Computer-Aided Static Analysis of Complex Prismatic Orthotropic Shell Structures by the Analytical Finite Strip Method

The paper describes a development of the analytical finite strip method (FSM) in displacements for linear elastic static analysis of simply supported at their transverse ends complex orthotropic prismatic shell structures with arbitrary open or closed deformable contour of the cross-section under general external loads. A number of bridge top structures, some roof structures and others are related to the studied class. By longitudinal sections the prismatic thin-walled structure is discretized to a limited number of plane straight strips which are connected continuously at their longitudinal ends to linear joints. As basic unknowns are assumed the three displacements of points from the joint lines and the rotation to these lines. In longitudinal direction of the strips the unknown quantities and external loads are presented by single Fourier series. In transverse direction of each strips the unknown values are expressed by hyperbolic functions presenting an exact solution of the corresponding differential equations of the plane straight strip. The basic equations and relations for the membrane state, for the bending state and for the total state of the finite strip are obtained. The rigidity matrix of the strip in the local and global co-ordinate systems is derived. The basic relations of the structure are given and the general stages of the analytical FSM are traced. For long structures FSM is more efficient than the classic finite element method (FEM), since the problem dimension is reduced by one and the number of unknowns decreases. In comparison with the semi-analytical FSM, the analytical FSM leads to a practically precise solution, especially for wider strips, and provides compatibility of the displacements and internal forces along the longitudinal linear joints