Discrete element analysis methods of generic differential quadratures.
The method of differential quadratures (DQ), proposed by R. Bellman, is an effective technique for solution of ordinary or partial differential equations. The DQ approximates a derivative or partial derivative of function with respect to a coordinate variable at a node as a weighted linear sum of the function values at all nodes along that coordinate direction. A discrete element analysis method - differential quadrature element method (DQEM) has been developed for solving scientific and engineering problems. Like finite element method, for the DQEM the domain of problem is separated into many subdomains or elements. The differential quadrature discretization can be carried out on an element basis. All discretized governing equations, transition conditions and boundary conditions have to be assembled to obtain a global algebraic system. The author presents a related novel discrete element method by using the extended differential quadrature based spatial and temporal elements. The corresponding numerical techniques for solution of various continuum mechanics problems are developed systematically. This numerical generic differential quadrature-based method is suitable for solution of problems with arbitrarily complex geometry. The ability of this method for solving scientific and engineering problems is demonstrated. Several comprehensive examples such as bars and beams, trusses, frames, general field problems, elasticity problems or bending of plates show that the numerical results converge fast to exact solutions by increasing the number of elements.
scientific article; zbMATH DE number 5015514