| Owing to the high specific stiffness and strength,load-carrying structures such as truss structures and stiffened structures have been widely used in automotive engineering,marine engineering,aerospace engineering and other engineering fields.The development trend of high load-carrying capacity and lightweight design is a huge challenge to the existing optimization design methods of load-carrying structures.At the initial design stage of load-carrying structures,the sizing and shape optimizations are mostly carried out for truss structure designs,making it difficult to break through the limitation of the connectivity of truss elements.Thus,the mechanical properties of truss structures are difficult to be greatly improved.Additionally,the existing design methods of stiffened structures are mainly based on engineering manuals and design experience to determine the initial stiffened configurations,and then the sizing optimization design is carried out.It limits the design space,and thus the design potential of load-carrying structures is not fully explored.Additionally,heuristic algorithms are widely used in the sizing optimization process,but the optimization efficiency is generally low.Therefore,it is urgent to optimize the size,shape and topology of load-carrying structures simultaneously to obtain an outstanding load-carrying structure design scheme.At the detailed design stage of load-carrying structures,the nonlinear analysis theory is more suitable to analyze the load-carrying structure in comparison to the linear analysis theory.However,the computational efficiency is lower.Moreover,the development of large and complex load-carrying structures leads to a significant increase in the degree of freedom of the finite element model.Thus,the computational efficiency would be further reduced due to the effect of geometric imperfection.Therefore,it is an urgent problem to improve the computational efficiency of load-carrying capacity analysis and imperfection sensitivity analysis.To solve the problems of low optimization ability and low computational efficiency of existing load-carrying structure design methods,an isogeometric analysis-based stiffness spreading method(IGA-based SSM)is firstly proposed to improve the optimization efficiency and optimization ability of the truss layout optimization,in which the size,shape and topology of the truss structure can be optimized simultaneously.Then,a stiffened layout optimization method is established by the IGA-based SSM to optimize the size and shape of stiffeners.The analysis and optimization efficiency of stiffened plates are improved by reducing the degree of freedom and the number of design variables.Moreover,the IGA-based SSM is further extended to the buckling optimization of the stiffened shell by combining the asymptotic homogenization method(AHM)with the Rayleigh-Ritz method to improve the load-carrying capacity of stiffened shells significantly.Finally,an accelerated Koiter method based on model reduction strategy is proposed to analyze the effect of small and middle amplitude geometric imperfections on the load-carrying capacity of stiffened shells efficiently and accurately.The main content of this thesis is as follows:(1)To solve the truss layout optimization problem,a novel truss layout optimization method is proposed in the IGA framework,namely IGA-based SSM.It is established based on energy conservation and non-uniform rational B-splines(NURBS)basis functions.The stiffness of the truss element is spread into the weak background grid.The independent movement of truss elements can be implemented without considering the connectivity of truss elements,which can simultaneously optimize the size,shape and topology of the truss structure.The IGA-based SSM can overcome the sensitivity discontinuity problem that occurred in the traditional finite element method and avoid the local minimum problem that occurred in SSM caused by radial basis function interpolations.Optimization results obtained by the IGA-based SSM are less dependent on initial layouts.Additionally,the IGA-based SSM is verified to achieve higher optimization efficiency and optimization ability than SSM.(2)To solve the layout optimization problem of stiffened plates,a novel stiffener layout optimization method is established based on the IGA-based SSM,in which the shape and size of stiffeners can be simultaneously optimized.The flat plate is simulated by the isogeometric degenerate shell element,which can ensure the continuity and smoothness of the sensitivity field.The stiffener is simulated by the Timoshenko beam element,which is convenient to establish the coupling relationship between the stiffener and the plate.The initial layout is generated by the ground structure to ensure the connectivity between stiffeners,and the inside radius constraints of triangles are employed to avoid the overlapping and intersection of the stiffeners.Compared with the traditional continuum topology optimization method,the proposed method can significantly reduce the number of degrees of freedom and design variables of the optimization problem,and can directly obtain clear and reasonable optimization results without additional complex feature extraction.(3)To solve the buckling optimization problem of the stiffened shell,a buckling optimization method of the stiffened shell based on the IGA-based SSM is proposed by combining the AHM with the Rayleigh-Ritz method.The stiffness matrix of the stiffened cell is calculated by the IGA-based SSM.AHM is employed to smear the skin and stiffeners into equivalent stiffness coefficients,and then equivalent stiffness coefficients are substituted into the Rayleigh-Ritz method to calculate the buckling load,which can significantly improve the computational efficiency of the stiffened shell.A penalty function is proposed to impose the minimum thickness constraint.Compared with the traditional design scheme of the stiffened shell,the proposed method can obtain an innovative stiffened cell configuration and greatly improve the buckling load of the stiffened shell.(4)To solve the problem of the low computational efficiency of the prediction of load-carrying capacity and imperfection sensitivity analysis of stiffened shells at the detailed design stage,an accelerated Koiter method based on model reduction strategy is proposed.Firstly,the stiffened cell is established by the beam-shell coupling model using the IGA-based SSM,and its equivalent stiffness coefficients are calculated by the AHM.Then,an iterative eigenvalue algorithm based on the combined approximation(CA)strategy is proposed,which can approach the limit load of the equivalent model accurately and efficiently.Moreover,the asymptotic expansion is carried out near the limit point of the equivalent model,and the reduced-order model is established based on the Koiter method considering pre-buckling nonlinearity.The effect of modal imperfection on the load-carrying capacity of the stiffened shells can be accurately predicted only by considering the imperfection terms each time.Compared with the Riks method,the accelerated Koiter method can significantly improve the computational efficiency of load-carrying analysis and small and middle amplitude imperfection sensitivity analysis. |
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