A simple Trefftz-type finite element method (TFEM) is proposed for solving certain potential problems in orthotropic media. The "body force", which is induced by internal sources or sinks, may produce domain integrals in the standard Trefftz finite element formulation. This will make the advantage "only-boundary integration" of TFEM lose entirely. To overcome this difficulty, the dual reciprocity method (DRM) is employed to transfer the original problem into a homogeneous one. Then, a particular solution (PS) Trefftz-type finite element model is established based on the modified functional. Three benchmark examples are investigated by the proposed approach and compared with the analytical solutions.

The evolutionary game of co-opetition relationship between regional logistics nodes is studied in this paper. A replicator dynamic model is built to obtain the Evolutionary Stable Strategy (ESS) of the game. Then, according to the status and level of logistics nodes, the symmetric and asymmetric game models based on evolutionary game theory are proposed, respectively. The former is used to analyze the changing trends of co-opetition relationship between logistics nodes from a same layer of a logistics network. While the latter can be used to deal with the relationship forecasting problems between logistics nodes from different layers. The result of the case study reveals that the proposed models have good practicability and accuracy in dealing with the relationship forecasting problems within a regional logistics network.