No abstract

No abstract

In-plane prebuckling stresses arise under axial edge loading as a result of a plate boundary being restrained from deformation in the plane of the plate. These stresses exhibit a uniform distribution only under a special set of boundary conditions and in general such uniform in-plane stress distributions do not exist under most boundary conditions encountered in practice. In the present study, in-plane prebuckling stresses are investigated for various in-plane boundary constraints and the stress contour lines are given for rectangular cross-ply laminated plates under linearly varying edge loads. The second part of the article involves the computation of the optimal layer thickness to maximize the buckling load under various combinations of in-plane boundary restraints. The numerical solutions are obtained by finite elements based on first-order shear deformable plate theory which include the in-plane deformations as nodal degrees of freedom. Numerical results show that the exclusion of the in-plane restraints may lead to errors in stability calculations and consequently in the design of laminated plates.

The optimum designs are given for clamped-clamped columns under concentrated and distributed axial loads. The design objective is the maximization of the buckling load subject to volume and maximum stress constraints. The results for a minimum area constraint are also obtained for comparison. In the case of a stress constraint, the minimum thickness of an optimal column is not known a priori, since it depends on the maximum buckling load, which in turn depends on the minimum thickness necessitating an iterative solution. An iterative solution method is developed based on finite elements, and the results are obtained for n = 1, 2, 3 defined as I = α n A n , with I being the moment of inertia, and A the crosssectional area. The iterations start using the unimodal optimality condition and continue with the bimodal optimality condition if the second buckling load becomes less than or equal to the first one. Numerical results show that the optimal columns become larger in the direction of the distributed load due to the increase in the stress in this direction. Even though the optimal columns are symmetrical with respect to their mid-points when the compressive load is concentrated at the end-points, in the case of the columns subject to distributed axial loads the optimal shapes are unsymmetrical.

No abstract