Tensor-decomposition based matrix computation: A fast method for the isogeometric FSDT analysis of laminated composite plate. (November 2019) - Fan, Kuan; Zeng, Jiani; Huang, Zhengdong; Liu, Qinghua
Abstract: This paper presents an efficient computation method for matrices in the isogeometric analysis (IGA) of laminated composite plates, based on the First order Shear Deformation Theory (FSDT). In the method, the stiffness matrix, mass matrix and geometric stiffness matrix for static, vibration and buckling analyses are adapted into tensor-product forms and 2D integrals of the matrices are decomposed into Kronecker product of 1D integrals, which leads to the improvement of computational efficiency. Several experiments that apply the method to the static analysis and design optimization of laminated composite plates are presented in this paper to demonstrate its effectiveness. The first experiment studies the case that the domain parameterization has a diagonal Jacobian matrix (rectangular plate), and the result shows that the computation time of global matrices is drastically reduced while their accuracy is not affected compared with traditional computation methods. The second experiment is about the case of non-diagonal Jacobian matrix. The results of circular plate, annular plate and square plate with complicated cutout show that the matrices calculation is also remarkably sped up when its model is formed in NURBS. Although the tensor-decomposition incurs certain approximation in the second case, the results still show high accuracy. The third and fourth ones study the computation efficiency of design optimization, respectively about the constant-stiffness and variable-stiffness designs when the proposed method is applied to the analysis in each iteration. All the experiments prove the high efficiency of the proposed method. Highlights: New formulae of the stiffness matrix, mass matrix and geometrical stiffness matrix for static, vibration and buckling analyses are derived in tensor-product forms. Computational efficiency of the analyses in the cases of both diagonal and non-diagonal Jacobian matrix is raised up. FPAT provides a feasible way to separate constant part and variable part of analysis computation in iterations of optimization, and thus the constant part could be stored without being repeatedly calculated and the optimization processes are further accelerated. Optimization processes of constant-stiffness and variable-stiffness plates for minimum compliance designs are sped up when FPAT is used.