Analysis of the changing geometry of flexible structure: 1. approach and formulation

An alternative approach for the analysis of flexible structure is presented. Instead of following theories of finite deformation, classical structural models with infinitesimal strain and engineering stress are assumed as the basis of formulation. A compatible concept of description is developed to handle the large geometrical change due to load. The article first discusses: (i) the condition that a classical model can be adopted to formulate a flexible theory of structure and (ii) the procedure to formulate a description of geometry that embraces assumptions of the classical model. Based on the discussion, a general procedure to develop the flexible structural model is proposed. Equations for the cylindrical deformation of a flexible panel are derived as an example. In an accompanying article: ‘Analysis of the changing geometry of flexible structure: 2. Analysis of flexible solid’, an algorithm is developed to study three-dimensional flexible solids. Numerical results are obtained to verify the concept and procedure.