In this paper, a multi-patch weakly singular isogeometric boundary element method (WSIGABEM) for two-dimensional elastostatics is proposed. Since the method is based on the weakly singular boundary integral equation, quadrature techniques, dedicated to the weakly singular and regular integrals, are applied in the method. A new formula for the generation of collocation points is suggested to take full advantage of the multi-patch technique. The generated collocation points are essentially inside the patches without any correction. If the boundary conditions are assumed to be continuous in every patch, no collocation point lies on the discontinuous boundaries, thus simplifying the implementation. The multi-patch WSIGABEM is verified by simple examples with analytical solutions. The features of the present multi-patch WSIGABEM are investigated by comparison with the traditional IGABEM. Furthermore, the combination of the present multi-patch WSIGABEM and the particle swarm optimization algorithm results in a shape optimization method in two-dimensional elastostatics. By changing some specific control points and their weights, the shape optimizations of the fillet corner, the spanner, and the arch bridge are verified to be effective.

Evaluating and selecting appropriate contractors is critical to the success of specific construction projects in the building industry. Existing approaches for addressing this problem are unsatisfactory due to the ignorance of the multi-dimensional nature of the evaluation process and inappropriate consideration of existent risks. This study presents a DEA game cross-efficiency model with loss aversion for evaluating and selecting specific contractors. The competitiveness of the evaluation process is modeled using game theory with respect to the adoption of the cross-efficiency model. The attitude of the decision maker toward risks is tackled with the use of loss aversion, which is a phenomenon formalized in prospect theory. As a result, the proposed approach can adequately screen available contractors through prequalification and adequately consider the attitude of the decision maker toward risks, leading to effective decisions being made. An example is presented to demonstrate the applicability of the proposed model in evaluating and selecting appropriate contractors for specific construction projects. The results show that the proposed model is effective and efficient in producing a unique solution for contractor selection through appropriate modeling of the multi-dimensional contractor selection process and adequate consideration of the competition between the contractors and the attitude of the decision maker toward risks in practical situations.