A Generalized Coordinate Differential Quadrature Element Method Chang-New Chen Department of Naval Architecture and Marine Engineering National Cheng Kung University, Tainan, Taiwan Abstract The method of differential quadrature approximates a partial derivative of a variable function with respect to a coordinate at a discrete point as a weighted linear sum of the function values at all discrete points along that coordinate direction. The differential quadrature can be generalized. The calculation of weighting coefficients is generic. The weighting coefficients for a grid model defined by a coordinate system having arbitrary dimensions can also be generated. The configuration of a grid model can be arbitrary. The generalized coordinate differential quadrature also has these characters. In the generalized coordinate differential quadrature, the variable function is approximated as the linear combination of one set of appropriate analytical functions and one set of generalized coordinates. Then, a partial derivative of a variable function with respect to a coordinate at a discrete point is expressed as a weighted linear sum of the generalized coordinates. In this paper, a generalized coordinate differential quadrature element method is proposed. In this method, the analysis domain of a problem is separated into a certain number of subdomains or elements. Then the differential quadrature discretization is carried out on an element-basis. The governing differential or partial differential equations defined on the elements, the transition conditions on inter-element boundaries and the boundary conditions on the analysis domain boundary are in computable algebraic forms after the differential quadrature discretization. In order to solve the problem, all discretized governing equations, transition conditions and boundary conditions have to be assembled to obtain a global algebraic system. Since all relations governing a continuous problem are satisfied, the essence of this method is to find a numerically rigorous solution. Numerical procedures for beam bending vibration and two-dimensional steady-state heat conduction problems are illustrated. Various techniques can be used to calculate the direction cosines of the outward unit normal vector on the element boundary in the two-dimensional simulation. The technique of secant approximation is illustrated and used in the sample analyses. 