An analytical model is developed to trace the linear response of folded plate and shell roof structures under the action of any type of loading. Through this model, the actual behavior of the structure could be achieved with the best possible economical and accurate solution.
A high-order finite strip forms the basis for the analytical model. The model is capable of analyzing isotropic, orthotropic or anisotropic folded plate structures with arbitrary boundary conditions. Structures under consideration may be, in the general form, composed of laminated composite materials with heterogeneous properties.
The formulation used in the present work to obtain stiffnesses of heterogeneous elements, is based on the classical lamination theory. The stress-strain relationships of sub-layers, forming the laminated composites, are defined. The force-deformation relations in laminated systems are derived from the strain-displacement relations.
Versatile displacement functions are used, in this model, to assure the continuity of strains and curvatures between strips. The formulation of strip stiffness matrix and load vector is obtained from the strip potential energy. The master stiffness matrix of the structure as well as the master load vector are obtained by applying the minimum total potential energy procedure on the system. The previous formulations are incorporated in a computer program.
Several numerical examples are presented to indicate the applicability and accuracy of the proposed model. These examples cover the analysis of plates, folded plates, and shell roof structures. Comparisons are made between the present results and other available results in the literature. The analytical model is also used to show the influence of the coupling between membrane and bending actions in the structures of heterogeneous properties and anisotropic nature. |
