中華民國第八屆結構工程研討會 The 8th National Conference on Structure Engineering

1. Null-field point Domain point A New Approach for Piezoelectricity with Circular Inclusions求解含圓形夾雜壓電問題之新方法 An-Chien Wu and Jeng-Tzong Chen Department of Harbor and River EngineeringNational Taiwan Ocean University Abstract In this paper, we derive the null-field integral equation for piezoelectricity problems with circular inclusions under remote anti-plane shears and in-plane electric fields in two directions. To fully capture circular geometries, separable expressions of fundamental solutions in the polar coordinate for field and source points and Fourier series for boundary densities are adopted to ensure the exponential convergence. Four gains are obtained, (1) well-posed model, (2) singularity free, (3) boundary-layer effect free and (4) exponential convergence. The solution is formulated in a manner of semi-analytical form since error purely attributes to the truncation of Fourier series. Problems with two piezoelectric inclusions for stress and electric displacement distributions are revisited to demonstrate the validity of our method. The main feature of the present paper is that the new formulation can be generalized to multiple circular inclusions in a straightforward way without any difficulty. Numerical examples Dual null-field integral equations Two piezoelectric circular inclusions embedded in a piezoelectric matrix under remote shear and electric loadings Dual boundary integral equations Degenerate kernels for fundamental solutions Fourier series for boundary densities Stress concentrations as a function of the ratio of piezoelectric constants with Electric field concentrations as a function of the ratio of piezoelectric constants with Adaptive observer system for the null-field and domain point Electric field concentrations as a function of the ratio of piezoelectric constants with Stress concentrations as a function of the ratio of piezoelectric constants with Present Method Conventional BEM 國立台灣海洋大學 National Taiwan Ocean University 力學聲響振動實驗室 Mechanics Sound Vibration Laboratory 中華民國第八屆結構工程研討會 The 8th National Conference on Structure Engineering Sun Moon Lake, Taiwan, R. O. C., 1- 3 Sept. 2006 Paper No. F-007