Buckling and Postbuckling of Composite Plates

[...]... death has prevented his witnessing the final outcome G J Turvey and I H Marshall Lancaster and Paisley, September 1994 Part One Basic Theory 1 Buckling and postbuckling theory for laminated composite plates A w Leissa 1.1 INTRODUCTION Laminated composite plates are fabricated oflaminae (also called layers or plies), where each lamina consists of high-strength fibres (e.g glass, boron, graphite) embedded... overview of the present (up to 1994) state of knowledge of laminated composite plate buckling response Other more mature engineers and academics engaged in the development and application of composite structures may find particular sections of the book useful in their day-to-day endeavours Lastly, we would like to believe (but shall never really know!) that we have managed to do justice to the vision of. .. presents the theory governing the buckling and postbuckling behaviour of laminated composite plates The resulting differential equations, boundary conditions and energy functionals may be used to analyse these behaviours by various solution techniques The subjeCt is divided into three parts Section 1.2 deals with the bifurcation buckling of thin laminates, where the effects of shear deformation in the transverse... values of the initial, tangential, body force components p~ and P:/, and given values of u' and v' and/ or their derivatives (i.e in-plane stresses) on the plate boundaries, one could solve eqns (1.19a) and (1.19b) for the displacement field u i and Vi and, if desired, the corresponding initial stress field For an unsymmetrically laminated plate, the B,} are not all zero, and the solutions for u i and. .. Equations (1.32) and (1.33) form a set of differential equations which are also of eighth order For symmetrically laminated plates B'J = 0, and equations (1.32) and (1.33) uncouple Equation (1.32) becomes the anisotropic, stress function form of the compatibility equation for plane elasticity, and equation (1.33) reduces to equation (1.23) 16 Buckling theory for laminated composite plates The classical,... in equations (1.38) and (1.39) For cross-ply plates having fibres parallel to the x and y axes, D 16 = D 26 = 0 in equations (1.38) and (1.39) The differential equations of buckling equilibrium and boundary conditions shown above may also be derived by means of variational principles based upon the potential energy of the system while it undergoes buckling Moreover, for many plate buckling problems,... been found to be less pronounced for laminated composite plates than for metal plates Theoretical analysis of postbuckling behaviour of plates is non-linear, even though the transverse displacements considered may be only 'moderately large' (i.e of the order of a few times the plate thickness) The initial non-linearity is due to additional in-plane strains (and stresses) caused by the transverse displacements... EO and K are 3 x 1 subvectors and A, Band D are the 3 x 3 submatrices delineated in equation (1.8) Multiplying through the first of the two sub matrix equations of equations (1.27) by A -I and solving for EO yields EO=A-IN-A-IBK (1.28) Substituting equation (1.28) into the second of equations (1.27) results in M = BA -IN - (D - BA -IB)K (1.29) 15 Thin plate buckling theory and equations (1.28) and. .. rotations t/lx and t/ly are independent of w, as discussed previously Moreover, uo, vo, t/lx, t/I,,, and w are all independent functions of x and y Substituting equations (1.47) into the strain-displacement and stressstrain equations of elasticity for the individual layers and integrating over the plate thickness as in equations (1.6) and (1.7), one obtains in-plane stress resultants (Nx,Ny,Nxy) and moment... isotropic plates these factors are usually taken to be either k = 5/6 = 0.833 [16] or 1[2/12 = 0.822 [17], and these values are often used for composite plates as well Substituting the kinematic relations (1.4) and (1.48) into the stiffness equations (1.8) and (1.49), and then these into the five equations of neutral equilibrium for a plate element in the buckled state arising from equations (1.10) and (1.11), . src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA24AAAUmCAIAAABh6HALAAAACXBIWXMAABYlAAAWJQFJUiTwAAAgAElEQVR42uzdb4jb9 2H4 cV27jbFYWGV4xQetZVp8y 1h2 cuWNso1aptDtQW5Wmi3F14QolJ7Zg+Fz/ax5YPlByxi5WH40zlAiQ+Owbk3kXhjdoLOuZVC6O6JbaJszLdGN7UybluiQm9HA8O/B57cP333153S6c +w4 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