Stress analysis of laminated composite annular disks subjected to a concentrated transverse load using layer-wise zig-zag theory

Abstract

This paper presents accurate inter-lamina stress distributions of laminated composite annular disks incorporating layer-wise zig-zag theory. This theory is based on the superposition of a global higher order shear deformation displacement field and a local linear zig-zag displacement field (RHOT). RHOT automatically satisfies displacement continuity at the layer interfaces and by further application of stress continuity at the layer interfaces and traction free boundary conditions, the unknown degrees of freedom are reduced to seven regardless of the number of layers. These are two in-plane displacements, two shear rotations, a transverse displacement and two section rotations. A four-node sector finite element in a cylindrical coordinate system is developed using RHOT. Two in-plane displacements and two shear rotations which are C0 continuous are interpolated using bilinear functions and a transverse displacement and two section rotations which are C1 continuous are interpolated using higher order Hermitian functions. In-plane normal stress and inter-lamina transverse shear stress variation through the thickness are calculated for laminated disks using a RHOT sector element and comparison is made with first order shear deformation theory predictions. The present work precedes the application of the zig-zag theory to transient dynamic analysis and is a first step at establishing the accuracy of implementing the zig-zag theory into a sector finite element.