Application of the Ritz method to plane elasticity problems for composite sheets with variable fibre spacing

Abstract

Abstract The plane stress problem of a parallel fibre, rectangular composite sheet with variable fibre content is investigated. The resulting sheets are governed by partial differential equations that have variable coefficients, which are generally unsolvable exactly. A Ritz method is used to approximate the solution and is checked against known problems having exact solutions. The method is found to determine closely both the displacements and the stresses with fewer than 200 degrees of freedom. It is then applied to two interesting problems for which no exact solutions exist, including that of uniform normal stress applied in the direction of the fibres.