An effective curved composite beam finite element based on the hybrid-mixed formulation

Abstract

A laminated curved-beam finite element with six displacement degrees of freedom and three stress parameters is derived and evaluated. Both thermal and hygrothermal effects are included. The element is based on the Hellinger-Reissner principle and the hybrid-mixed formulation. The Timoshenko beam theory and classical lamination theory are employed in the finite element description. Within an element linear displacement interpolation is used; the generalized stresses are interpolated by either stress functions based on the equilibrium equations ( P 1) or constant stress approximation ( P 2). The beam element stiffness is obtained explicitly and numerical results show very good displacement prediction compared to analytical solutions. Generalized stresses are predicted accurately at the mid-point of the finite element only for constant stress interpolation. The P 1-type element yields more accurate displacement and stress prediction.