A Triangular Plate Bending Element Based on Discrete Kirchhoff Theory with Simple Explicit Expression

A Simple three-node Discrete Kirchhoff Triangular (SDKT) plate bending element is proposed in this study to overcome some inherent difficulties and provide efficient and dependable solutions in engineering practice for thin plate structure analyses. Different from the popular DKT (Discrete Kirchhoff Theory) triangular element, using the compatible trial function for the transverse displacement along the element sides, the construction of the present SDKT element is based on a specially designed trial function for the transverse displacement over the element, which satisfies interpolation conditions for the transverse displacements and the rotations at the three corner nodes. Numerical investigations of thin plate structures were conducted, using the proposed SDKT element. The results were compared with those by other prevalent plate elements, including the analytical solutions. It was shown that the present element has the simplest explicit expression of the nine-DOF (Degree of Freedom) triangular plate bending elements currently available that can pass the patch test. The numerical examples indicate that the present element has a good convergence rate and possesses high precision.

Low-Cost Calibration of Matching Error between Lidar and Motor for a Rotating 2D Lidar

For a rotating 2D lidar, the inaccurate matching between the 2D lidar and the motor is an important error resource of the 3D point cloud, where the error is shown both in shape and attitude. Existing methods need to measure the angle position of the motor shaft in real time to synchronize the 2D lidar data and the motor shaft angle. However, the sensor used for measurement is usually expensive, which can increase the cost. Therefore, we propose a low-cost method to calibrate the matching error between the 2D lidar and the motor, without using an angular sensor. First, the sequence between the motor and the 2D lidar is optimized to eliminate the shape error of the 3D point cloud. Next, we eliminate the attitude error with uncertainty of the 3D point cloud by installing a triangular plate on the prototype. Finally, the Levenberg–Marquardt method is used to calibrate the installation error of the triangular plate. Experiments verified that the accuracy of our method can meet the requirements of the 3D mapping of indoor autonomous mobile robots. While we use a 2D lidar Hokuyo UST-10LX with an accuracy of ±40 mm in our prototype, we can limit the mapping error within ±50 mm when the distance is no more than 2.2996 m for a 1 s scan (mode 1), and we can limit the mapping error within ±50 mm at the measuring range 10 m for a 16 s scan (mode 7). Our method can reduce the cost while the accuracy is ensured, which can make a rotating 2D lidar cheaper.

RANCANG BANGUN KOMPONEN TUMPUAN PENDORONG KAYU CHIP PADA CHAIN FEED TO CHIPPER

Chain Feed to Chipper is one of the equipment in the Wood Handling machine of the paper company PT. Indah Kiat Pulp & Paper Perawang, whose main function is to carry logs before chipping by the Chipper machine as raw material for making Pulp, but in the process it works Chain The feed has not been damaged at the deadline, namely the bearings of the Chain Feed made of solid iron are damaged, loose and enter the Chipper engine, thus damaging the parts in the Chipper engine, this of course requires a large cost in repairing the parts that are Therefore, research on the cause of damage or bearing limits of the Chain Feed was carried out and finally redesigned the Chain Feed, namely redesigning it by removing the bearings on the chain, by designing adding a triangular plate to replace the bearings as a means of carrying logs on the chain. Chain Feed. After re-designing the Chain Feed, the risk of damage to the bearings entering the Chipper engine is no longer there

Direct Numerical Simulations on the Flow Normal to a Plate With Transit Shape From Circular Disk to Triangle

This paper presents a numerical study of the flow normal to a triangular plate. A total of four plates with the same frontal area Ar and different curved edges are used. The curvature of edges is determined by the compression ratio k (k = 0.3, 0.4, 0.5, 0.8; the large value of k corresponds to the large curvature of the edges). A disk of χ = 50 (χ is the diameter-thickness aspect ratio) is used as the reference disk. The Reynolds number Re based on the characteristic length is up to 250. Four states are observed and denoted as: (I) steady and geometric symmetry state (SG); (II) steady and reflectional symmetry state (SR); (III) reflectional symmetry breaking with periodic flow (RSB); (IV) chaotic state (CS). The critical Reynolds numbers at the first two stages (Rec1, Rec2) decrease with the increasing k, indicating that flow of the plates with a larger curvature is more unstable. Therefore, we believe that the flow around a triangular plate is more stable than that around a circular disk.