Report

+ Laminated plates + definitions Unidirectional: orientation direction is identical for all laminates Angle-ply: Cross ply: Fiber orientation alternates between +theta to –theta from the stress normal …/q/-q/q/-q/… Fibers in alternating plies are at right angles to each other …/0/90/0/90/… Symmetric: fiber orientation in the stack is symmetric about the center line of the laminate + Symmetric laminate examples 7 ply stack: This stack is symmetrical about the centerline of the 4th ply The stack order is a ‘mirror’ reflection about the centerline We will need the average height of the ply above the centerline. Ply # orientation Distance above ctrln 1 0 +3 2 +45 +2 3 -45 +1 4 90 0 5 -45 -1 6 +45 -2 7 0 -3 + Symmetric laminate examples 8 ply stack: This stack is symmetrical about the interface between ply 4 and ply 5 The stack order is a ‘mirror’ reflection about the centerline We will need the average height of the ply above the centerline. Ply # orientation Distance above ctrln 1 0 +3½h 2 +45 +2 ½ h 3 -45 +1½h 4 90 +½h 5 90 -½h 6 -45 -1½h 7 +45 -2½h 8 0 -3 ½ h + Antisymmetric Ply orientation is antisymmetric about the centerline of the laminate For each ply with fiber orientation angle, q, above the midplane, this is a ply of fiber orientation angle, –q, with identical material and thickness and equal distance below the midplane q(z)=-q(-z) q/-q/q/-q is antisymmetric q/-q/-q/q is symmetric + Unsymmetric laminate Unsymmetric: q1/q2/q3; random placement of angles Quasi-isotropic laminate: equal angles between adjacent lamina, increment is p/n +60/0/-60 +45/0/-45/-90 0/+60/-60 0/+45/-45/90 + Quasi-isotropic laminates Quasi-isotropic laminate: equal angles between adjacent lamina, increment is p/n +60/0/-60 +45/0/-45/-90 0/+60/-60 0/+45/-45/90 A common quasi-isotropic symmetrical stacking sequence is: [0/±45/90]s + Code examples [0/45/90]s: 1st angle is for the outermost ply, last angle is for the innermost ply; s subscript means symmetrical The bar over 90 indicates that the plan of symmetry passes midway through the thickness of the 90 degree laminate ±45 implies adjacent +45 and -45 degrees laminates 04: four adjacent zero degree plies (±45)2: two grouped, adjacent ±45 degree plies + In-class examples Sketch the following: [0/45/90]s [0/-45/90]s [0/±45/90]s Young B35 classroom (30 student seats and 1 teacher station) Thursday 4/3 3:30pm-4:45pm Thursday 4/10 3:30pm-4:45pm Peggy M. Akridge Manager, Student Computing Services UK Analytics and Technologies University of Kentucky + Lamination theory + Step-by-step procedure 1. Calculate stiffness matrices for the laminate 2. Calculate the midplane strains and curatures for the laminate due to specific applied forces 3. Calculate in-plane stresses, exx, eyy, gxy, for each lamina 4. Calculate in-plane strains, sxx, syy, txy, for each lamina + Assumptions Laminate is thin, wide: w>>t Perfect interlaminar bonds Strain distribution in the thickness direction is linear All laminas are macroscopically homogeneous and behave linearly elastically + Laminate strains Since strain distribution in z direction is linear, e xx = e + z × kxx 0 xx • Geometric midplane = xy axes, z axis defines thickness direction • Total laminate thickness = h • Thickness of various lamina are ti • Total lamina = N e yy = e + z × kyy 0 yy g xy = g + z × kxy 0 xy + Laminate strains Since strain distribution in z direction is linear, e xx = e + z × kxx 0 xx • • • • e0ii = midplane normal strains g0xy = midplane shear strain Kii bending curvatures of laminate Kxy = twisting curvature of laminate e yy = e + z × kyy 0 yy g xy = g + z × kxy 0 xy + e xx = e xx0 + z × kxx e yy = e yy0 + z × kyy g xy = g xy0 + z × kxy + + +