Stress Analysis of Symmetrical and Unsymmetrical Laminates Having Cut-Outs of Arbitrary Shape Subjected to Different Loading Conditions

Abstract

The composite materials find a wide variety of applications in Civil, Mechanical and Aerospace engineering due to their superior material properties compared to isotropic metals. The holes/cut-outs are inevitable in plate-like structural elements. These cut-outs may be of different shapes depending upon the requirement. The holes adversely affect the stresses and moments in the structural/mechanical components. Thus, it is a need to quantify stresses and moments around different shaped holes under various types of loading conditions for symmetric and unsymmetric laminated composite plates.

In this work, a general solution is developed to determine the stress concentration around holes/cut-out of different shape in an infinite anisotropic plate. The analytical solution is obtained using Muskhelishvili's complex variable approach for composite plate. The generalized mapping function used is for hypotrochoidal and oval shape. Using different constants, these mapping functions can produce shapes like circle, ellipse, square, rectangle, triangle, line (crack), eye shape, hypocycloids etc. The present solution gives stress concentration around the hole with rounded corners and stress intensity factors at cusp points. The stress field around different shaped cut-outs (hypotrochoid, oval and its variance) in infinite isotropic plate and composite plate having symmetric and un-symmetric material property variation from mid plane are presented. The effect of cut-out geometry, stacking sequence, material properties and loading angle on stresses and moments around the hole is studied. The numerical results are presented for different materials like Graphite/epoxy, Glass/Epoxy, Carbon/Epoxy, Boron/Epoxy and isotropic material. The results are also presented for functionally graded plate using a complex variable approach to solve for stresses and moments around the hole with through thickness variation of material properties. The computer implementation of present solution is simple and gives results very fast. Some of the results are compared with existing literature and results from conventional finite element analysis software and found in close agreement.