The finite spectral method for composite structures

Abstract

The paper produces the associated stiffness matrices from the non-symmetric differential matrices of the differential quadrature and the spectral methods for composite structures. For specific differential matrices, the error decreases exponentially with the increasing order of the differentiation matrix or the number of discrete points. So far, only single domain problems have been solved except for simple frame problems and no provision has been given to couple with finite elements or other similar methods. It is the purpose of the paper to form very accurate super-elements in terms of only boundary unknowns to be coupled with general finite elements using differential matrices so that commercial packages can be developed for engineering analyses. The paper will concentrate on linear one, two and three-dimensional composite elasticity, beam and plate problems. The main idea is that, in order to form the stiffness matrix, one must employ the variational consistence natural boundary conditions so that the generalized displacements and forces are dual to each other satisfying the reciprocal theorem. We shall develop the theory in rectangular domains initially and in other shapes using transformation. Thirteen numerical examples are given.