BUCKLING OF CLAMPED ORTHOTROPIC PLATE IN SHEAR

摘要

Response of plates in shear is a classical plate buckling problem. This problem was first formulated and solved for isotropic plates by Southwell [1] For orthotropic plates this problem was solved by Lekhnitskii [2]. The case with clamped edges was first analyzed by Budiansky [3]. These classical solutions are still of practical significance and are used in the engineering calculations for composite plates [4,5]. An inherent characteristic of all the solutions mentioned above is that the critical buckling load factor is determined as the smallest eigenvalue of a corresponding system of linear algebraic equations. Computation of the eigenvalues is typically performed for a specified set of stiffness and geometric parameters for the plate. In the design of the composite plates, especially when the design is formulated as an optimization problem, the solution of the eigenvalue problem for each combination of design data repetitively tends to increase the computational effort considerably. For orthotropic laminated plates the problem of determination of the critical buckling load as a function of several parameters may be reduced to the problem of determination of a certain buckling coefficient, which is the function of only two parameters. These parameters contain all necessary information about plate dimensions and stiffnesses. Such an approach to the problem was introduced by Azikov [6] for simply supported orthotropic plates loaded by combined in-plane compression and shear. This method of attack was used by Lopatin [7] for orthotropic plate under combined compression and in-plane bending. It was demonstrated that the range of variation of these parameters for the most practical orthotropic laminated plates is well defined. Hence it will not be necessary to repeatedly perform the eigenvalue analysis for the determination of the buckling load. Instead the obtained results could be used. In this paper the buckling problem for clamped orthotropic laminated plates subjected to shearing loads is solved.