Doubly Curved Laminated Composite Shells with Hygrothermal Conditioning and Dynamic Loads, Part 1: A Theoretical Development and Semielastic Solution Using a Higher-Order Displacement Field

Abstract

A hierarchical higher-order shear deformation theory for the analysis of composite shells is presented. The structural performance of doubly curved anisotropic laminated shells in adverse hygrothermal conditions is analyzed under static and dynamic loads. The development of such a theory is more appealing, as the thickness direction of the laminates plays a dominant role due to hygroscopic diffusion and heat conduction in that direction. This model further becomes important as much weaker material properties are experienced in the transverse direction compared to that in the fiber direction. The present theory can be applied with any desirable degrees of freedom in any coordinate direction. And as a result, remodeling is not necessary in the application to solve problems. The strain-displacement relations of a laminated shell are derived with equal emphasis paid to all components of the strain tensor. The equilibrium at ply interfaces is satisfied when the laminated shells are made of angle-ply setups or unidirectional plies. The variation principle is the basis of the formulation, and top and bottom surface stress boundary conditions are applied using Lagrange multipliers. These constraints result in an interdependency between the displacement components. The hygrothermal effects are introduced in terms of trigonometric functions as have been derived by classical moisture diffusion and heat conduction equations. The material properties are updated by a micromechanics model. The application of this theory to various static and dynamic problems is presented in Part 2 of this work.