Abstract: We combined the 3D lattice Boltzmann method (LBM) with the immersed boundary method (IBM) to study the flow physics induced by an elastic rectangular container undergoing harmonic oscillations surrounding a viscous fluid. We propose a semi-microscopic expression for the drag force to compute the hydrodynamic forces at the boundary nodes. An analytical deformation solution is used based on a thin plate elastic deformation theory to calculate the displacement experienced by the boundary. The numerical simulation result(All the results on figure axes, in this article, are displayed in lattice units.) based on the proposed method agreed with the theoretical predictions for channel flow with stationary boundary. The oscillating boundary simulation exhibits the expected flow pattern in line with theory.
Abstract: Structural health monitoring is an important means to guarantee the continuing safe operation of aircrafts, and makes a key technique for unmanned aerial vehicles’ (UAVs’) development and certification. For a UAV fuselage, the structural acceleration responses, strain signals and modal parameters were acquired on-line from different sensor measurements in dynamic structure simulation. The normalized wavelet packet energy change rate index, the strain energy change rate index, the modal frequency change rate index and the mixed damage evaluation indices were built to indicate the structural health condition. The integrated multi-source data fusion technique, including data-level fusion, feature-level fusion and Bayesian probabilistic neural network-based decision-level fusion, was used with the rough set reduction successively to significantly decrease the spatial dimension of data. The mapping between structural damage information, like damage severity, damage locations and health evaluation indices, was established, and the comprehensive decision of the structural damage model was achieved. An example for the health monitoring of an unmanned helicopter was demonstrated. The experimental results verify the accuracy of the proposed data fusion technique for damage identification of multi-damage aircraft structures, and show the validity of multi-data fusion in UAV health monitoring.
Abstract: To overcome the numerical oscillation in solving transient temperature fields with the finite element method, the heat conduction matrix and the heat capacity matrix were analyzed, and the cause for the oscillation of numerical solution as well as the method of eliminating oscillation were studied. According to the results, the cause for the numerical oscillation is that the thermal conduction matrix violates the second law of thermodynamics, and at the beginning of the iteration, the continuity hypothesis of the temperature change rate of the elements in the heat capacity matrix is far from the actual situation. Regularization of element shapes and application of appropriate lumped mass heat capacity matrices can effectively eliminate the numerical oscillation. With an infinite plate in the heat transfer process as an example, the conclusion was verified through comparison between different calculation methods.
Abstract: The generalized Pareto distribution (GPD) is a classical asymptotically motivated model for excesses above a high threshold based on the extreme value theory, which is useful for the high reliability index estimation. In the GPD there are 2 unknown parameters which could be estimated with the least-squares fitting method and the maximum likelihood method. Both methods need all the tail samples of a distribution in previous studies. However, for the GPD estimation, the better accuracy would lead to a much higher computational cost. So a least-squares fitting method based on the quantiles was proposed to obtain the unknown parameters in the GPD. The 2-stage-updating method for the Kriging model was also given to calculate the quantiles. Compared with the GPD based on the maximum likelihood method and the Monte-Carlo method, the 2-stage-updating method for the Kriging model helps find the specified quantiles accurately and efficiently, and the least-squares fitting method based on the quantiles also performs well.
Abstract: The polish mapping and the filter mapping in the ICM (independent continuous mapping) method for topology optimization were extended, and the composite function was used to coordinate the filter function. Due to the superposed discrete effects of composite functions, the composite function of the power function and the sine function was introduced to identify the presence and absence of the elements. The ICM method was used to establish the topology optimization model for the continuum structure with the minimum weight under the displacement constraints, which was solved with the exact dual algorithm of the quadratic programming. Then based on the dynamic inversion strategy, the rational inversion function was constructed with the optimal threshold to obtain the most strict discrete solution. Moreover, the 2-stage ‘discrete-continuous’ and ‘continuous-discrete’ solution method was established for topology optimization. Moreover, a calculator program was developed and compiled based on the MATLAB according to this new method. The results show that the proposed method has the advantages of higher computational efficiency, less optimal gray values and less structural weight after inversion, and gives a more reasonable structural topology.
Abstract: The response analysis of tall buildings under earthquake action is a difficult task in civil engineering design. With the symplectic precise integration method, which has advantages of high precision of the precise integration method and excellent long-time numerical stability of the symplectic method, the seismic response analysis of a tall building was performed and the elastic/elasto-plastic time-history results of the structure were obtained. Comparison of the numerical results between the symplectic precise integration method and the EPDA software shows the feasibility and the effectiveness of the symplectic precise integration method for seismic response analysis of tall buildings.
Abstract: Using 3 parameters to describe finite rotations will inevitably have the singularity problem, which leads to numerical difficulties in solving the rotational parameters from the integration of the angular velocity. Based on systematical studies of the singularity of the rotation vector, a new numerical integration method, which can overcome singular points of the rotation vector, was proposed. With the property that the 2 rotation vectors with the same direction but different norms correspond to the same finite rotation, the rotation vector near the singular point was switched to its corresponding one far away from the singular point and in the numerical stability region, during the numerical integration. This method can avoid the difficulties in the numerical integration caused by the singularity of rotation vectors for the angular velocity vectors. Numerical examples show that the proposed method is simple, stable and effective.
Abstract: In order to reduce the condition number of the coefficient matrix of ill-conditioned linear equations, according to the equilibration thought for matrices, a 1-norm equilibration method was proposed to properly reduce the condition number of the matrix, and expanded to the norm equilibration methods. Then, the norm equilibration method together with the precise integration method was combined for solving ill-conditioned linear equations. The numerical results confirm that, the accuracy, efficiency and application scope of the preconditioned precise integration method for ill-conditioned linear equations all improve significantly (the number of significant digits increases by more than 5 and the number of iterations decreases by about 15). In these methods, the preconditioned precise integration method of 1-norm equilibration is the best.
Abstract: An interpolating boundary element-free method was presented for solving interior and exterior boundary value problems of 2D Helmholtz equations. According to the indirect potential theory and the characteristics of the fundamental solution of Laplace’s equation, a regularized boundary integration equation formulation was established to avoid the computation of the strongly singular integration. Besides, through expansion of the global distance into power series in the form of the local distance, the limit expressions of the distance derivative and the difference between 2 normal derivatives were deduced in detail. Finally, 4 numerical examples were given to show the feasibility and efficiency of the proposed method.
Abstract: The numerical solution of obstacle problems with 2ndorder semilinear elliptic partial differential equations (PDEs) was addressed. The nonlinear obstacle problem was solved with the monotone iteration method, and the adjoint elliptic differential equations with the Dirichlet boundary conditions on irregular domains were solved with the fictitious domain method. In the calculation process, the conventional finite element discretization resulted in the trouble of computing integrals on the irregular body boundaries with the regular mesh of the extended domain. To overcome this difficulty, a new algorithm was designed based on the finite difference method allowing the use of fast solvers for PDEs. The proposed algorithm has a simple structure and is easily programmable. The numerical simulation of a steady state problem of the logistic population model with diffusion and obstacle to growth shows that the proposed method is feasible and efficient.