tailieunhanh - Introduction to Elasticity Part 8

Tham khảo tài liệu 'introduction to elasticity part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | f AL Q 10 4. a - b Determine the deflection curves for the beams shown here. Plot these curves for the the values as needed L 25 in a 5 in w 10 lb in P 150 lb. Prob. 4 5. a Determine the deflection of a coil spring under the influence of an axial force F including the contribution of bending direct shear and torsional shear effects. Using r 1 mm and R 10 mm compute the relative magnitudes of the three contributions. b Repeat the solution in a but take the axial load to be placed at the outer radius of the coil. Prob. 5 6. a - c Use the method of superposition to write expressions for the deflection curve ổ x for the cases shown here. 11 3T 9 QOJ J d LAMINATED COMPOSITE PLATES David Roylance Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge MA 02139 February 10 2000 Introduction This document is intended to outline the mechanics of fiber-reinforced laminated plates leading to a computational scheme that relates the in-plane strain and curvature of a laminate to the tractions and bending moments imposed on it. Although this is a small part of the overall field of fiber-reinforced composites or even of laminate theory it is an important technique that should be understood by all composites engineers. In the sections to follow we will review the constitutive relations for isotropic materials in matrix form then show that the extension to transversely isotropic composite laminae is very straightforward. Since each ply in a laminate may be oriented arbitrarily we will then show how the elastic properties of the individual laminae can be transformed to a common direction. Finally we will balance the individual ply stresses against the applied tractions and moments to develop matrix governing relations for the laminate as a whole. The calculations for laminate mechanics are best done by computer and algorithms are outlined for elastic laminates laminates exhibiting thermal expansion effects and laminates exhibiting viscoelastic