K-barrier coverage is an important coverage model for achieving robust barrier coverage in wireless sensor networks. After initial random sensor deployment, k-barrier coverage can be achieved by moving mobile sensors to form k barriers consisting of k sensor chains crossing the region. In mobile sensor network, it is challenging to reduce the moving distances of mobile sensors to prolong the network lifetime. Existing work mostly focused on forming linear barriers, that is the final positions of sensors are on a straight line, which resulted in large redundant movements. However, the moving cost of sensors can be further reduced if nonlinear barriers are allowed, which means that sensors? final positions need not be on a straight line. In this paper, we propose two algorithms of forming non-linear k barriers energy-efficiently. The algorithms use a novel model, called horizontal virtual force model, which considers both the euclidean distance and horizontal angle between two sensors. Then we propose two barrier forming algorithms. To construct a barrier, one algorithm always chooses the mobile sensor chain with the largest horizontal virtual force and then flattens it, called sensor chain algorithm. The other chooses the mobile sensor with the largest horizontal virtual force to construct the barrier, other than the mobile sensor chain, called single sensor algorithm. Simulation results show that the algorithms significantly reduce the movements of mobile sensors compared to a linear k-barrier coverage algorithm. Besides, the sensor chain algorithm outperforms the single sensor algorithm when the sensor density becomes higher.
On pure bending in non-linear elasticity: A circular closed-form 2D solution for semi-linear orthotropic material
