Stability and Vibration Analysis of Non-prismatic Thin-walled Composite Spatial Members of Generic Section

This paper presents a detailed treatment of the formulation of static, bucking and vibration analysis of non-prismatic thin-walled composite spatial members of generic section. The theory is limited to small strains, moderate deflections and small rotations. The torsional shear strain on the middle surface of the beam wall is zero for an open contour while it corresponds to constant shear flow for a closed contour. Rigorous expressions for strains based on membrane theory of shells are obtained through which the effect of nonlinear tapering is considered. Solutions for classical buckling and vibration analysis by the finite element method are discussed. Numerical integration by using Gaussian quadrature on the cross-sections for the computation of sectorial properties and stress resultants and over the length for the computation of flexural, geometric and mass matrices is suggested. Some examples are solved and critical bucking loads, natural frequencies and the corresponding buckled and mode shapes are obtained by the Jacobi iteration procedure.