Isogeometric Analysis And Optimization Of Variable-Stiffness Panels With Cutouts Via Level Set Method

Variable-stiffness panel with curvilinear fiber path is a promising structural strengthening concept for composite structures under complex loads.The design flexibility of this type of structure is more abundant than that of the simple linear fiber laying sequence due to the uneven distribution of plane stress and stiffness.In order to meet the requirements of equipment installation,pipeline laying and cooling,cutouts inevitably exist in aerospace structures,which will greatly reduce the bearing capacity of structures.Accurate and efficient analysis of variable-stiffness structures with cutouts is an important research direction.In the variable-stiffness design,the fiber path is curved,and the in-plane stiffness varies continuously in the whole structure space.According to the actual working conditions,the strength and stiffness of the local area can be increased or reduced,and the stress distribution in the panel can be changed.Thus,the overall bearing capacity of the structure can be effectively improved.When the traditional finite element analysis(FEA)is used to analyze composite panels with cutouts,the computational elements are discrete.The smooth and continuous fiber angle in variable-stiffness design cannot be guaranteed.The refinement of elements will lead to a sharp increase in computational costs.And Isogeometric Analysis(IGA)method uses NURBS function which can accurately describe the geometric model as the basis function,avoiding the errors caused by the calculation model.It is especially suitable for mechanical analysis of variable-stiffness panels.In this dissertation,a linear variation function is used to describe the fiber path,and the effects of boundary conditions and manufacturing constraints are considered.Level set function is used to describe the cutouts area.IGA method is used to analyze buckling problem of variable-stiffness panel.In view of the problem of artificial modes and calculation errors caused by the treatment of stiffness matrix and initial stress matrix,corresponding improvements are made on this method.The results show that this method can accurately and efficiently analyze the buckling problem of variable-stiffness panel with cutouts.It is further confirmed that the variable-stiffness optimization design can obtain more diversified fiber layers and provide more structural forms that can meet the design requirements.On this basis,the IGA buckling optimization design framework based on the analytical sensitivity of buckling problem is established in this dissertation.The load-bearing performance of rectangular variable-stiffness panel with multiple cutouts under combined axial compression and shear loads is studied.The buckling resistance of the structure can be improved by optimizing the fiber layers.The results show that the optimization method based on level set and IGA methods combined with analytical sensitivity has higher computational efficiency and better optimization results.This is mainly due to the precise sensitivity and high order continuity of IGA.Then,the fiber angle description of interpolation function is used to optimize the local area of the cutouts.And the non-linear distribution of fiber angle is postprocessed.Finally,the curvilinear fiber layers are obtained.In this dissertation,the optimization design of variable-stiffness laminates is carried out by using the global-local method of fiber layers.Combined with IGA buckling optimization design framework,the bearing capacity of variable-stiffness panel can be greatly improved,and the variable-stiffness design with better performance can be obtained.It has certain application reference value for the structure design and manufacture of industrial equipment.