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1,209 results on '"Liu, Hai-Tao"'

18. Linear Adjusting Programming in Factor Space

Author

He, Jing, Kong, Qi-Wei, Lui, Ho-Chung, Liu, Hai-Tao, Ji, Yi-Mu, Yao, Hai-Chang, and Liu, Mo-Zhengfu

Subjects
Mathematics - Optimization and Control
Abstract

The definition of factor space and a unified optimization based classification model were developed for linear programming. Intelligent behaviour appeared in a decision process can be treated as a point y, the dynamic state observed and controlled by the agent, moving in a factor space impelled by the goal factor and blocked by the constraint factors. Suppose that the feasible region is cut by a group of hyperplanes, when point y reaches the region's wall, a hyperplane will block the moving and the agent needs to adjust the moving direction such that the target is pursued as faithful as possible. Since the wall is not able to be represented to a differentiable function, the gradient method cannot be applied to describe the adjusting process. We, therefore, suggest a new model, named linear adjusting programming (LAP) in this paper. LAP is similar as a kind of relaxed linear programming (LP), and the difference between LP and LAP is: the former aims to find out the ultimate optimal point, while the latter just does a direct action in short period. You may ask: Where will a blocker encounter? How can the moving direction be adjusted? Where further blockers may be encountered next, and how should the direction be adjusted again? We request at least an adjusting should be achieved at the first time. If a hyperplane blocks y going ahead along with the direction d, then we must adjust the new direction d' as the projection of g in the blocking plane. If there is only one blocker at a time, it is straightforward to calculate the projection, but how to calculate the projection when there are more than one blocker encountered simultaneously? We suggest a projection calculation by means of the Hat matrix in this paper. Linear adjusting programming will attract interest in many fields. It might bring a new light to solve the linear programming problem with a strong polynomial solution.

Published
2020

48. In‐Plane Energy Absorption Properties of Novel Curved‐Ligaments Auxetic Cellular Structures with Dual‐Platform Performance.

Author

Liu, Xu, Liu, Hai‐Tao, and Wang, Shun

Subjects
*IMPACT loads, *CELL anatomy, *HONEYCOMB structures, *ABSORPTION, *DEFORMATIONS (Mechanics), *POISSON'S ratio
Abstract

To improve the energy absorption capacity of honeycomb, four novel curved‐ligaments auxetic cellular structures (CLACS‐i [i = 1, 2, 3, 4]) based on the Diabolo‐shaped honeycomb (DSH) are introduced in this article. In the simulation results, it is demonstrated that the energy absorption performance of CLACS‐i (i = 1, 2, 3, 4) surpasses that of DSH under low‐, medium‐, and high‐velocity impacts. However, the negative Poisson's ratio effect of novel structures is inferior to that of DSH. With the increase in impact velocity, the inertial effect of the structure is enhanced, and the deformation mode of the structure changes from global deformation to local deformation. Furthermore, different impact velocities and geometric parameters also affect the energy absorption capacity of the structures. Platform stress and specific energy absorption (SEA) of CLACS‐i (i = 1, 2, 3, 4) increase with the increase of velocity. Under medium‐velocity impact loading, the platform stress and SEA of CLACS‐i (i = 1, 2, 3, 4) increase as the geometric parameter θ decreases and the wall thickness t increases. In this study, a reference is provided for the optimal design and application of honeycomb energy‐absorbing components. [ABSTRACT FROM AUTHOR]

Published
2024
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