https://scholars.lib.cycu.edu.tw/handle/123456789/12 Tue, 21 Jul 2026 06:58:53 GMT 2026-07-21T06:58:53Z https://scholars.lib.cycu.edu.tw/handle/123456789/8067 Title: A Home Health Care Routing and Scheduling Problem with Synchronization, Precedence Relation, and Working Time Balancing Authors: 林耘竹; 陶昱翔; Lin, Yun-Zhu; Tao, Yu-hsiang Mon, 01 Jan 202210 00:00:00 GMT https://scholars.lib.cycu.edu.tw/handle/123456789/8067 202210-01-01T00:00:00Z https://scholars.lib.cycu.edu.tw/handle/123456789/8035 Title: A Unified Singular Solution of Laplace’s Equation with Neumann and Dirichlet Boundary Conditions Authors: Jyh-Haw Tang; Chao-Kang Feng Abstract: Laplace’s equation is one of the important equations in studying applied mathematics and engineering problems including the study of temperature distribution of steady-state heat conduction or the concentration distribution of steady-state diffusion problems. In this study, the analytical method has been applied to solve the Laplace's equation in a two-dimensional domain. For the specified Neumann or Dirichlet boundary conditions, the analytical solution of temperature distribution in the quarter-plane can be found by several methods including the Fourier transform method, similarity method, and the method of Green’s function with images. For different boundary conditions, the solution of temperature distribution of the Laplace’s equation will be in a totally different form. Nevertheless, the merit of this research is that the solutions of steady-state temperature distribution in the quarter plane with Neumann and Dirichlet boundary conditions are unified under the singular similarity solution with source type singularity. With the typical benchmarked examples for finding the temperature distribution by the numerical integral method, it is shown that Gibbs phenomenon behaves at a jump discontinuity, where serious oscillation result was found especially near the singular points of the boundary. In addition, the temperature distribution in the domain can be easily calculated without oscillation phenomenon near the singular points from the similarity solutions. Sat, 01 Jan 2022 00:00:00 GMT https://scholars.lib.cycu.edu.tw/handle/123456789/8035 2022-01-01T00:00:00Z https://scholars.lib.cycu.edu.tw/handle/123456789/8036 Title: On the Performance Evaluation of a Collaborative Swarm Intelligence Approach Particle Bee Algorithm Authors: Lien, Li-Chuan; Dolgorsuren Unurjargal Abstract: Swarm intelligence (SI), an artificial intelligence (AI) approach widely used in many complex optimization problems, models the collective behavior of social systems such as honeybees and birds. This study evaluated a collaborative swarm intelligence approach optimization algorithm, named the particle bee algorithm (PBA). The PBA is based on a particular aspect of bird (particle swarm optimization, PSO) and honeybee swarm (bee algorithm, BA) behaviors that integrates their advantages and proposes a self-parameter-updating technique to prevent being trapped into a local optimum in high dimensional problems. This study compares the performance of PBA with that of differential evolution (DE), evolutionary algorithms (EA), particle swarm optimization (PSO) and bee algorithm (BA) for multi-dimensional numeric problems. For test problems carried out in this work, colony sizes ranging from 75 to 100 of PBA can provide an acceptable convergence speed for an optimization search. Besides, elite and best bee PSO iteration sizes of (15, 9) to (30, 18) can provide an acceptable convergence speed for an optimization search. Results show PBA performance to be comparable to that of mentioned algorithms, and the potential for its being efficiently employed to solve benchmark numerical problems with high dimensionality. Fri, 01 Jan 2021 00:00:00 GMT https://scholars.lib.cycu.edu.tw/handle/123456789/8036 2021-01-01T00:00:00Z https://scholars.lib.cycu.edu.tw/handle/123456789/7798 Title: Analysis of mode III stress fields around a line crack at the corner of a semicircular cavity Authors: Chang, Kao-Hao; Chou, An-Chieh; Huang, Chang-Wei; Chuang, Ching Chiang Abstract: The analysis of mode III stress fields surrounding crack tips remains a fundamental concern across multiple engineering fields. This study presents a simplified model of a semicircular cavity with a corner line crack under remote antiplane loading conditions. A semi-analytical, mesh-free method incorporating the region-point- matching technique is established to address horizontally oriented line cracks. This method employs singular eigenfunctions to characterize the crack-tip singularity and satisfy zero-stress conditions along the crack surface. The accuracy of the semi-analytical method is verified through extended finite element method (XFEM) simulations conducted using Abaqus. The analyses are extended to cases of inclined line cracks, revealing a "cavity shielding" effect where specific orientations reduce stress intensity factors (SIFs). The horizontal crack configuration provides upper-bound SIF values, enhancing the practical utility of the proposed semi-analytical solution. Comparative analyses between circular and semicircular cavities demonstrate a notable reversal in SIFs at a crack length to cavity radius ratio of 0.75. An approximate formula for SIFs of horizontally oriented cracks is established and validated within its applicable range. Wed, 01 Jan 2025 00:00:00 GMT https://scholars.lib.cycu.edu.tw/handle/123456789/7798 2025-01-01T00:00:00Z