Extended Peridynamics and Parameter Optimization Study Based on Moving Least Squares Method

Based on the theory of peridynamics, the least squares and the moving least squares method are proposed to fit the physical information at nondiscrete points. It makes up for the shortcomings of the peridynamic method that only solves the discrete nodes and cannot obtain the physical information of other blank areas. The extended method is used to fit the one-way vibration problem of the rod, and the curve of the displacement of a nondiscrete node in the rod is extracted with time. The fitted displacement results are compared with the theoretical results to verify the feasibility of the fitting method. At the same time, the parameters in the fitting of the moving least squares method are optimized, and the effects of different tight weight functions and influence ranges on the results are analyzed. The results show that when the weight function is a power exponential function, the fitting effect increases with the decrease in the coefficient. When the weight function is a cubic spline weight function, a better fitting effect is obtained. And in the case of ensuring the fitting result, the affected area should be reduced as much as possible, and the calculation efficiency and precision can be improved.

Fitting CAD data to scanned data with large deformation☆

Recently, largely deformed simulation models, such as car crash simulations, have been in high demand. To evaluate such models, it is necessary to use actual deformation results to compare and validate them. When measuring actual deformed objects, an X-ray CT is useful because it is non-destructive. However, matching undeformed CAD data and scanned deformation data is difficult. We propose a system for users to set control points or control lines on feature points and predict deformation using affine transformation with the moving least squares method. In the proposed method, undesirable distortions are reduced by evaluating scaling using singular value index and introducing offset control points. The deformed CAD data are obtained by matching predicted CAD data and a polygon mesh generated by deformed CT data. In addition, the surface elements of the generated deformed CAD data are evaluated for CAE.

POINT CLOUD SMOOTH SAMPLING AND SURFACE RECONSTRUCTION BASED ON MOVING LEAST SQUARES

In point cloud data processing, smooth sampling and surface reconstruction are important aspects of point cloud data processing. In view of the current point cloud sampling method, the point cloud distribution is not uniform, the point cloud feature information is incomplete, and the reconstructed model surface is not smooth. This paper proposes a method of smoothing sampling processing and surface reconstruction using point cloud using moving least squares method. This paper first introduces the traditional moving least squares method in detail, and then proposes an improved moving least squares method for point cloud smooth sampling and surface reconstruction. In this paper, the algorithm is designed for the proposed theory, combined with C++ and point cloud library PCL programming, using voxel grid sampling and uniform sampling and moving least squares smooth sampling comparison, after sampling, using greedy triangulation algorithm surface reconstruction. The experimental results show that the improved moving least squares method performs point cloud smooth sampling more uniformly than the voxel grid sampling and the feature information is more prominent. The surface reconstructed by the moving least squares method is smooth, the surface reconstructed by the voxel grid sampling and the uniformly sampled data surface is rough, and the surface has a rough triangular surface. Point cloud smooth sampling and surface reconstruction based on moving least squares method can better maintain point cloud feature information and smooth model smoothness. The superiority and effectiveness of the method are demonstrated, which provides a reference for the subsequent study of point cloud sampling and surface reconstruction.