Computational model for doubly curved laminated shells based on a refined asymptotic theory

摘要

A multilevel computational model based on a refined asymptotic theory is presented. The formulation begins with a Hellinger-Reissner (H-R) functional where the displacements and transverse stresses are taken as the functions subject to variation. Upon introducing a set of appropriate dimensionles scaling and bringing the transverse shear deformations to the stage at the leading-order level, the weak formulation is asymptotically expanded as a series of weak-form equations for various orders. In the multilevel computational model, the transverse stresses and displacements can be interpolated independently. Through successive integration, the transverse stress degrees-of-freedom (DOF) are condensed in the element level. As a result, three midsurface displacment DOF and two rotation DOF for each node in an element are taken as the independent unknowns in the system equations for various orders. The element stiffness matrix for each order level remains unchanged and the forcing vector can be computed from the lower-order solutions. Thus, the solution procedure can be repeated level-by-level in a consistent and hierarchic way. Application of this multilevel computational model to a benchmark problem is demonstrated.