In general, when the number of structural responses is more than design variables, the direct analytical method is more efficient, otherwise the adjoint variable method is more efficient. Secondly, to improve the efficiency of linear buckling eigenvalue sensitivity of large-scale structure, OpenMp parallel computing technique and code optimization technique based on this algorithm software system are adopted. Thirdly, the substructure technique is applied to improve the efficiency of the direct analytical design sensitivity calculation for large-scale structure optimazition. In addition, in large-scale structural sensitivity analysis, beside the efficiency of the design sensitivity computation, the implementation difficulty of different kinds of structural responses is also an important consideration. Through comprehensive comparison on the five given kinds of structural response, the most suitable sensitivity analysis method is introduced for each kind of structural response.(5) Based on the muli-boundary global stiffness matrix technique, the determination method of rigid surface and elastic axis for wing structure is developed, and also the numerical computine technique of the stiffness of wing is proposed. Finally, the long-span wing is applied to test the mentioned method, and reasonable numerical results are obtained.